Sample records for accurate numerical scheme

  1. A fast numerical scheme for causal relativistic hydrodynamics with dissipation

    DOE Office of Scientific and Technical Information (OSTI.GOV)

    Takamoto, Makoto, E-mail: takamoto@tap.scphys.kyoto-u.ac.jp; Inutsuka, Shu-ichiro

    2011-08-01

    Highlights: {yields} We have developed a new multi-dimensional numerical scheme for causal relativistic hydrodynamics with dissipation. {yields} Our new scheme can calculate the evolution of dissipative relativistic hydrodynamics faster and more effectively than existing schemes. {yields} Since we use the Riemann solver for solving the advection steps, our method can capture shocks very accurately. - Abstract: In this paper, we develop a stable and fast numerical scheme for relativistic dissipative hydrodynamics based on Israel-Stewart theory. Israel-Stewart theory is a stable and causal description of dissipation in relativistic hydrodynamics although it includes relaxation process with the timescale for collision of constituentmore » particles, which introduces stiff equations and makes practical numerical calculation difficult. In our new scheme, we use Strang's splitting method, and use the piecewise exact solutions for solving the extremely short timescale problem. In addition, since we split the calculations into inviscid step and dissipative step, Riemann solver can be used for obtaining numerical flux for the inviscid step. The use of Riemann solver enables us to capture shocks very accurately. Simple numerical examples are shown. The present scheme can be applied to various high energy phenomena of astrophysics and nuclear physics.« less

  2. Numerical experiments with a symmetric high-resolution shock-capturing scheme

    NASA Technical Reports Server (NTRS)

    Yee, H. C.

    1986-01-01

    Characteristic-based explicit and implicit total variation diminishing (TVD) schemes for the two-dimensional compressible Euler equations have recently been developed. This is a generalization of recent work of Roe and Davis to a wider class of symmetric (non-upwind) TVD schemes other than Lax-Wendroff. The Roe and Davis schemes can be viewed as a subset of the class of explicit methods. The main properties of the present class of schemes are that they can be implicit, and, when steady-state calculations are sought, the numerical solution is independent of the time step. In a recent paper, a comparison of a linearized form of the present implicit symmetric TVD scheme with an implicit upwind TVD scheme originally developed by Harten and modified by Yee was given. Results favored the symmetric method. It was found that the latter is just as accurate as the upwind method while requiring less computational effort. Currently, more numerical experiments are being conducted on time-accurate calculations and on the effect of grid topology, numerical boundary condition procedures, and different flow conditions on the behavior of the method for steady-state applications. The purpose here is to report experiences with this type of scheme and give guidelines for its use.

  3. Efficient and accurate numerical schemes for a hydro-dynamically coupled phase field diblock copolymer model

    NASA Astrophysics Data System (ADS)

    Cheng, Qing; Yang, Xiaofeng; Shen, Jie

    2017-07-01

    In this paper, we consider numerical approximations of a hydro-dynamically coupled phase field diblock copolymer model, in which the free energy contains a kinetic potential, a gradient entropy, a Ginzburg-Landau double well potential, and a long range nonlocal type potential. We develop a set of second order time marching schemes for this system using the "Invariant Energy Quadratization" approach for the double well potential, the projection method for the Navier-Stokes equation, and a subtle implicit-explicit treatment for the stress and convective term. The resulting schemes are linear and lead to symmetric positive definite systems at each time step, thus they can be efficiently solved. We further prove that these schemes are unconditionally energy stable. Various numerical experiments are performed to validate the accuracy and energy stability of the proposed schemes.

  4. High Order Schemes in Bats-R-US for Faster and More Accurate Predictions

    NASA Astrophysics Data System (ADS)

    Chen, Y.; Toth, G.; Gombosi, T. I.

    2014-12-01

    BATS-R-US is a widely used global magnetohydrodynamics model that originally employed second order accurate TVD schemes combined with block based Adaptive Mesh Refinement (AMR) to achieve high resolution in the regions of interest. In the last years we have implemented fifth order accurate finite difference schemes CWENO5 and MP5 for uniform Cartesian grids. Now the high order schemes have been extended to generalized coordinates, including spherical grids and also to the non-uniform AMR grids including dynamic regridding. We present numerical tests that verify the preservation of free-stream solution and high-order accuracy as well as robust oscillation-free behavior near discontinuities. We apply the new high order accurate schemes to both heliospheric and magnetospheric simulations and show that it is robust and can achieve the same accuracy as the second order scheme with much less computational resources. This is especially important for space weather prediction that requires faster than real time code execution.

  5. A simple, robust and efficient high-order accurate shock-capturing scheme for compressible flows: Towards minimalism

    NASA Astrophysics Data System (ADS)

    Ohwada, Taku; Shibata, Yuki; Kato, Takuma; Nakamura, Taichi

    2018-06-01

    Developed is a high-order accurate shock-capturing scheme for the compressible Euler/Navier-Stokes equations; the formal accuracy is 5th order in space and 4th order in time. The performance and efficiency of the scheme are validated in various numerical tests. The main ingredients of the scheme are nothing special; they are variants of the standard numerical flux, MUSCL, the usual Lagrange's polynomial and the conventional Runge-Kutta method. The scheme can compute a boundary layer accurately with a rational resolution and capture a stationary contact discontinuity sharply without inner points. And yet it is endowed with high resistance against shock anomalies (carbuncle phenomenon, post-shock oscillations, etc.). A good balance between high robustness and low dissipation is achieved by blending three types of numerical fluxes according to physical situation in an intuitively easy-to-understand way. The performance of the scheme is largely comparable to that of WENO5-Rusanov, while its computational cost is 30-40% less than of that of the advanced scheme.

  6. Time-Accurate Numerical Simulations of Synthetic Jet Quiescent Air

    NASA Technical Reports Server (NTRS)

    Rupesh, K-A. B.; Ravi, B. R.; Mittal, R.; Raju, R.; Gallas, Q.; Cattafesta, L.

    2007-01-01

    The unsteady evolution of three-dimensional synthetic jet into quiescent air is studied by time-accurate numerical simulations using a second-order accurate mixed explicit-implicit fractional step scheme on Cartesian grids. Both two-dimensional and three-dimensional calculations of synthetic jet are carried out at a Reynolds number (based on average velocity during the discharge phase of the cycle V(sub j), and jet width d) of 750 and Stokes number of 17.02. The results obtained are assessed against PIV and hotwire measurements provided for the NASA LaRC workshop on CFD validation of synthetic jets.

  7. Numerical pricing of options using high-order compact finite difference schemes

    NASA Astrophysics Data System (ADS)

    Tangman, D. Y.; Gopaul, A.; Bhuruth, M.

    2008-09-01

    We consider high-order compact (HOC) schemes for quasilinear parabolic partial differential equations to discretise the Black-Scholes PDE for the numerical pricing of European and American options. We show that for the heat equation with smooth initial conditions, the HOC schemes attain clear fourth-order convergence but fail if non-smooth payoff conditions are used. To restore the fourth-order convergence, we use a grid stretching that concentrates grid nodes at the strike price for European options. For an American option, an efficient procedure is also described to compute the option price, Greeks and the optimal exercise curve. Comparisons with a fourth-order non-compact scheme are also done. However, fourth-order convergence is not experienced with this strategy. To improve the convergence rate for American options, we discuss the use of a front-fixing transformation with the HOC scheme. We also show that the HOC scheme with grid stretching along the asset price dimension gives accurate numerical solutions for European options under stochastic volatility.

  8. A Hermite WENO reconstruction for fourth order temporal accurate schemes based on the GRP solver for hyperbolic conservation laws

    NASA Astrophysics Data System (ADS)

    Du, Zhifang; Li, Jiequan

    2018-02-01

    This paper develops a new fifth order accurate Hermite WENO (HWENO) reconstruction method for hyperbolic conservation schemes in the framework of the two-stage fourth order accurate temporal discretization in Li and Du (2016) [13]. Instead of computing the first moment of the solution additionally in the conventional HWENO or DG approach, we can directly take the interface values, which are already available in the numerical flux construction using the generalized Riemann problem (GRP) solver, to approximate the first moment. The resulting scheme is fourth order temporal accurate by only invoking the HWENO reconstruction twice so that it becomes more compact. Numerical experiments show that such compactness makes significant impact on the resolution of nonlinear waves.

  9. Calculations of steady and transient channel flows with a time-accurate L-U factorization scheme

    NASA Technical Reports Server (NTRS)

    Kim, S.-W.

    1991-01-01

    Calculations of steady and unsteady, transonic, turbulent channel flows with a time accurate, lower-upper (L-U) factorization scheme are presented. The L-U factorization scheme is formally second-order accurate in time and space, and it is an extension of the steady state flow solver (RPLUS) used extensively to solve compressible flows. A time discretization method and the implementation of a consistent boundary condition specific to the L-U factorization scheme are also presented. The turbulence is described by the Baldwin-Lomax algebraic turbulence model. The present L-U scheme yields stable numerical results with the use of much smaller artificial dissipations than those used in the previous steady flow solver for steady and unsteady channel flows. The capability to solve time dependent flows is shown by solving very weakly excited and strongly excited, forced oscillatory, channel flows.

  10. Numerical study of read scheme in one-selector one-resistor crossbar array

    NASA Astrophysics Data System (ADS)

    Kim, Sungho; Kim, Hee-Dong; Choi, Sung-Jin

    2015-12-01

    A comprehensive numerical circuit analysis of read schemes of a one selector-one resistance change memory (1S1R) crossbar array is carried out. Three schemes-the ground, V/2, and V/3 schemes-are compared with each other in terms of sensing margin and power consumption. Without the aid of a complex analytical approach or SPICE-based simulation, a simple numerical iteration method is developed to simulate entire current flows and node voltages within a crossbar array. Understanding such phenomena is essential in successfully evaluating the electrical specifications of selectors for suppressing intrinsic drawbacks of crossbar arrays, such as sneaky current paths and series line resistance problems. This method provides a quantitative tool for the accurate analysis of crossbar arrays and provides guidelines for developing an optimal read scheme, array configuration, and selector device specifications.

  11. A more accurate scheme for calculating Earth's skin temperature

    NASA Astrophysics Data System (ADS)

    Tsuang, Ben-Jei; Tu, Chia-Ying; Tsai, Jeng-Lin; Dracup, John A.; Arpe, Klaus; Meyers, Tilden

    2009-02-01

    The theoretical framework of the vertical discretization of a ground column for calculating Earth’s skin temperature is presented. The suggested discretization is derived from the evenly heat-content discretization with the optimal effective thickness for layer-temperature simulation. For the same level number, the suggested discretization is more accurate in skin temperature as well as surface ground heat flux simulations than those used in some state-of-the-art models. A proposed scheme (“op(3,2,0)”) can reduce the normalized root-mean-square error (or RMSE/STD ratio) of the calculated surface ground heat flux of a cropland site significantly to 2% (or 0.9 W m-2), from 11% (or 5 W m-2) by a 5-layer scheme used in ECMWF, from 19% (or 8 W m-2) by a 5-layer scheme used in ECHAM, and from 74% (or 32 W m-2) by a single-layer scheme used in the UCLA GCM. Better accuracy can be achieved by including more layers to the vertical discretization. Similar improvements are expected for other locations with different land types since the numerical error is inherited into the models for all the land types. The proposed scheme can be easily implemented into state-of-the-art climate models for the temperature simulation of snow, ice and soil.

  12. A numerical study of the axisymmetric Couette-Taylor problem using a fast high-resolution second-order central scheme

    DOE Office of Scientific and Technical Information (OSTI.GOV)

    Kupferman, R.

    The author presents a numerical study of the axisymmetric Couette-Taylor problem using a finite difference scheme. The scheme is based on a staggered version of a second-order central-differencing method combined with a discrete Hodge projection. The use of central-differencing operators obviates the need to trace the characteristic flow associated with the hyperbolic terms. The result is a simple and efficient scheme which is readily adaptable to other geometries and to more complicated flows. The scheme exhibits competitive performance in terms of accuracy, resolution, and robustness. The numerical results agree accurately with linear stability theory and with previous numerical studies.

  13. A second-order accurate finite volume scheme with the discrete maximum principle for solving Richards’ equation on unstructured meshes

    DOE PAGES

    Svyatsky, Daniil; Lipnikov, Konstantin

    2017-03-18

    Richards’s equation describes steady-state or transient flow in a variably saturated medium. For a medium having multiple layers of soils that are not aligned with coordinate axes, a mesh fitted to these layers is no longer orthogonal and the classical two-point flux approximation finite volume scheme is no longer accurate. Here, we propose new second-order accurate nonlinear finite volume (NFV) schemes for the head and pressure formulations of Richards’ equation. We prove that the discrete maximum principles hold for both formulations at steady-state which mimics similar properties of the continuum solution. The second-order accuracy is achieved using high-order upwind algorithmsmore » for the relative permeability. Numerical simulations of water infiltration into a dry soil show significant advantage of the second-order NFV schemes over the first-order NFV schemes even on coarse meshes. Since explicit calculation of the Jacobian matrix becomes prohibitively expensive for high-order schemes due to build-in reconstruction and slope limiting algorithms, we study numerically the preconditioning strategy introduced recently in Lipnikov et al. (2016) that uses a stable approximation of the continuum Jacobian. Lastly, numerical simulations show that the new preconditioner reduces computational cost up to 2–3 times in comparison with the conventional preconditioners.« less

  14. A second-order accurate finite volume scheme with the discrete maximum principle for solving Richards’ equation on unstructured meshes

    DOE Office of Scientific and Technical Information (OSTI.GOV)

    Svyatsky, Daniil; Lipnikov, Konstantin

    Richards’s equation describes steady-state or transient flow in a variably saturated medium. For a medium having multiple layers of soils that are not aligned with coordinate axes, a mesh fitted to these layers is no longer orthogonal and the classical two-point flux approximation finite volume scheme is no longer accurate. Here, we propose new second-order accurate nonlinear finite volume (NFV) schemes for the head and pressure formulations of Richards’ equation. We prove that the discrete maximum principles hold for both formulations at steady-state which mimics similar properties of the continuum solution. The second-order accuracy is achieved using high-order upwind algorithmsmore » for the relative permeability. Numerical simulations of water infiltration into a dry soil show significant advantage of the second-order NFV schemes over the first-order NFV schemes even on coarse meshes. Since explicit calculation of the Jacobian matrix becomes prohibitively expensive for high-order schemes due to build-in reconstruction and slope limiting algorithms, we study numerically the preconditioning strategy introduced recently in Lipnikov et al. (2016) that uses a stable approximation of the continuum Jacobian. Lastly, numerical simulations show that the new preconditioner reduces computational cost up to 2–3 times in comparison with the conventional preconditioners.« less

  15. Numerical simulation of the rapid intensification of Hurricane Katrina (2005): Sensitivity to boundary layer parameterization schemes

    NASA Astrophysics Data System (ADS)

    Liu, Jianjun; Zhang, Feimin; Pu, Zhaoxia

    2017-04-01

    Accurate forecasting of the intensity changes of hurricanes is an important yet challenging problem in numerical weather prediction. The rapid intensification of Hurricane Katrina (2005) before its landfall in the southern US is studied with the Advanced Research version of the WRF (Weather Research and Forecasting) model. The sensitivity of numerical simulations to two popular planetary boundary layer (PBL) schemes, the Mellor-Yamada-Janjic (MYJ) and the Yonsei University (YSU) schemes, is investigated. It is found that, compared with the YSU simulation, the simulation with the MYJ scheme produces better track and intensity evolution, better vortex structure, and more accurate landfall time and location. Large discrepancies (e.g., over 10 hPa in simulated minimum sea level pressure) are found between the two simulations during the rapid intensification period. Further diagnosis indicates that stronger surface fluxes and vertical mixing in the PBL from the simulation with the MYJ scheme lead to enhanced air-sea interaction, which helps generate more realistic simulations of the rapid intensification process. Overall, the results from this study suggest that improved representation of surface fluxes and vertical mixing in the PBL is essential for accurate prediction of hurricane intensity changes.

  16. An accurate front capturing scheme for tumor growth models with a free boundary limit

    NASA Astrophysics Data System (ADS)

    Liu, Jian-Guo; Tang, Min; Wang, Li; Zhou, Zhennan

    2018-07-01

    We consider a class of tumor growth models under the combined effects of density-dependent pressure and cell multiplication, with a free boundary model as its singular limit when the pressure-density relationship becomes highly nonlinear. In particular, the constitutive law connecting pressure p and density ρ is p (ρ) = m/m-1 ρ m - 1, and when m ≫ 1, the cell density ρ may evolve its support according to a pressure-driven geometric motion with sharp interface along its boundary. The nonlinearity and degeneracy in the diffusion bring great challenges in numerical simulations. Prior to the present paper, there is lack of standard mechanism to numerically capture the front propagation speed as m ≫ 1. In this paper, we develop a numerical scheme based on a novel prediction-correction reformulation that can accurately approximate the front propagation even when the nonlinearity is extremely strong. We show that the semi-discrete scheme naturally connects to the free boundary limit equation as m → ∞. With proper spatial discretization, the fully discrete scheme has improved stability, preserves positivity, and can be implemented without nonlinear solvers. Finally, extensive numerical examples in both one and two dimensions are provided to verify the claimed properties in various applications.

  17. A time-accurate high-resolution TVD scheme for solving the Navier-Stokes equations

    NASA Technical Reports Server (NTRS)

    Kim, Hyun Dae; Liu, Nan-Suey

    1992-01-01

    A total variation diminishing (TVD) scheme has been developed and incorporated into an existing time-accurate high-resolution Navier-Stokes code. The accuracy and the robustness of the resulting solution procedure have been assessed by performing many calculations in four different areas: shock tube flows, regular shock reflection, supersonic boundary layer, and shock boundary layer interactions. These numerical results compare well with corresponding exact solutions or experimental data.

  18. Stochastic porous media modeling and high-resolution schemes for numerical simulation of subsurface immiscible fluid flow transport

    NASA Astrophysics Data System (ADS)

    Brantson, Eric Thompson; Ju, Binshan; Wu, Dan; Gyan, Patricia Semwaah

    2018-04-01

    This paper proposes stochastic petroleum porous media modeling for immiscible fluid flow simulation using Dykstra-Parson coefficient (V DP) and autocorrelation lengths to generate 2D stochastic permeability values which were also used to generate porosity fields through a linear interpolation technique based on Carman-Kozeny equation. The proposed method of permeability field generation in this study was compared to turning bands method (TBM) and uniform sampling randomization method (USRM). On the other hand, many studies have also reported that, upstream mobility weighting schemes, commonly used in conventional numerical reservoir simulators do not accurately capture immiscible displacement shocks and discontinuities through stochastically generated porous media. This can be attributed to high level of numerical smearing in first-order schemes, oftentimes misinterpreted as subsurface geological features. Therefore, this work employs high-resolution schemes of SUPERBEE flux limiter, weighted essentially non-oscillatory scheme (WENO), and monotone upstream-centered schemes for conservation laws (MUSCL) to accurately capture immiscible fluid flow transport in stochastic porous media. The high-order schemes results match well with Buckley Leverett (BL) analytical solution without any non-oscillatory solutions. The governing fluid flow equations were solved numerically using simultaneous solution (SS) technique, sequential solution (SEQ) technique and iterative implicit pressure and explicit saturation (IMPES) technique which produce acceptable numerical stability and convergence rate. A comparative and numerical examples study of flow transport through the proposed method, TBM and USRM permeability fields revealed detailed subsurface instabilities with their corresponding ultimate recovery factors. Also, the impact of autocorrelation lengths on immiscible fluid flow transport were analyzed and quantified. A finite number of lines used in the TBM resulted into visual

  19. Higher-Order Compact Schemes for Numerical Simulation of Incompressible Flows

    NASA Technical Reports Server (NTRS)

    Wilson, Robert V.; Demuren, Ayodeji O.; Carpenter, Mark

    1998-01-01

    A higher order accurate numerical procedure has been developed for solving incompressible Navier-Stokes equations for 2D or 3D fluid flow problems. It is based on low-storage Runge-Kutta schemes for temporal discretization and fourth and sixth order compact finite-difference schemes for spatial discretization. The particular difficulty of satisfying the divergence-free velocity field required in incompressible fluid flow is resolved by solving a Poisson equation for pressure. It is demonstrated that for consistent global accuracy, it is necessary to employ the same order of accuracy in the discretization of the Poisson equation. Special care is also required to achieve the formal temporal accuracy of the Runge-Kutta schemes. The accuracy of the present procedure is demonstrated by application to several pertinent benchmark problems.

  20. A time accurate finite volume high resolution scheme for three dimensional Navier-Stokes equations

    NASA Technical Reports Server (NTRS)

    Liou, Meng-Sing; Hsu, Andrew T.

    1989-01-01

    A time accurate, three-dimensional, finite volume, high resolution scheme for solving the compressible full Navier-Stokes equations is presented. The present derivation is based on the upwind split formulas, specifically with the application of Roe's (1981) flux difference splitting. A high-order accurate (up to the third order) upwind interpolation formula for the inviscid terms is derived to account for nonuniform meshes. For the viscous terms, discretizations consistent with the finite volume concept are described. A variant of second-order time accurate method is proposed that utilizes identical procedures in both the predictor and corrector steps. Avoiding the definition of midpoint gives a consistent and easy procedure, in the framework of finite volume discretization, for treating viscous transport terms in the curvilinear coordinates. For the boundary cells, a new treatment is introduced that not only avoids the use of 'ghost cells' and the associated problems, but also satisfies the tangency conditions exactly and allows easy definition of viscous transport terms at the first interface next to the boundary cells. Numerical tests of steady and unsteady high speed flows show that the present scheme gives accurate solutions.

  1. A new flux-conserving numerical scheme for the steady, incompressible Navier-Stokes equations

    NASA Technical Reports Server (NTRS)

    Scott, James R.

    1994-01-01

    This paper is concerned with the continued development of a new numerical method, the space-time solution element (STS) method, for solving conservation laws. The present work focuses on the two-dimensional, steady, incompressible Navier-Stokes equations. Using first an integral approach, and then a differential approach, the discrete flux conservation equations presented in a recent paper are rederived. Here a simpler method for determining the flux expressions at cell interfaces is given; a systematic and rigorous derivation of the conditions used to simulate the differential form of the governing conservation law(s) is provided; necessary and sufficient conditions for a discrete approximation to satisfy a conservation law in E2 are derived; and an estimate of the local truncation error is given. A specific scheme is then constructed for the solution of the thin airfoil boundary layer problem. Numerical results are presented which demonstrate the ability of the scheme to accurately resolve the developing boundary layer and wake regions using grids which are much coarser than those employed by other numerical methods. It is shown that ten cells in the cross-stream direction are sufficient to accurately resolve the developing airfoil boundary layer.

  2. Second-order accurate nonoscillatory schemes for scalar conservation laws

    NASA Technical Reports Server (NTRS)

    Huynh, Hung T.

    1989-01-01

    Explicit finite difference schemes for the computation of weak solutions of nonlinear scalar conservation laws is presented and analyzed. These schemes are uniformly second-order accurate and nonoscillatory in the sense that the number of extrema of the discrete solution is not increasing in time.

  3. Time accurate application of the MacCormack 2-4 scheme on massively parallel computers

    NASA Technical Reports Server (NTRS)

    Hudson, Dale A.; Long, Lyle N.

    1995-01-01

    Many recent computational efforts in turbulence and acoustics research have used higher order numerical algorithms. One popular method has been the explicit MacCormack 2-4 scheme. The MacCormack 2-4 scheme is second order accurate in time and fourth order accurate in space, and is stable for CFL's below 2/3. Current research has shown that the method can give accurate results but does exhibit significant Gibbs phenomena at sharp discontinuities. The impact of adding Jameson type second, third, and fourth order artificial viscosity was examined here. Category 2 problems, the nonlinear traveling wave and the Riemann problem, were computed using a CFL number of 0.25. This research has found that dispersion errors can be significantly reduced or nearly eliminated by using a combination of second and third order terms in the damping. Use of second and fourth order terms reduced the magnitude of dispersion errors but not as effectively as the second and third order combination. The program was coded using Thinking Machine's CM Fortran, a variant of Fortran 90/High Performance Fortran, and was executed on a 2K CM-200. Simple extrapolation boundary conditions were used for both problems.

  4. Unconditionally stable, second-order accurate schemes for solid state phase transformations driven by mechano-chemical spinodal decomposition

    DOE PAGES

    Sagiyama, Koki; Rudraraju, Shiva; Garikipati, Krishna

    2016-09-13

    Here, we consider solid state phase transformations that are caused by free energy densities with domains of non-convexity in strain-composition space; we refer to the non-convex domains as mechano-chemical spinodals. The non-convexity with respect to composition and strain causes segregation into phases with different crystal structures. We work on an existing model that couples the classical Cahn-Hilliard model with Toupin’s theory of gradient elasticity at finite strains. Both systems are represented by fourth-order, nonlinear, partial differential equations. The goal of this work is to develop unconditionally stable, second-order accurate time-integration schemes, motivated by the need to carry out large scalemore » computations of dynamically evolving microstructures in three dimensions. We also introduce reduced formulations naturally derived from these proposed schemes for faster computations that are still second-order accurate. Although our method is developed and analyzed here for a specific class of mechano-chemical problems, one can readily apply the same method to develop unconditionally stable, second-order accurate schemes for any problems for which free energy density functions are multivariate polynomials of solution components and component gradients. Apart from an analysis and construction of methods, we present a suite of numerical results that demonstrate the schemes in action.« less

  5. Multi-symplectic integrators: numerical schemes for Hamiltonian PDEs that conserve symplecticity

    NASA Astrophysics Data System (ADS)

    Bridges, Thomas J.; Reich, Sebastian

    2001-06-01

    The symplectic numerical integration of finite-dimensional Hamiltonian systems is a well established subject and has led to a deeper understanding of existing methods as well as to the development of new very efficient and accurate schemes, e.g., for rigid body, constrained, and molecular dynamics. The numerical integration of infinite-dimensional Hamiltonian systems or Hamiltonian PDEs is much less explored. In this Letter, we suggest a new theoretical framework for generalizing symplectic numerical integrators for ODEs to Hamiltonian PDEs in R2: time plus one space dimension. The central idea is that symplecticity for Hamiltonian PDEs is directional: the symplectic structure of the PDE is decomposed into distinct components representing space and time independently. In this setting PDE integrators can be constructed by concatenating uni-directional ODE symplectic integrators. This suggests a natural definition of multi-symplectic integrator as a discretization that conserves a discrete version of the conservation of symplecticity for Hamiltonian PDEs. We show that this approach leads to a general framework for geometric numerical schemes for Hamiltonian PDEs, which have remarkable energy and momentum conservation properties. Generalizations, including development of higher-order methods, application to the Euler equations in fluid mechanics, application to perturbed systems, and extension to more than one space dimension are also discussed.

  6. An Optimally Stable and Accurate Second-Order SSP Runge-Kutta IMEX Scheme for Atmospheric Applications

    NASA Astrophysics Data System (ADS)

    Rokhzadi, Arman; Mohammadian, Abdolmajid; Charron, Martin

    2018-01-01

    The objective of this paper is to develop an optimized implicit-explicit (IMEX) Runge-Kutta scheme for atmospheric applications focusing on stability and accuracy. Following the common terminology, the proposed method is called IMEX-SSP2(2,3,2), as it has second-order accuracy and is composed of diagonally implicit two-stage and explicit three-stage parts. This scheme enjoys the Strong Stability Preserving (SSP) property for both parts. This new scheme is applied to nonhydrostatic compressible Boussinesq equations in two different arrangements, including (i) semiimplicit and (ii) Horizontally Explicit-Vertically Implicit (HEVI) forms. The new scheme preserves the SSP property for larger regions of absolute monotonicity compared to the well-studied scheme in the same class. In addition, numerical tests confirm that the IMEX-SSP2(2,3,2) improves the maximum stable time step as well as the level of accuracy and computational cost compared to other schemes in the same class. It is demonstrated that the A-stability property as well as satisfying "second-stage order" and stiffly accurate conditions lead the proposed scheme to better performance than existing schemes for the applications examined herein.

  7. Implicit and semi-implicit schemes in the Versatile Advection Code: numerical tests

    NASA Astrophysics Data System (ADS)

    Toth, G.; Keppens, R.; Botchev, M. A.

    1998-04-01

    We describe and evaluate various implicit and semi-implicit time integration schemes applied to the numerical simulation of hydrodynamical and magnetohydrodynamical problems. The schemes were implemented recently in the software package Versatile Advection Code, which uses modern shock capturing methods to solve systems of conservation laws with optional source terms. The main advantage of implicit solution strategies over explicit time integration is that the restrictive constraint on the allowed time step can be (partially) eliminated, thus the computational cost is reduced. The test problems cover one and two dimensional, steady state and time accurate computations, and the solutions contain discontinuities. For each test, we confront explicit with implicit solution strategies.

  8. Influence of the Numerical Scheme on the Solution Quality of the SWE for Tsunami Numerical Codes: The Tohoku-Oki, 2011Example.

    NASA Astrophysics Data System (ADS)

    Reis, C.; Clain, S.; Figueiredo, J.; Baptista, M. A.; Miranda, J. M. A.

    2015-12-01

    Numerical tools turn to be very important for scenario evaluations of hazardous phenomena such as tsunami. Nevertheless, the predictions highly depends on the numerical tool quality and the design of efficient numerical schemes still receives important attention to provide robust and accurate solutions. In this study we propose a comparative study between the efficiency of two volume finite numerical codes with second-order discretization implemented with different method to solve the non-conservative shallow water equations, the MUSCL (Monotonic Upstream-Centered Scheme for Conservation Laws) and the MOOD methods (Multi-dimensional Optimal Order Detection) which optimize the accuracy of the approximation in function of the solution local smoothness. The MUSCL is based on a priori criteria where the limiting procedure is performed before updated the solution to the next time-step leading to non-necessary accuracy reduction. On the contrary, the new MOOD technique uses a posteriori detectors to prevent the solution from oscillating in the vicinity of the discontinuities. Indeed, a candidate solution is computed and corrections are performed only for the cells where non-physical oscillations are detected. Using a simple one-dimensional analytical benchmark, 'Single wave on a sloping beach', we show that the classical 1D shallow-water system can be accurately solved with the finite volume method equipped with the MOOD technique and provide better approximation with sharper shock and less numerical diffusion. For the code validation, we also use the Tohoku-Oki 2011 tsunami and reproduce two DART records, demonstrating that the quality of the solution may deeply interfere with the scenario one can assess. This work is funded by the Portugal-France research agreement, through the research project GEONUM FCT-ANR/MAT-NAN/0122/2012.Numerical tools turn to be very important for scenario evaluations of hazardous phenomena such as tsunami. Nevertheless, the predictions highly

  9. Numerical viscosity and the entropy condition for conservative difference schemes

    NASA Technical Reports Server (NTRS)

    Tadmor, E.

    1983-01-01

    Consider a scalar, nonlinear conservative difference scheme satisfying the entropy condition. It is shown that difference schemes containing more numerical viscosity will necessarily converge to the unique, physically relevant weak solution of the approximated conservation equation. In particular, entropy satisfying convergence follows for E schemes - those containing more numerical viscosity than Godunov's scheme.

  10. High order parallel numerical schemes for solving incompressible flows

    NASA Technical Reports Server (NTRS)

    Lin, Avi; Milner, Edward J.; Liou, May-Fun; Belch, Richard A.

    1992-01-01

    The use of parallel computers for numerically solving flow fields has gained much importance in recent years. This paper introduces a new high order numerical scheme for computational fluid dynamics (CFD) specifically designed for parallel computational environments. A distributed MIMD system gives the flexibility of treating different elements of the governing equations with totally different numerical schemes in different regions of the flow field. The parallel decomposition of the governing operator to be solved is the primary parallel split. The primary parallel split was studied using a hypercube like architecture having clusters of shared memory processors at each node. The approach is demonstrated using examples of simple steady state incompressible flows. Future studies should investigate the secondary split because, depending on the numerical scheme that each of the processors applies and the nature of the flow in the specific subdomain, it may be possible for a processor to seek better, or higher order, schemes for its particular subcase.

  11. Accurate Monotonicity - Preserving Schemes With Runge-Kutta Time Stepping

    NASA Technical Reports Server (NTRS)

    Suresh, A.; Huynh, H. T.

    1997-01-01

    A new class of high-order monotonicity-preserving schemes for the numerical solution of conservation laws is presented. The interface value in these schemes is obtained by limiting a higher-order polynominal reconstruction. The limiting is designed to preserve accuracy near extrema and to work well with Runge-Kutta time stepping. Computational efficiency is enhanced by a simple test that determines whether the limiting procedure is needed. For linear advection in one dimension, these schemes are shown as well as the Euler equations also confirm their high accuracy, good shock resolution, and computational efficiency.

  12. Adaptive Numerical Dissipation Control in High Order Schemes for Multi-D Non-Ideal MHD

    NASA Technical Reports Server (NTRS)

    Yee, H. C.; Sjoegreen, B.

    2005-01-01

    The required type and amount of numerical dissipation/filter to accurately resolve all relevant multiscales of complex MHD unsteady high-speed shock/shear/turbulence/combustion problems are not only physical problem dependent, but also vary from one flow region to another. In addition, proper and efficient control of the divergence of the magnetic field (Div(B)) numerical error for high order shock-capturing methods poses extra requirements for the considered type of CPU intensive computations. The goal is to extend our adaptive numerical dissipation control in high order filter schemes and our new divergence-free methods for ideal MHD to non-ideal MHD that include viscosity and resistivity. The key idea consists of automatic detection of different flow features as distinct sensors to signal the appropriate type and amount of numerical dissipation/filter where needed and leave the rest of the region free from numerical dissipation contamination. These scheme-independent detectors are capable of distinguishing shocks/shears, flame sheets, turbulent fluctuations and spurious high-frequency oscillations. The detection algorithm is based on an artificial compression method (ACM) (for shocks/shears), and redundant multiresolution wavelets (WAV) (for the above types of flow feature). These filters also provide a natural and efficient way for the minimization of Div(B) numerical error.

  13. Implicit Space-Time Conservation Element and Solution Element Schemes

    NASA Technical Reports Server (NTRS)

    Chang, Sin-Chung; Himansu, Ananda; Wang, Xiao-Yen

    1999-01-01

    Artificial numerical dissipation is in important issue in large Reynolds number computations. In such computations, the artificial dissipation inherent in traditional numerical schemes can overwhelm the physical dissipation and yield inaccurate results on meshes of practical size. In the present work, the space-time conservation element and solution element method is used to construct new and accurate implicit numerical schemes such that artificial numerical dissipation will not overwhelm physical dissipation. Specifically, these schemes have the property that numerical dissipation vanishes when the physical viscosity goes to zero. These new schemes therefore accurately model the physical dissipation even when it is extremely small. The new schemes presented are two highly accurate implicit solvers for a convection-diffusion equation. The two schemes become identical in the pure convection case, and in the pure diffusion case. The implicit schemes are applicable over the whole Reynolds number range, from purely diffusive equations to convection-dominated equations with very small viscosity. The stability and consistency of the schemes are analysed, and some numerical results are presented. It is shown that, in the inviscid case, the new schemes become explicit and their amplification factors are identical to those of the Leapfrog scheme. On the other hand, in the pure diffusion case, their principal amplification factor becomes the amplification factor of the Crank-Nicolson scheme.

  14. High-Order Finite-Difference Schemes for Numerical Simulation of Hypersonic Boundary-Layer Transition

    NASA Astrophysics Data System (ADS)

    Zhong, Xiaolin

    1998-08-01

    Direct numerical simulation (DNS) has become a powerful tool in studying fundamental phenomena of laminar-turbulent transition of high-speed boundary layers. Previous DNS studies of supersonic and hypersonic boundary layer transition have been limited to perfect-gas flow over flat-plate boundary layers without shock waves. For hypersonic boundary layers over realistic blunt bodies, DNS studies of transition need to consider the effects of bow shocks, entropy layers, surface curvature, and finite-rate chemistry. It is necessary that numerical methods for such studies are robust and high-order accurate both in resolving wide ranges of flow time and length scales and in resolving the interaction between the bow shocks and flow disturbance waves. This paper presents a new high-order shock-fitting finite-difference method for the DNS of the stability and transition of hypersonic boundary layers over blunt bodies with strong bow shocks and with (or without) thermo-chemical nonequilibrium. The proposed method includes a set of new upwind high-order finite-difference schemes which are stable and are less dissipative than a straightforward upwind scheme using an upwind-bias grid stencil, a high-order shock-fitting formulation, and third-order semi-implicit Runge-Kutta schemes for temporal discretization of stiff reacting flow equations. The accuracy and stability of the new schemes are validated by numerical experiments of the linear wave equation and nonlinear Navier-Stokes equations. The algorithm is then applied to the DNS of the receptivity of hypersonic boundary layers over a parabolic leading edge to freestream acoustic disturbances.

  15. The Space-Time Conservative Schemes for Large-Scale, Time-Accurate Flow Simulations with Tetrahedral Meshes

    NASA Technical Reports Server (NTRS)

    Venkatachari, Balaji Shankar; Streett, Craig L.; Chang, Chau-Lyan; Friedlander, David J.; Wang, Xiao-Yen; Chang, Sin-Chung

    2016-01-01

    Despite decades of development of unstructured mesh methods, high-fidelity time-accurate simulations are still predominantly carried out on structured, or unstructured hexahedral meshes by using high-order finite-difference, weighted essentially non-oscillatory (WENO), or hybrid schemes formed by their combinations. In this work, the space-time conservation element solution element (CESE) method is used to simulate several flow problems including supersonic jet/shock interaction and its impact on launch vehicle acoustics, and direct numerical simulations of turbulent flows using tetrahedral meshes. This paper provides a status report for the continuing development of the space-time conservation element solution element (CESE) numerical and software framework under the Revolutionary Computational Aerosciences (RCA) project. Solution accuracy and large-scale parallel performance of the numerical framework is assessed with the goal of providing a viable paradigm for future high-fidelity flow physics simulations.

  16. Efficient numerical schemes for viscoplastic avalanches. Part 2: The 2D case

    NASA Astrophysics Data System (ADS)

    Fernández-Nieto, Enrique D.; Gallardo, José M.; Vigneaux, Paul

    2018-01-01

    This paper deals with the numerical resolution of a shallow water viscoplastic flow model. Viscoplastic materials are characterized by the existence of a yield stress: below a certain critical threshold in the imposed stress, there is no deformation and the material behaves like a rigid solid, but when that yield value is exceeded, the material flows like a fluid. In the context of avalanches, it means that after going down a slope, the material can stop and its free surface has a non-trivial shape, as opposed to the case of water (Newtonian fluid). The model involves variational inequalities associated with the yield threshold: finite volume schemes are used together with duality methods (namely Augmented Lagrangian and Bermúdez-Moreno) to discretize the problem. To be able to accurately simulate the stopping behavior of the avalanche, new schemes need to be designed, involving the classical notion of well-balancing. In the present context, it needs to be extended to take into account the viscoplastic nature of the material as well as general bottoms with wet/dry fronts which are encountered in geophysical geometries. Here we derive such schemes in 2D as the follow up of the companion paper treating the 1D case. Numerical tests include in particular a generalized 2D benchmark for Bingham codes (the Bingham-Couette flow with two non-zero boundary conditions on the velocity) and a simulation of the avalanche path of Taconnaz in Chamonix-Mont-Blanc to show the usability of these schemes on real topographies from digital elevation models (DEM).

  17. ACCURATE ORBITAL INTEGRATION OF THE GENERAL THREE-BODY PROBLEM BASED ON THE D'ALEMBERT-TYPE SCHEME

    DOE Office of Scientific and Technical Information (OSTI.GOV)

    Minesaki, Yukitaka

    2013-03-15

    We propose an accurate orbital integration scheme for the general three-body problem that retains all conserved quantities except angular momentum. The scheme is provided by an extension of the d'Alembert-type scheme for constrained autonomous Hamiltonian systems. Although the proposed scheme is merely second-order accurate, it can precisely reproduce some periodic, quasiperiodic, and escape orbits. The Levi-Civita transformation plays a role in designing the scheme.

  18. COMPARISON OF NUMERICAL SCHEMES FOR SOLVING A SPHERICAL PARTICLE DIFFUSION EQUATION

    EPA Science Inventory

    A new robust iterative numerical scheme was developed for a nonlinear diffusive model that described sorption dynamics in spherical particle suspensions. he numerical scheme had been applied to finite difference and finite element models that showed rapid convergence and stabilit...

  19. Numerical Schemes for the Hamilton-Jacobi and Level Set Equations on Triangulated Domains

    NASA Technical Reports Server (NTRS)

    Barth, Timothy J.; Sethian, James A.

    2006-01-01

    Borrowing from techniques developed for conservation law equations, we have developed both monotone and higher order accurate numerical schemes which discretize the Hamilton-Jacobi and level set equations on triangulated domains. The use of unstructured meshes containing triangles (2D) and tetrahedra (3D) easily accommodates mesh adaptation to resolve disparate level set feature scales with a minimal number of solution unknowns. The minisymposium talk will discuss these algorithmic developments and present sample calculations using our adaptive triangulation algorithm applied to various moving interface problems such as etching, deposition, and curvature flow.

  20. Numerical solution of special ultra-relativistic Euler equations using central upwind scheme

    NASA Astrophysics Data System (ADS)

    Ghaffar, Tayabia; Yousaf, Muhammad; Qamar, Shamsul

    2018-06-01

    This article is concerned with the numerical approximation of one and two-dimensional special ultra-relativistic Euler equations. The governing equations are coupled first-order nonlinear hyperbolic partial differential equations. These equations describe perfect fluid flow in terms of the particle density, the four-velocity and the pressure. A high-resolution shock-capturing central upwind scheme is employed to solve the model equations. To avoid excessive numerical diffusion, the considered scheme avails the specific information of local propagation speeds. By using Runge-Kutta time stepping method and MUSCL-type initial reconstruction, we have obtained 2nd order accuracy of the proposed scheme. After discussing the model equations and the numerical technique, several 1D and 2D test problems are investigated. For all the numerical test cases, our proposed scheme demonstrates very good agreement with the results obtained by well-established algorithms, even in the case of highly relativistic 2D test problems. For validation and comparison, the staggered central scheme and the kinetic flux-vector splitting (KFVS) method are also implemented to the same model. The robustness and efficiency of central upwind scheme is demonstrated by the numerical results.

  1. Numerical Schemes for the Hamilton-Jacobi and Level Set Equations on Triangulated Domains

    NASA Technical Reports Server (NTRS)

    Barth, Timothy J.; Sethian, James A.

    1997-01-01

    Borrowing from techniques developed for conservation law equations, numerical schemes which discretize the Hamilton-Jacobi (H-J), level set, and Eikonal equations on triangulated domains are presented. The first scheme is a provably monotone discretization for certain forms of the H-J equations. Unfortunately, the basic scheme lacks proper Lipschitz continuity of the numerical Hamiltonian. By employing a virtual edge flipping technique, Lipschitz continuity of the numerical flux is restored on acute triangulations. Next, schemes are introduced and developed based on the weaker concept of positive coefficient approximations for homogeneous Hamiltonians. These schemes possess a discrete maximum principle on arbitrary triangulations and naturally exhibit proper Lipschitz continuity of the numerical Hamiltonian. Finally, a class of Petrov-Galerkin approximations are considered. These schemes are stabilized via a least-squares bilinear form. The Petrov-Galerkin schemes do not possess a discrete maximum principle but generalize to high order accuracy.

  2. On a fourth order accurate implicit finite difference scheme for hyperbolic conservation laws. II - Five-point schemes

    NASA Technical Reports Server (NTRS)

    Harten, A.; Tal-Ezer, H.

    1981-01-01

    This paper presents a family of two-level five-point implicit schemes for the solution of one-dimensional systems of hyperbolic conservation laws, which generalized the Crank-Nicholson scheme to fourth order accuracy (4-4) in both time and space. These 4-4 schemes are nondissipative and unconditionally stable. Special attention is given to the system of linear equations associated with these 4-4 implicit schemes. The regularity of this system is analyzed and efficiency of solution-algorithms is examined. A two-datum representation of these 4-4 implicit schemes brings about a compactification of the stencil to three mesh points at each time-level. This compact two-datum representation is particularly useful in deriving boundary treatments. Numerical results are presented to illustrate some properties of the proposed scheme.

  3. A fourth order accurate finite difference scheme for the computation of elastic waves

    NASA Technical Reports Server (NTRS)

    Bayliss, A.; Jordan, K. E.; Lemesurier, B. J.; Turkel, E.

    1986-01-01

    A finite difference for elastic waves is introduced. The model is based on the first order system of equations for the velocities and stresses. The differencing is fourth order accurate on the spatial derivatives and second order accurate in time. The model is tested on a series of examples including the Lamb problem, scattering from plane interf aces and scattering from a fluid-elastic interface. The scheme is shown to be effective for these problems. The accuracy and stability is insensitive to the Poisson ratio. For the class of problems considered here it is found that the fourth order scheme requires for two-thirds to one-half the resolution of a typical second order scheme to give comparable accuracy.

  4. Unconditionally energy stable numerical schemes for phase-field vesicle membrane model

    NASA Astrophysics Data System (ADS)

    Guillén-González, F.; Tierra, G.

    2018-02-01

    Numerical schemes to simulate the deformation of vesicles membranes via minimizing the bending energy have been widely studied in recent times due to its connection with many biological motivated problems. In this work we propose a new unconditionally energy stable numerical scheme for a vesicle membrane model that satisfies exactly the conservation of volume constraint and penalizes the surface area constraint. Moreover, we extend these ideas to present an unconditionally energy stable splitting scheme decoupling the interaction of the vesicle with a surrounding fluid. Finally, the well behavior of the proposed schemes are illustrated through several computational experiments.

  5. Stable and Spectrally Accurate Schemes for the Navier-Stokes Equations

    DOE Office of Scientific and Technical Information (OSTI.GOV)

    Jia, Jun; Liu, Jie

    2011-01-01

    In this paper, we present an accurate, efficient and stable numerical method for the incompressible Navier-Stokes equations (NSEs). The method is based on (1) an equivalent pressure Poisson equation formulation of the NSE with proper pressure boundary conditions, which facilitates the design of high-order and stable numerical methods, and (2) the Krylov deferred correction (KDC) accelerated method of lines transpose (mbox MoL{sup T}), which is very stable, efficient, and of arbitrary order in time. Numerical tests with known exact solutions in three dimensions show that the new method is spectrally accurate in time, and a numerical order of convergence 9more » was observed. Two-dimensional computational results of flow past a cylinder and flow in a bifurcated tube are also reported.« less

  6. Eulerian-Lagrangian numerical scheme for simulating advection, dispersion, and transient storage in streams and a comparison of numerical methods

    USGS Publications Warehouse

    Cox, T.J.; Runkel, R.L.

    2008-01-01

    Past applications of one-dimensional advection, dispersion, and transient storage zone models have almost exclusively relied on a central differencing, Eulerian numerical approximation to the nonconservative form of the fundamental equation. However, there are scenarios where this approach generates unacceptable error. A new numerical scheme for this type of modeling is presented here that is based on tracking Lagrangian control volumes across a fixed (Eulerian) grid. Numerical tests are used to provide a direct comparison of the new scheme versus nonconservative Eulerian numerical methods, in terms of both accuracy and mass conservation. Key characteristics of systems for which the Lagrangian scheme performs better than the Eulerian scheme include: nonuniform flow fields, steep gradient plume fronts, and pulse and steady point source loadings in advection-dominated systems. A new analytical derivation is presented that provides insight into the loss of mass conservation in the nonconservative Eulerian scheme. This derivation shows that loss of mass conservation in the vicinity of spatial flow changes is directly proportional to the lateral inflow rate and the change in stream concentration due to the inflow. While the nonconservative Eulerian scheme has clearly worked well for past published applications, it is important for users to be aware of the scheme's limitations. ?? 2008 ASCE.

  7. Higher-order accurate space-time schemes for computational astrophysics—Part I: finite volume methods

    NASA Astrophysics Data System (ADS)

    Balsara, Dinshaw S.

    2017-12-01

    As computational astrophysics comes under pressure to become a precision science, there is an increasing need to move to high accuracy schemes for computational astrophysics. The algorithmic needs of computational astrophysics are indeed very special. The methods need to be robust and preserve the positivity of density and pressure. Relativistic flows should remain sub-luminal. These requirements place additional pressures on a computational astrophysics code, which are usually not felt by a traditional fluid dynamics code. Hence the need for a specialized review. The focus here is on weighted essentially non-oscillatory (WENO) schemes, discontinuous Galerkin (DG) schemes and PNPM schemes. WENO schemes are higher order extensions of traditional second order finite volume schemes. At third order, they are most similar to piecewise parabolic method schemes, which are also included. DG schemes evolve all the moments of the solution, with the result that they are more accurate than WENO schemes. PNPM schemes occupy a compromise position between WENO and DG schemes. They evolve an Nth order spatial polynomial, while reconstructing higher order terms up to Mth order. As a result, the timestep can be larger. Time-dependent astrophysical codes need to be accurate in space and time with the result that the spatial and temporal accuracies must be matched. This is realized with the help of strong stability preserving Runge-Kutta schemes and ADER (Arbitrary DERivative in space and time) schemes, both of which are also described. The emphasis of this review is on computer-implementable ideas, not necessarily on the underlying theory.

  8. An implicit higher-order spatially accurate scheme for solving time dependent flows on unstructured meshes

    NASA Astrophysics Data System (ADS)

    Tomaro, Robert F.

    1998-07-01

    The present research is aimed at developing a higher-order, spatially accurate scheme for both steady and unsteady flow simulations using unstructured meshes. The resulting scheme must work on a variety of general problems to ensure the creation of a flexible, reliable and accurate aerodynamic analysis tool. To calculate the flow around complex configurations, unstructured grids and the associated flow solvers have been developed. Efficient simulations require the minimum use of computer memory and computational times. Unstructured flow solvers typically require more computer memory than a structured flow solver due to the indirect addressing of the cells. The approach taken in the present research was to modify an existing three-dimensional unstructured flow solver to first decrease the computational time required for a solution and then to increase the spatial accuracy. The terms required to simulate flow involving non-stationary grids were also implemented. First, an implicit solution algorithm was implemented to replace the existing explicit procedure. Several test cases, including internal and external, inviscid and viscous, two-dimensional, three-dimensional and axi-symmetric problems, were simulated for comparison between the explicit and implicit solution procedures. The increased efficiency and robustness of modified code due to the implicit algorithm was demonstrated. Two unsteady test cases, a plunging airfoil and a wing undergoing bending and torsion, were simulated using the implicit algorithm modified to include the terms required for a moving and/or deforming grid. Secondly, a higher than second-order spatially accurate scheme was developed and implemented into the baseline code. Third- and fourth-order spatially accurate schemes were implemented and tested. The original dissipation was modified to include higher-order terms and modified near shock waves to limit pre- and post-shock oscillations. The unsteady cases were repeated using the higher

  9. Conservative properties of finite difference schemes for incompressible flow

    NASA Technical Reports Server (NTRS)

    Morinishi, Youhei

    1995-01-01

    The purpose of this research is to construct accurate finite difference schemes for incompressible unsteady flow simulations such as LES (large-eddy simulation) or DNS (direct numerical simulation). In this report, conservation properties of the continuity, momentum, and kinetic energy equations for incompressible flow are specified as analytical requirements for a proper set of discretized equations. Existing finite difference schemes in staggered grid systems are checked for satisfaction of the requirements. Proper higher order accurate finite difference schemes in a staggered grid system are then proposed. Plane channel flow is simulated using the proposed fourth order accurate finite difference scheme and the results compared with those of the second order accurate Harlow and Welch algorithm.

  10. A fast and accurate dihedral interpolation loop subdivision scheme

    NASA Astrophysics Data System (ADS)

    Shi, Zhuo; An, Yalei; Wang, Zhongshuai; Yu, Ke; Zhong, Si; Lan, Rushi; Luo, Xiaonan

    2018-04-01

    In this paper, we propose a fast and accurate dihedral interpolation Loop subdivision scheme for subdivision surfaces based on triangular meshes. In order to solve the problem of surface shrinkage, we keep the limit condition unchanged, which is important. Extraordinary vertices are handled using modified Butterfly rules. Subdivision schemes are computationally costly as the number of faces grows exponentially at higher levels of subdivision. To address this problem, our approach is to use local surface information to adaptively refine the model. This is achieved simply by changing the threshold value of the dihedral angle parameter, i.e., the angle between the normals of a triangular face and its adjacent faces. We then demonstrate the effectiveness of the proposed method for various 3D graphic triangular meshes, and extensive experimental results show that it can match or exceed the expected results at lower computational cost.

  11. Numerical experiments on the accuracy of ENO and modified ENO schemes

    NASA Technical Reports Server (NTRS)

    Shu, Chi-Wang

    1990-01-01

    Further numerical experiments are made assessing an accuracy degeneracy phenomena. A modified essentially non-oscillatory (ENO) scheme is proposed, which recovers the correct order of accuracy for all the test problems with smooth initial conditions and gives comparable results with the original ENO schemes for discontinuous problems.

  12. Kalman filters for assimilating near-surface observations into the Richards equation - Part 1: Retrieving state profiles with linear and nonlinear numerical schemes

    NASA Astrophysics Data System (ADS)

    Chirico, G. B.; Medina, H.; Romano, N.

    2014-07-01

    This paper examines the potential of different algorithms, based on the Kalman filtering approach, for assimilating near-surface observations into a one-dimensional Richards equation governing soil water flow in soil. Our specific objectives are: (i) to compare the efficiency of different Kalman filter algorithms in retrieving matric pressure head profiles when they are implemented with different numerical schemes of the Richards equation; (ii) to evaluate the performance of these algorithms when nonlinearities arise from the nonlinearity of the observation equation, i.e. when surface soil water content observations are assimilated to retrieve matric pressure head values. The study is based on a synthetic simulation of an evaporation process from a homogeneous soil column. Our first objective is achieved by implementing a Standard Kalman Filter (SKF) algorithm with both an explicit finite difference scheme (EX) and a Crank-Nicolson (CN) linear finite difference scheme of the Richards equation. The Unscented (UKF) and Ensemble Kalman Filters (EnKF) are applied to handle the nonlinearity of a backward Euler finite difference scheme. To accomplish the second objective, an analogous framework is applied, with the exception of replacing SKF with the Extended Kalman Filter (EKF) in combination with a CN numerical scheme, so as to handle the nonlinearity of the observation equation. While the EX scheme is computationally too inefficient to be implemented in an operational assimilation scheme, the retrieval algorithm implemented with a CN scheme is found to be computationally more feasible and accurate than those implemented with the backward Euler scheme, at least for the examined one-dimensional problem. The UKF appears to be as feasible as the EnKF when one has to handle nonlinear numerical schemes or additional nonlinearities arising from the observation equation, at least for systems of small dimensionality as the one examined in this study.

  13. A New Time-Space Accurate Scheme for Hyperbolic Problems. 1; Quasi-Explicit Case

    NASA Technical Reports Server (NTRS)

    Sidilkover, David

    1998-01-01

    This paper presents a new discretization scheme for hyperbolic systems of conservations laws. It satisfies the TVD property and relies on the new high-resolution mechanism which is compatible with the genuinely multidimensional approach proposed recently. This work can be regarded as a first step towards extending the genuinely multidimensional approach to unsteady problems. Discontinuity capturing capabilities and accuracy of the scheme are verified by a set of numerical tests.

  14. Adaptive Numerical Dissipative Control in High Order Schemes for Multi-D Non-Ideal MHD

    NASA Technical Reports Server (NTRS)

    Yee, H. C.; Sjoegreen, B.

    2004-01-01

    The goal is to extend our adaptive numerical dissipation control in high order filter schemes and our new divergence-free methods for ideal MHD to non-ideal MHD that include viscosity and resistivity. The key idea consists of automatic detection of different flow features as distinct sensors to signal the appropriate type and amount of numerical dissipation/filter where needed and leave the rest of the region free of numerical dissipation contamination. These scheme-independent detectors are capable of distinguishing shocks/shears, flame sheets, turbulent fluctuations and spurious high-frequency oscillations. The detection algorithm is based on an artificial compression method (ACM) (for shocks/shears), and redundant multi-resolution wavelets (WAV) (for the above types of flow feature). These filter approaches also provide a natural and efficient way for the minimization of Div(B) numerical error. The filter scheme consists of spatially sixth order or higher non-dissipative spatial difference operators as the base scheme for the inviscid flux derivatives. If necessary, a small amount of high order linear dissipation is used to remove spurious high frequency oscillations. For example, an eighth-order centered linear dissipation (AD8) might be included in conjunction with a spatially sixth-order base scheme. The inviscid difference operator is applied twice for the viscous flux derivatives. After the completion of a full time step of the base scheme step, the solution is adaptively filtered by the product of a 'flow detector' and the 'nonlinear dissipative portion' of a high-resolution shock-capturing scheme. In addition, the scheme independent wavelet flow detector can be used in conjunction with spatially compact, spectral or spectral element type of base schemes. The ACM and wavelet filter schemes using the dissipative portion of a second-order shock-capturing scheme with sixth-order spatial central base scheme for both the inviscid and viscous MHD flux

  15. An efficient numerical scheme for the study of equal width equation

    NASA Astrophysics Data System (ADS)

    Ghafoor, Abdul; Haq, Sirajul

    2018-06-01

    In this work a new numerical scheme is proposed in which Haar wavelet method is coupled with finite difference scheme for the solution of a nonlinear partial differential equation. The scheme transforms the partial differential equation to a system of algebraic equations which can be solved easily. The technique is applied to equal width equation in order to study the behaviour of one, two, three solitary waves, undular bore and soliton collision. For efficiency and accuracy of the scheme, L2 and L∞ norms and invariants are computed. The results obtained are compared with already existing results in literature.

  16. Building fast well-balanced two-stage numerical schemes for a model of two-phase flows

    NASA Astrophysics Data System (ADS)

    Thanh, Mai Duc

    2014-06-01

    We present a set of well-balanced two-stage schemes for an isentropic model of two-phase flows arisen from the modeling of deflagration-to-detonation transition in granular materials. The first stage is to absorb the source term in nonconservative form into equilibria. Then in the second stage, these equilibria will be composed into a numerical flux formed by using a convex combination of the numerical flux of a stable Lax-Friedrichs-type scheme and the one of a higher-order Richtmyer-type scheme. Numerical schemes constructed in such a way are expected to get the interesting property: they are fast and stable. Tests show that the method works out until the parameter takes on the value CFL, and so any value of the parameter between zero and this value is expected to work as well. All the schemes in this family are shown to capture stationary waves and preserves the positivity of the volume fractions. The special values of the parameter 0,1/2,1/(1+CFL), and CFL in this family define the Lax-Friedrichs-type, FAST1, FAST2, and FAST3 schemes, respectively. These schemes are shown to give a desirable accuracy. The errors and the CPU time of these schemes and the Roe-type scheme are calculated and compared. The constructed schemes are shown to be well-balanced and faster than the Roe-type scheme.

  17. An efficient and accurate two-stage fourth-order gas-kinetic scheme for the Euler and Navier-Stokes equations

    NASA Astrophysics Data System (ADS)

    Pan, Liang; Xu, Kun; Li, Qibing; Li, Jiequan

    2016-12-01

    For computational fluid dynamics (CFD), the generalized Riemann problem (GRP) solver and the second-order gas-kinetic scheme (GKS) provide a time-accurate flux function starting from a discontinuous piecewise linear flow distributions around a cell interface. With the adoption of time derivative of the flux function, a two-stage Lax-Wendroff-type (L-W for short) time stepping method has been recently proposed in the design of a fourth-order time accurate method for inviscid flow [21]. In this paper, based on the same time-stepping method and the second-order GKS flux function [42], a fourth-order gas-kinetic scheme is constructed for the Euler and Navier-Stokes (NS) equations. In comparison with the formal one-stage time-stepping third-order gas-kinetic solver [24], the current fourth-order method not only reduces the complexity of the flux function, but also improves the accuracy of the scheme. In terms of the computational cost, a two-dimensional third-order GKS flux function takes about six times of the computational time of a second-order GKS flux function. However, a fifth-order WENO reconstruction may take more than ten times of the computational cost of a second-order GKS flux function. Therefore, it is fully legitimate to develop a two-stage fourth order time accurate method (two reconstruction) instead of standard four stage fourth-order Runge-Kutta method (four reconstruction). Most importantly, the robustness of the fourth-order GKS is as good as the second-order one. In the current computational fluid dynamics (CFD) research, it is still a difficult problem to extend the higher-order Euler solver to the NS one due to the change of governing equations from hyperbolic to parabolic type and the initial interface discontinuity. This problem remains distinctively for the hypersonic viscous and heat conducting flow. The GKS is based on the kinetic equation with the hyperbolic transport and the relaxation source term. The time-dependent GKS flux function

  18. 3 Lectures: "Lagrangian Models", "Numerical Transport Schemes", and "Chemical and Transport Models"

    NASA Technical Reports Server (NTRS)

    Douglass, A.

    2005-01-01

    The topics for the three lectures for the Canadian Summer School are Lagrangian Models, numerical transport schemes, and chemical and transport models. In the first lecture I will explain the basic components of the Lagrangian model (a trajectory code and a photochemical code), the difficulties in using such a model (initialization) and show some applications in interpretation of aircraft and satellite data. If time permits I will show some results concerning inverse modeling which is being used to evaluate sources of tropospheric pollutants. In the second lecture I will discuss one of the core components of any grid point model, the numerical transport scheme. I will explain the basics of shock capturing schemes, and performance criteria. I will include an example of the importance of horizontal resolution to polar processes. We have learned from NASA's global modeling initiative that horizontal resolution matters for predictions of the future evolution of the ozone hole. The numerical scheme will be evaluated using performance metrics based on satellite observations of long-lived tracers. The final lecture will discuss the evolution of chemical transport models over the last decade. Some of the problems with assimilated winds will be demonstrated, using satellite data to evaluate the simulations.

  19. CONDIF - A modified central-difference scheme for convective flows

    NASA Technical Reports Server (NTRS)

    Runchal, Akshai K.

    1987-01-01

    The paper presents a method, called CONDIF, which modifies the CDS (central-difference scheme) by introducing a controlled amount of numerical diffusion based on the local gradients. The numerical diffusion can be adjusted to be negligibly low for most problems. CONDIF results are significantly more accurate than those obtained from the hybrid scheme when the Peclet number is very high and the flow is at large angles to the grid.

  20. A numerical scheme for nonlinear Helmholtz equations with strong nonlinear optical effects.

    PubMed

    Xu, Zhengfu; Bao, Gang

    2010-11-01

    A numerical scheme is presented to solve the nonlinear Helmholtz (NLH) equation modeling second-harmonic generation (SHG) in photonic bandgap material doped with a nonlinear χ((2)) effect and the NLH equation modeling wave propagation in Kerr type gratings with a nonlinear χ((3)) effect in the one-dimensional case. Both of these nonlinear phenomena arise as a result of the combination of high electromagnetic mode density and nonlinear reaction from the medium. When the mode intensity of the incident wave is significantly strong, which makes the nonlinear effect non-negligible, numerical methods based on the linearization of the essentially nonlinear problem will become inadequate. In this work, a robust, stable numerical scheme is designed to simulate the NLH equations with strong nonlinearity.

  1. Ancient numerical daemons of conceptual hydrological modeling: 1. Fidelity and efficiency of time stepping schemes

    NASA Astrophysics Data System (ADS)

    Clark, Martyn P.; Kavetski, Dmitri

    2010-10-01

    A major neglected weakness of many current hydrological models is the numerical method used to solve the governing model equations. This paper thoroughly evaluates several classes of time stepping schemes in terms of numerical reliability and computational efficiency in the context of conceptual hydrological modeling. Numerical experiments are carried out using 8 distinct time stepping algorithms and 6 different conceptual rainfall-runoff models, applied in a densely gauged experimental catchment, as well as in 12 basins with diverse physical and hydroclimatic characteristics. Results show that, over vast regions of the parameter space, the numerical errors of fixed-step explicit schemes commonly used in hydrology routinely dwarf the structural errors of the model conceptualization. This substantially degrades model predictions, but also, disturbingly, generates fortuitously adequate performance for parameter sets where numerical errors compensate for model structural errors. Simply running fixed-step explicit schemes with shorter time steps provides a poor balance between accuracy and efficiency: in some cases daily-step adaptive explicit schemes with moderate error tolerances achieved comparable or higher accuracy than 15 min fixed-step explicit approximations but were nearly 10 times more efficient. From the range of simple time stepping schemes investigated in this work, the fixed-step implicit Euler method and the adaptive explicit Heun method emerge as good practical choices for the majority of simulation scenarios. In combination with the companion paper, where impacts on model analysis, interpretation, and prediction are assessed, this two-part study vividly highlights the impact of numerical errors on critical performance aspects of conceptual hydrological models and provides practical guidelines for robust numerical implementation.

  2. Numerical solution of transport equation for applications in environmental hydraulics and hydrology

    NASA Astrophysics Data System (ADS)

    Rashidul Islam, M.; Hanif Chaudhry, M.

    1997-04-01

    The advective term in the one-dimensional transport equation, when numerically discretized, produces artificial diffusion. To minimize such artificial diffusion, which vanishes only for Courant number equal to unity, transport owing to advection has been modeled separately. The numerical solution of the advection equation for a Gaussian initial distribution is well established; however, large oscillations are observed when applied to an initial distribution with sleep gradients, such as trapezoidal distribution of a constituent or propagation of mass from a continuous input. In this study, the application of seven finite-difference schemes and one polynomial interpolation scheme is investigated to solve the transport equation for both Gaussian and non-Gaussian (trapezoidal) initial distributions. The results obtained from the numerical schemes are compared with the exact solutions. A constant advective velocity is assumed throughout the transport process. For a Gaussian distribution initial condition, all eight schemes give excellent results, except the Lax scheme which is diffusive. In application to the trapezoidal initial distribution, explicit finite-difference schemes prove to be superior to implicit finite-difference schemes because the latter produce large numerical oscillations near the steep gradients. The Warming-Kutler-Lomax (WKL) explicit scheme is found to be better among this group. The Hermite polynomial interpolation scheme yields the best result for a trapezoidal distribution among all eight schemes investigated. The second-order accurate schemes are sufficiently accurate for most practical problems, but the solution of unusual problems (concentration with steep gradient) requires the application of higher-order (e.g. third- and fourth-order) accurate schemes.

  3. On numerically accurate finite element

    NASA Technical Reports Server (NTRS)

    Nagtegaal, J. C.; Parks, D. M.; Rice, J. R.

    1974-01-01

    A general criterion for testing a mesh with topologically similar repeat units is given, and the analysis shows that only a few conventional element types and arrangements are, or can be made suitable for computations in the fully plastic range. Further, a new variational principle, which can easily and simply be incorporated into an existing finite element program, is presented. This allows accurate computations to be made even for element designs that would not normally be suitable. Numerical results are given for three plane strain problems, namely pure bending of a beam, a thick-walled tube under pressure, and a deep double edge cracked tensile specimen. The effects of various element designs and of the new variational procedure are illustrated. Elastic-plastic computation at finite strain are discussed.

  4. Efficient Low Dissipative High Order Schemes for Multiscale MHD Flows

    NASA Technical Reports Server (NTRS)

    Sjoegreen, Bjoern; Yee, Helen C.; Mansour, Nagi (Technical Monitor)

    2002-01-01

    Accurate numerical simulations of complex multiscale compressible viscous flows, especially high speed turbulence combustion and acoustics, demand high order schemes with adaptive numerical dissipation controls. Standard high resolution shock-capturing methods are too dissipative to capture the small scales and/or long-time wave propagations without extreme grid refinements and small time steps. An integrated approach for the control of numerical dissipation in high order schemes for the compressible Euler and Navier-Stokes equations has been developed and verified by the authors and collaborators. These schemes are suitable for the problems in question. Basically, the scheme consists of sixth-order or higher non-dissipative spatial difference operators as the base scheme. To control the amount of numerical dissipation, multiresolution wavelets are used as sensors to adaptively limit the amount and to aid the selection and/or blending of the appropriate types of numerical dissipation to be used. Magnetohydrodynamics (MHD) waves play a key role in drag reduction in highly maneuverable high speed combat aircraft, in space weather forecasting, and in the understanding of the dynamics of the evolution of our solar system and the main sequence stars. Although there exist a few well-studied second and third-order high-resolution shock-capturing schemes for the MHD in the literature, these schemes are too diffusive and not practical for turbulence/combustion MHD flows. On the other hand, extension of higher than third-order high-resolution schemes to the MHD system of equations is not straightforward. Unlike the hydrodynamic equations, the inviscid MHD system is non-strictly hyperbolic with non-convex fluxes. The wave structures and shock types are different from their hydrodynamic counterparts. Many of the non-traditional hydrodynamic shocks are not fully understood. Consequently, reliable and highly accurate numerical schemes for multiscale MHD equations pose a great

  5. Weighted Non-linear Compact Schemes for the Direct Numerical Simulation of Compressible, Turbulent Flows

    DOE Office of Scientific and Technical Information (OSTI.GOV)

    Ghosh, Debojyoti; Baeder, James D.

    2014-01-21

    A new class of compact-reconstruction weighted essentially non-oscillatory (CRWENO) schemes were introduced (Ghosh and Baeder in SIAM J Sci Comput 34(3): A1678–A1706, 2012) with high spectral resolution and essentially non-oscillatory behavior across discontinuities. The CRWENO schemes use solution-dependent weights to combine lower-order compact interpolation schemes and yield a high-order compact scheme for smooth solutions and a non-oscillatory compact scheme near discontinuities. The new schemes result in lower absolute errors, and improved resolution of discontinuities and smaller length scales, compared to the weighted essentially non-oscillatory (WENO) scheme of the same order of convergence. Several improvements to the smoothness-dependent weights, proposed inmore » the literature in the context of the WENO schemes, address the drawbacks of the original formulation. This paper explores these improvements in the context of the CRWENO schemes and compares the different formulations of the non-linear weights for flow problems with small length scales as well as discontinuities. Simplified one- and two-dimensional inviscid flow problems are solved to demonstrate the numerical properties of the CRWENO schemes and its different formulations. Canonical turbulent flow problems—the decay of isotropic turbulence and the shock-turbulence interaction—are solved to assess the performance of the schemes for the direct numerical simulation of compressible, turbulent flows« less

  6. On numerical instabilities of Godunov-type schemes for strong shocks

    NASA Astrophysics Data System (ADS)

    Xie, Wenjia; Li, Wei; Li, Hua; Tian, Zhengyu; Pan, Sha

    2017-12-01

    It is well known that low diffusion Riemann solvers with minimal smearing on contact and shear waves are vulnerable to shock instability problems, including the carbuncle phenomenon. In the present study, we concentrate on exploring where the instability grows out and how the dissipation inherent in Riemann solvers affects the unstable behaviors. With the help of numerical experiments and a linearized analysis method, it has been found that the shock instability is strongly related to the unstable modes of intermediate states inside the shock structure. The consistency of mass flux across the normal shock is needed for a Riemann solver to capture strong shocks stably. The famous carbuncle phenomenon is interpreted as the consequence of the inconsistency of mass flux across the normal shock for a low diffusion Riemann solver. Based on the results of numerical experiments and the linearized analysis, a robust Godunov-type scheme with a simple cure for the shock instability is suggested. With only the dissipation corresponding to shear waves introduced in the vicinity of strong shocks, the instability problem is circumvented. Numerical results of several carefully chosen strong shock wave problems are investigated to demonstrate the robustness of the proposed scheme.

  7. Efficient and accurate time-stepping schemes for integrate-and-fire neuronal networks.

    PubMed

    Shelley, M J; Tao, L

    2001-01-01

    To avoid the numerical errors associated with resetting the potential following a spike in simulations of integrate-and-fire neuronal networks, Hansel et al. and Shelley independently developed a modified time-stepping method. Their particular scheme consists of second-order Runge-Kutta time-stepping, a linear interpolant to find spike times, and a recalibration of postspike potential using the spike times. Here we show analytically that such a scheme is second order, discuss the conditions under which efficient, higher-order algorithms can be constructed to treat resets, and develop a modified fourth-order scheme. To support our analysis, we simulate a system of integrate-and-fire conductance-based point neurons with all-to-all coupling. For six-digit accuracy, our modified Runge-Kutta fourth-order scheme needs a time-step of Delta(t) = 0.5 x 10(-3) seconds, whereas to achieve comparable accuracy using a recalibrated second-order or a first-order algorithm requires time-steps of 10(-5) seconds or 10(-9) seconds, respectively. Furthermore, since the cortico-cortical conductances in standard integrate-and-fire neuronal networks do not depend on the value of the membrane potential, we can attain fourth-order accuracy with computational costs normally associated with second-order schemes.

  8. A Non-Dissipative Staggered Fourth-Order Accurate Explicit Finite Difference Scheme for the Time-Domain Maxwell's Equations

    NASA Technical Reports Server (NTRS)

    Yefet, Amir; Petropoulos, Peter G.

    1999-01-01

    We consider a divergence-free non-dissipative fourth-order explicit staggered finite difference scheme for the hyperbolic Maxwell's equations. Special one-sided difference operators are derived in order to implement the scheme near metal boundaries and dielectric interfaces. Numerical results show the scheme is long-time stable, and is fourth-order convergent over complex domains that include dielectric interfaces and perfectly conducting surfaces. We also examine the scheme's behavior near metal surfaces that are not aligned with the grid axes, and compare its accuracy to that obtained by the Yee scheme.

  9. Fourth order scheme for wavelet based solution of Black-Scholes equation

    NASA Astrophysics Data System (ADS)

    Finěk, Václav

    2017-12-01

    The present paper is devoted to the numerical solution of the Black-Scholes equation for pricing European options. We apply the Crank-Nicolson scheme with Richardson extrapolation for time discretization and Hermite cubic spline wavelets with four vanishing moments for space discretization. This scheme is the fourth order accurate both in time and in space. Computational results indicate that the Crank-Nicolson scheme with Richardson extrapolation significantly decreases the amount of computational work. We also numerically show that optimal convergence rate for the used scheme is obtained without using startup procedure despite the data irregularities in the model.

  10. High resolution schemes and the entropy condition

    NASA Technical Reports Server (NTRS)

    Osher, S.; Chakravarthy, S.

    1983-01-01

    A systematic procedure for constructing semidiscrete, second order accurate, variation diminishing, five point band width, approximations to scalar conservation laws, is presented. These schemes are constructed to also satisfy a single discrete entropy inequality. Thus, in the convex flux case, convergence is proven to be the unique physically correct solution. For hyperbolic systems of conservation laws, this construction is used formally to extend the first author's first order accurate scheme, and show (under some minor technical hypotheses) that limit solutions satisfy an entropy inequality. Results concerning discrete shocks, a maximum principle, and maximal order of accuracy are obtained. Numerical applications are also presented.

  11. Low- and high-order accurate boundary conditions: From Stokes to Darcy porous flow modeled with standard and improved Brinkman lattice Boltzmann schemes

    NASA Astrophysics Data System (ADS)

    Silva, Goncalo; Talon, Laurent; Ginzburg, Irina

    2017-04-01

    is thoroughly evaluated in three benchmark tests, which are run throughout three distinctive permeability regimes. The first configuration is a horizontal porous channel, studied with a symbolic approach, where we construct the exact solutions of FEM and BF/IBF with different boundary schemes. The second problem refers to an inclined porous channel flow, which brings in as new challenge the formation of spurious boundary layers in LBM; that is, numerical artefacts that arise due to a deficient accommodation of the bulk solution by the low-accurate boundary scheme. The third problem considers a porous flow past a periodic square array of solid cylinders, which intensifies the previous two tests with the simulation of a more complex flow pattern. The ensemble of numerical tests provides guidelines on the effect of grid resolution and the TRT free collision parameter over the accuracy and the quality of the velocity field, spanning from Stokes to Darcy permeability regimes. It is shown that, with the use of the high-order accurate boundary schemes, the simple, uniform-mesh-based TRT-LBM formulation can even surpass the accuracy of FEM employing hardworking body-fitted meshes.

  12. A practically unconditionally gradient stable scheme for the N-component Cahn-Hilliard system

    NASA Astrophysics Data System (ADS)

    Lee, Hyun Geun; Choi, Jeong-Whan; Kim, Junseok

    2012-02-01

    We present a practically unconditionally gradient stable conservative nonlinear numerical scheme for the N-component Cahn-Hilliard system modeling the phase separation of an N-component mixture. The scheme is based on a nonlinear splitting method and is solved by an efficient and accurate nonlinear multigrid method. The scheme allows us to convert the N-component Cahn-Hilliard system into a system of N-1 binary Cahn-Hilliard equations and significantly reduces the required computer memory and CPU time. We observe that our numerical solutions are consistent with the linear stability analysis results. We also demonstrate the efficiency of the proposed scheme with various numerical experiments.

  13. Numerical scheme approximating solution and parameters in a beam equation

    NASA Astrophysics Data System (ADS)

    Ferdinand, Robert R.

    2003-12-01

    We present a mathematical model which describes vibration in a metallic beam about its equilibrium position. This model takes the form of a nonlinear second-order (in time) and fourth-order (in space) partial differential equation with boundary and initial conditions. A finite-element Galerkin approximation scheme is used to estimate model solution. Infinite-dimensional model parameters are then estimated numerically using an inverse method procedure which involves the minimization of a least-squares cost functional. Numerical results are presented and future work to be done is discussed.

  14. Implicit Total Variation Diminishing (TVD) schemes for steady-state calculations

    NASA Technical Reports Server (NTRS)

    Yee, H. C.; Warming, R. F.; Harten, A.

    1983-01-01

    The application of a new implicit unconditionally stable high resolution total variation diminishing (TVD) scheme to steady state calculations. It is a member of a one parameter family of explicit and implicit second order accurate schemes developed by Harten for the computation of weak solutions of hyperbolic conservation laws. This scheme is guaranteed not to generate spurious oscillations for a nonlinear scalar equation and a constant coefficient system. Numerical experiments show that this scheme not only has a rapid convergence rate, but also generates a highly resolved approximation to the steady state solution. A detailed implementation of the implicit scheme for the one and two dimensional compressible inviscid equations of gas dynamics is presented. Some numerical computations of one and two dimensional fluid flows containing shocks demonstrate the efficiency and accuracy of this new scheme.

  15. Numerical investigation of complex flooding schemes for surfactant polymer based enhanced oil recovery

    NASA Astrophysics Data System (ADS)

    Dutta, Sourav; Daripa, Prabir

    2015-11-01

    Surfactant-polymer flooding is a widely used method of chemical enhanced oil recovery (EOR) in which an array of complex fluids containing suitable and varying amounts of surfactant or polymer or both mixed with water is injected into the reservoir. This is an example of multiphase, multicomponent and multiphysics porous media flow which is characterized by the spontaneous formation of complex viscous fingering patterns and is modeled by a system of strongly coupled nonlinear partial differential equations with appropriate initial and boundary conditions. Here we propose and discuss a modern, hybrid method based on a combination of a discontinuous, multiscale finite element formulation and the method of characteristics to accurately solve the system. Several types of flooding schemes and rheological properties of the injected fluids are used to numerically study the effectiveness of various injection policies in minimizing the viscous fingering and maximizing oil recovery. Numerical simulations are also performed to investigate the effect of various other physical and model parameters such as heterogeneity, relative permeability and residual saturation on the quantities of interest like cumulative oil recovery, sweep efficiency, fingering intensity to name a few. Supported by the grant NPRP 08-777-1-141 from the Qatar National Research Fund (a member of The Qatar Foundation).

  16. Parameter estimation in IMEX-trigonometrically fitted methods for the numerical solution of reaction-diffusion problems

    NASA Astrophysics Data System (ADS)

    D'Ambrosio, Raffaele; Moccaldi, Martina; Paternoster, Beatrice

    2018-05-01

    In this paper, an adapted numerical scheme for reaction-diffusion problems generating periodic wavefronts is introduced. Adapted numerical methods for such evolutionary problems are specially tuned to follow prescribed qualitative behaviors of the solutions, making the numerical scheme more accurate and efficient as compared with traditional schemes already known in the literature. Adaptation through the so-called exponential fitting technique leads to methods whose coefficients depend on unknown parameters related to the dynamics and aimed to be numerically computed. Here we propose a strategy for a cheap and accurate estimation of such parameters, which consists essentially in minimizing the leading term of the local truncation error whose expression is provided in a rigorous accuracy analysis. In particular, the presented estimation technique has been applied to a numerical scheme based on combining an adapted finite difference discretization in space with an implicit-explicit time discretization. Numerical experiments confirming the effectiveness of the approach are also provided.

  17. A strong shock tube problem calculated by different numerical schemes

    NASA Astrophysics Data System (ADS)

    Lee, Wen Ho; Clancy, Sean P.

    1996-05-01

    Calculated results are presented for the solution of a very strong shock tube problem on a coarse mesh using (1) MESA code, (2) UNICORN code, (3) Schulz hydro, and (4) modified TVD scheme. The first two codes are written in Eulerian coordinates, whereas methods (3) and (4) are in Lagrangian coordinates. MESA and UNICORN codes are both of second order and use different monotonic advection method to avoid the Gibbs phenomena. Code (3) uses typical artificial viscosity for inviscid flow, whereas code (4) uses a modified TVD scheme. The test problem is a strong shock tube problem with a pressure ratio of 109 and density ratio of 103 in an ideal gas. For no mass-matching case, Schulz hydro is better than TVD scheme. In the case of mass-matching, there is no difference between them. MESA and UNICORN results are nearly the same. However, the computed positions such as the contact discontinuity (i.e. the material interface) are not as accurate as the Lagrangian methods.

  18. An Energy Decaying Scheme for Nonlinear Dynamics of Shells

    NASA Technical Reports Server (NTRS)

    Bottasso, Carlo L.; Bauchau, Olivier A.; Choi, Jou-Young; Bushnell, Dennis M. (Technical Monitor)

    2000-01-01

    A novel integration scheme for nonlinear dynamics of geometrically exact shells is developed based on the inextensible director assumption. The new algorithm is designed so as to imply the strict decay of the system total mechanical energy at each time step, and consequently unconditional stability is achieved in the nonlinear regime. Furthermore, the scheme features tunable high frequency numerical damping and it is therefore stiffly accurate. The method is tested for a finite element spatial formulation of shells based on mixed interpolations of strain tensorial components and on a two-parameter representation of director rotations. The robustness of the, scheme is illustrated with the help of numerical examples.

  19. A Continuing Search for a Near-Perfect Numerical Flux Scheme. Part 1; [AUSM+

    NASA Technical Reports Server (NTRS)

    Liou, Meng-Sing

    1994-01-01

    While enjoying demonstrated improvement in accuracy, efficiency, and robustness over existing schemes, the Advection Upstream Splitting Scheme (AUSM) was found to have some deficiencies in extreme cases. This recent progress towards improving the AUSM while retaining its advantageous features is described. The new scheme, termed AUSM+, features: unification of velocity and Mach number splitting; exact capture of a single stationary shock; and improvement in accuracy. A general construction of the AUSM+ scheme is layed out and then focus is on the analysis of the a scheme and its mathematical properties, heretofore unreported. Monotonicity and positivity are proved, and a CFL-like condition is given for first and second order schemes and for generalized curvilinear co-ordinates. Finally, results of numerical tests on many problems are given to confirm the capability and improvements on a variety of problems including those failed by prominent schemes.

  20. ADER discontinuous Galerkin schemes for general-relativistic ideal magnetohydrodynamics

    NASA Astrophysics Data System (ADS)

    Fambri, F.; Dumbser, M.; Köppel, S.; Rezzolla, L.; Zanotti, O.

    2018-07-01

    We present a new class of high-order accurate numerical algorithms for solving the equations of general-relativistic ideal magnetohydrodynamics in curved space-times. In this paper, we assume the background space-time to be given and static, i.e. we make use of the Cowling approximation. The governing partial differential equations are solved via a new family of fully discrete and arbitrary high-order accurate path-conservative discontinuous Galerkin (DG) finite-element methods combined with adaptive mesh refinement and time accurate local time-stepping. In order to deal with shock waves and other discontinuities, the high-order DG schemes are supplemented with a novel a posteriori subcell finite-volume limiter, which makes the new algorithms as robust as classical second-order total-variation diminishing finite-volume methods at shocks and discontinuities, but also as accurate as unlimited high-order DG schemes in smooth regions of the flow. We show the advantages of this new approach by means of various classical two- and three-dimensional benchmark problems on fixed space-times. Finally, we present a performance and accuracy comparisons between Runge-Kutta DG schemes and ADER high-order finite-volume schemes, showing the higher efficiency of DG schemes.

  1. ADER discontinuous Galerkin schemes for general-relativistic ideal magnetohydrodynamics

    NASA Astrophysics Data System (ADS)

    Fambri, F.; Dumbser, M.; Köppel, S.; Rezzolla, L.; Zanotti, O.

    2018-03-01

    We present a new class of high-order accurate numerical algorithms for solving the equations of general-relativistic ideal magnetohydrodynamics in curved spacetimes. In this paper we assume the background spacetime to be given and static, i.e. we make use of the Cowling approximation. The governing partial differential equations are solved via a new family of fully-discrete and arbitrary high-order accurate path-conservative discontinuous Galerkin (DG) finite-element methods combined with adaptive mesh refinement and time accurate local timestepping. In order to deal with shock waves and other discontinuities, the high-order DG schemes are supplemented with a novel a-posteriori subcell finite-volume limiter, which makes the new algorithms as robust as classical second-order total-variation diminishing finite-volume methods at shocks and discontinuities, but also as accurate as unlimited high-order DG schemes in smooth regions of the flow. We show the advantages of this new approach by means of various classical two- and three-dimensional benchmark problems on fixed spacetimes. Finally, we present a performance and accuracy comparisons between Runge-Kutta DG schemes and ADER high-order finite-volume schemes, showing the higher efficiency of DG schemes.

  2. Accurate B-spline-based 3-D interpolation scheme for digital volume correlation

    NASA Astrophysics Data System (ADS)

    Ren, Maodong; Liang, Jin; Wei, Bin

    2016-12-01

    An accurate and efficient 3-D interpolation scheme, based on sampling theorem and Fourier transform technique, is proposed to reduce the sub-voxel matching error caused by intensity interpolation bias in digital volume correlation. First, the influence factors of the interpolation bias are investigated theoretically using the transfer function of an interpolation filter (henceforth filter) in the Fourier domain. A law that the positional error of a filter can be expressed as a function of fractional position and wave number is found. Then, considering the above factors, an optimized B-spline-based recursive filter, combining B-spline transforms and least squares optimization method, is designed to virtually eliminate the interpolation bias in the process of sub-voxel matching. Besides, given each volumetric image containing different wave number ranges, a Gaussian weighting function is constructed to emphasize or suppress certain of wave number ranges based on the Fourier spectrum analysis. Finally, a novel software is developed and series of validation experiments were carried out to verify the proposed scheme. Experimental results show that the proposed scheme can reduce the interpolation bias to an acceptable level.

  3. Optimisation of colour schemes to accurately display mass spectrometry imaging data based on human colour perception.

    PubMed

    Race, Alan M; Bunch, Josephine

    2015-03-01

    The choice of colour scheme used to present data can have a dramatic effect on the perceived structure present within the data. This is of particular significance in mass spectrometry imaging (MSI), where ion images that provide 2D distributions of a wide range of analytes are used to draw conclusions about the observed system. Commonly employed colour schemes are generally suboptimal for providing an accurate representation of the maximum amount of data. Rainbow-based colour schemes are extremely popular within the community, but they introduce well-documented artefacts which can be actively misleading in the interpretation of the data. In this article, we consider the suitability of colour schemes and composite image formation found in MSI literature in the context of human colour perception. We also discuss recommendations of rules for colour scheme selection for ion composites and multivariate analysis techniques such as principal component analysis (PCA).

  4. Low- and high-order accurate boundary conditions: From Stokes to Darcy porous flow modeled with standard and improved Brinkman lattice Boltzmann schemes

    DOE Office of Scientific and Technical Information (OSTI.GOV)

    Silva, Goncalo, E-mail: goncalo.nuno.silva@gmail.com; Talon, Laurent, E-mail: talon@fast.u-psud.fr; Ginzburg, Irina, E-mail: irina.ginzburg@irstea.fr

    of LBM and FEM is thoroughly evaluated in three benchmark tests, which are run throughout three distinctive permeability regimes. The first configuration is a horizontal porous channel, studied with a symbolic approach, where we construct the exact solutions of FEM and BF/IBF with different boundary schemes. The second problem refers to an inclined porous channel flow, which brings in as new challenge the formation of spurious boundary layers in LBM; that is, numerical artefacts that arise due to a deficient accommodation of the bulk solution by the low-accurate boundary scheme. The third problem considers a porous flow past a periodic square array of solid cylinders, which intensifies the previous two tests with the simulation of a more complex flow pattern. The ensemble of numerical tests provides guidelines on the effect of grid resolution and the TRT free collision parameter over the accuracy and the quality of the velocity field, spanning from Stokes to Darcy permeability regimes. It is shown that, with the use of the high-order accurate boundary schemes, the simple, uniform-mesh-based TRT-LBM formulation can even surpass the accuracy of FEM employing hardworking body-fitted meshes.« less

  5. High-order conservative finite difference GLM-MHD schemes for cell-centered MHD

    NASA Astrophysics Data System (ADS)

    Mignone, Andrea; Tzeferacos, Petros; Bodo, Gianluigi

    2010-08-01

    We present and compare third- as well as fifth-order accurate finite difference schemes for the numerical solution of the compressible ideal MHD equations in multiple spatial dimensions. The selected methods lean on four different reconstruction techniques based on recently improved versions of the weighted essentially non-oscillatory (WENO) schemes, monotonicity preserving (MP) schemes as well as slope-limited polynomial reconstruction. The proposed numerical methods are highly accurate in smooth regions of the flow, avoid loss of accuracy in proximity of smooth extrema and provide sharp non-oscillatory transitions at discontinuities. We suggest a numerical formulation based on a cell-centered approach where all of the primary flow variables are discretized at the zone center. The divergence-free condition is enforced by augmenting the MHD equations with a generalized Lagrange multiplier yielding a mixed hyperbolic/parabolic correction, as in Dedner et al. [J. Comput. Phys. 175 (2002) 645-673]. The resulting family of schemes is robust, cost-effective and straightforward to implement. Compared to previous existing approaches, it completely avoids the CPU intensive workload associated with an elliptic divergence cleaning step and the additional complexities required by staggered mesh algorithms. Extensive numerical testing demonstrate the robustness and reliability of the proposed framework for computations involving both smooth and discontinuous features.

  6. On a fourth order accurate implicit finite difference scheme for hyperbolic conservation laws. I - Nonstiff strongly dynamic problems

    NASA Technical Reports Server (NTRS)

    Harten, A.; Tal-Ezer, H.

    1981-01-01

    An implicit finite difference method of fourth order accuracy in space and time is introduced for the numerical solution of one-dimensional systems of hyperbolic conservation laws. The basic form of the method is a two-level scheme which is unconditionally stable and nondissipative. The scheme uses only three mesh points at level t and three mesh points at level t + delta t. The dissipative version of the basic method given is conditionally stable under the CFL (Courant-Friedrichs-Lewy) condition. This version is particularly useful for the numerical solution of problems with strong but nonstiff dynamic features, where the CFL restriction is reasonable on accuracy grounds. Numerical results are provided to illustrate properties of the proposed method.

  7. A computationally efficient scheme for the non-linear diffusion equation

    NASA Astrophysics Data System (ADS)

    Termonia, P.; Van de Vyver, H.

    2009-04-01

    This Letter proposes a new numerical scheme for integrating the non-linear diffusion equation. It is shown that it is linearly stable. Some tests are presented comparing this scheme to a popular decentered version of the linearized Crank-Nicholson scheme, showing that, although this scheme is slightly less accurate in treating the highly resolved waves, (i) the new scheme better treats highly non-linear systems, (ii) better handles the short waves, (iii) for a given test bed turns out to be three to four times more computationally cheap, and (iv) is easier in implementation.

  8. A Fast and Accurate Method of Radiation Hydrodynamics Calculation in Spherical Symmetry

    NASA Astrophysics Data System (ADS)

    Stamer, Torsten; Inutsuka, Shu-ichiro

    2018-06-01

    We develop a new numerical scheme for solving the radiative transfer equation in a spherically symmetric system. This scheme does not rely on any kind of diffusion approximation, and it is accurate for optically thin, thick, and intermediate systems. In the limit of a homogeneously distributed extinction coefficient, our method is very accurate and exceptionally fast. We combine this fast method with a slower but more generally applicable method to describe realistic problems. We perform various test calculations, including a simplified protostellar collapse simulation. We also discuss possible future improvements.

  9. Highly accurate adaptive finite element schemes for nonlinear hyperbolic problems

    NASA Astrophysics Data System (ADS)

    Oden, J. T.

    1992-08-01

    This document is a final report of research activities supported under General Contract DAAL03-89-K-0120 between the Army Research Office and the University of Texas at Austin from July 1, 1989 through June 30, 1992. The project supported several Ph.D. students over the contract period, two of which are scheduled to complete dissertations during the 1992-93 academic year. Research results produced during the course of this effort led to 6 journal articles, 5 research reports, 4 conference papers and presentations, 1 book chapter, and two dissertations (nearing completion). It is felt that several significant advances were made during the course of this project that should have an impact on the field of numerical analysis of wave phenomena. These include the development of high-order, adaptive, hp-finite element methods for elastodynamic calculations and high-order schemes for linear and nonlinear hyperbolic systems. Also, a theory of multi-stage Taylor-Galerkin schemes was developed and implemented in the analysis of several wave propagation problems, and was configured within a general hp-adaptive strategy for these types of problems. Further details on research results and on areas requiring additional study are given in the Appendix.

  10. Efficient adaptive pseudo-symplectic numerical integration techniques for Landau-Lifshitz dynamics

    NASA Astrophysics Data System (ADS)

    d'Aquino, M.; Capuano, F.; Coppola, G.; Serpico, C.; Mayergoyz, I. D.

    2018-05-01

    Numerical time integration schemes for Landau-Lifshitz magnetization dynamics are considered. Such dynamics preserves the magnetization amplitude and, in the absence of dissipation, also implies the conservation of the free energy. This property is generally lost when time discretization is performed for the numerical solution. In this work, explicit numerical schemes based on Runge-Kutta methods are introduced. The schemes are termed pseudo-symplectic in that they are accurate to order p, but preserve magnetization amplitude and free energy to order q > p. An effective strategy for adaptive time-stepping control is discussed for schemes of this class. Numerical tests against analytical solutions for the simulation of fast precessional dynamics are performed in order to point out the effectiveness of the proposed methods.

  11. An explicit scheme for ohmic dissipation with smoothed particle magnetohydrodynamics

    NASA Astrophysics Data System (ADS)

    Tsukamoto, Yusuke; Iwasaki, Kazunari; Inutsuka, Shu-ichiro

    2013-09-01

    In this paper, we present an explicit scheme for Ohmic dissipation with smoothed particle magnetohydrodynamics (SPMHD). We propose an SPH discretization of Ohmic dissipation and solve Ohmic dissipation part of induction equation with the super-time-stepping method (STS) which allows us to take a longer time step than Courant-Friedrich-Levy stability condition. Our scheme is second-order accurate in space and first-order accurate in time. Our numerical experiments show that optimal choice of the parameters of STS for Ohmic dissipation of SPMHD is νsts ˜ 0.01 and Nsts ˜ 5.

  12. A pyramid scheme for three-dimensional diffusion equations on polyhedral meshes

    NASA Astrophysics Data System (ADS)

    Wang, Shuai; Hang, Xudeng; Yuan, Guangwei

    2017-12-01

    In this paper, a new cell-centered finite volume scheme is proposed for three-dimensional diffusion equations on polyhedral meshes, which is called as pyramid scheme (P-scheme). The scheme is designed for polyhedral cells with nonplanar cell-faces. The normal flux on a nonplanar cell-face is discretized on a planar face, which is determined by a simple optimization procedure. The resulted discrete form of the normal flux involves only cell-centered and cell-vertex unknowns, and is free from face-centered unknowns. In the case of hexahedral meshes with skewed nonplanar cell-faces, a quite simple expression is obtained for the discrete normal flux. Compared with the second order accurate O-scheme [31], the P-scheme is more robust and the discretization cost is reduced remarkably. Numerical results are presented to show the performance of the P-scheme on various kinds of distorted meshes. In particular, the P-scheme is shown to be second order accurate.

  13. Implicit time accurate simulation of unsteady flow

    NASA Astrophysics Data System (ADS)

    van Buuren, René; Kuerten, Hans; Geurts, Bernard J.

    2001-03-01

    Implicit time integration was studied in the context of unsteady shock-boundary layer interaction flow. With an explicit second-order Runge-Kutta scheme, a reference solution to compare with the implicit second-order Crank-Nicolson scheme was determined. The time step in the explicit scheme is restricted by both temporal accuracy as well as stability requirements, whereas in the A-stable implicit scheme, the time step has to obey temporal resolution requirements and numerical convergence conditions. The non-linear discrete equations for each time step are solved iteratively by adding a pseudo-time derivative. The quasi-Newton approach is adopted and the linear systems that arise are approximately solved with a symmetric block Gauss-Seidel solver. As a guiding principle for properly setting numerical time integration parameters that yield an efficient time accurate capturing of the solution, the global error caused by the temporal integration is compared with the error resulting from the spatial discretization. Focus is on the sensitivity of properties of the solution in relation to the time step. Numerical simulations show that the time step needed for acceptable accuracy can be considerably larger than the explicit stability time step; typical ratios range from 20 to 80. At large time steps, convergence problems that are closely related to a highly complex structure of the basins of attraction of the iterative method may occur. Copyright

  14. Multiplicative noise removal through fractional order tv-based model and fast numerical schemes for its approximation

    NASA Astrophysics Data System (ADS)

    Ullah, Asmat; Chen, Wen; Khan, Mushtaq Ahmad

    2017-07-01

    This paper introduces a fractional order total variation (FOTV) based model with three different weights in the fractional order derivative definition for multiplicative noise removal purpose. The fractional-order Euler Lagrange equation which is a highly non-linear partial differential equation (PDE) is obtained by the minimization of the energy functional for image restoration. Two numerical schemes namely an iterative scheme based on the dual theory and majorization- minimization algorithm (MMA) are used. To improve the restoration results, we opt for an adaptive parameter selection procedure for the proposed model by applying the trial and error method. We report numerical simulations which show the validity and state of the art performance of the fractional-order model in visual improvement as well as an increase in the peak signal to noise ratio comparing to corresponding methods. Numerical experiments also demonstrate that MMAbased methodology is slightly better than that of an iterative scheme.

  15. Application of high-order numerical schemes and Newton-Krylov method to two-phase drift-flux model

    DOE Office of Scientific and Technical Information (OSTI.GOV)

    Zou, Ling; Zhao, Haihua; Zhang, Hongbin

    This study concerns the application and solver robustness of the Newton-Krylov method in solving two-phase flow drift-flux model problems using high-order numerical schemes. In our previous studies, the Newton-Krylov method has been proven as a promising solver for two-phase flow drift-flux model problems. However, these studies were limited to use first-order numerical schemes only. Moreover, the previous approach to treating the drift-flux closure correlations was later revealed to cause deteriorated solver convergence performance, when the mesh was highly refined, and also when higher-order numerical schemes were employed. In this study, a second-order spatial discretization scheme that has been tested withmore » two-fluid two-phase flow model was extended to solve drift-flux model problems. In order to improve solver robustness, and therefore efficiency, a new approach was proposed to treating the mean drift velocity of the gas phase as a primary nonlinear variable to the equation system. With this new approach, significant improvement in solver robustness was achieved. With highly refined mesh, the proposed treatment along with the Newton-Krylov solver were extensively tested with two-phase flow problems that cover a wide range of thermal-hydraulics conditions. Satisfactory convergence performances were observed for all test cases. Numerical verification was then performed in the form of mesh convergence studies, from which expected orders of accuracy were obtained for both the first-order and the second-order spatial discretization schemes. Finally, the drift-flux model, along with numerical methods presented, were validated with three sets of flow boiling experiments that cover different flow channel geometries (round tube, rectangular tube, and rod bundle), and a wide range of test conditions (pressure, mass flux, wall heat flux, inlet subcooling and outlet void fraction).« less

  16. Application of high-order numerical schemes and Newton-Krylov method to two-phase drift-flux model

    DOE PAGES

    Zou, Ling; Zhao, Haihua; Zhang, Hongbin

    2017-08-07

    This study concerns the application and solver robustness of the Newton-Krylov method in solving two-phase flow drift-flux model problems using high-order numerical schemes. In our previous studies, the Newton-Krylov method has been proven as a promising solver for two-phase flow drift-flux model problems. However, these studies were limited to use first-order numerical schemes only. Moreover, the previous approach to treating the drift-flux closure correlations was later revealed to cause deteriorated solver convergence performance, when the mesh was highly refined, and also when higher-order numerical schemes were employed. In this study, a second-order spatial discretization scheme that has been tested withmore » two-fluid two-phase flow model was extended to solve drift-flux model problems. In order to improve solver robustness, and therefore efficiency, a new approach was proposed to treating the mean drift velocity of the gas phase as a primary nonlinear variable to the equation system. With this new approach, significant improvement in solver robustness was achieved. With highly refined mesh, the proposed treatment along with the Newton-Krylov solver were extensively tested with two-phase flow problems that cover a wide range of thermal-hydraulics conditions. Satisfactory convergence performances were observed for all test cases. Numerical verification was then performed in the form of mesh convergence studies, from which expected orders of accuracy were obtained for both the first-order and the second-order spatial discretization schemes. Finally, the drift-flux model, along with numerical methods presented, were validated with three sets of flow boiling experiments that cover different flow channel geometries (round tube, rectangular tube, and rod bundle), and a wide range of test conditions (pressure, mass flux, wall heat flux, inlet subcooling and outlet void fraction).« less

  17. An unstaggered central scheme on nonuniform grids for the simulation of a compressible two-phase flow model

    DOE Office of Scientific and Technical Information (OSTI.GOV)

    Touma, Rony; Zeidan, Dia

    In this paper we extend a central finite volume method on nonuniform grids to the case of drift-flux two-phase flow problems. The numerical base scheme is an unstaggered, non oscillatory, second-order accurate finite volume scheme that evolves a piecewise linear numerical solution on a single grid and uses dual cells intermediately while updating the numerical solution to avoid the resolution of the Riemann problems arising at the cell interfaces. We then apply the numerical scheme and solve a classical drift-flux problem. The obtained results are in good agreement with corresponding ones appearing in the recent literature, thus confirming the potentialmore » of the proposed scheme.« less

  18. Accurate complex scaling of three dimensional numerical potentials

    DOE Office of Scientific and Technical Information (OSTI.GOV)

    Cerioni, Alessandro; Genovese, Luigi; Duchemin, Ivan

    2013-05-28

    The complex scaling method, which consists in continuing spatial coordinates into the complex plane, is a well-established method that allows to compute resonant eigenfunctions of the time-independent Schroedinger operator. Whenever it is desirable to apply the complex scaling to investigate resonances in physical systems defined on numerical discrete grids, the most direct approach relies on the application of a similarity transformation to the original, unscaled Hamiltonian. We show that such an approach can be conveniently implemented in the Daubechies wavelet basis set, featuring a very promising level of generality, high accuracy, and no need for artificial convergence parameters. Complex scalingmore » of three dimensional numerical potentials can be efficiently and accurately performed. By carrying out an illustrative resonant state computation in the case of a one-dimensional model potential, we then show that our wavelet-based approach may disclose new exciting opportunities in the field of computational non-Hermitian quantum mechanics.« less

  19. Ancient numerical daemons of conceptual hydrological modeling: 2. Impact of time stepping schemes on model analysis and prediction

    NASA Astrophysics Data System (ADS)

    Kavetski, Dmitri; Clark, Martyn P.

    2010-10-01

    Despite the widespread use of conceptual hydrological models in environmental research and operations, they remain frequently implemented using numerically unreliable methods. This paper considers the impact of the time stepping scheme on model analysis (sensitivity analysis, parameter optimization, and Markov chain Monte Carlo-based uncertainty estimation) and prediction. It builds on the companion paper (Clark and Kavetski, 2010), which focused on numerical accuracy, fidelity, and computational efficiency. Empirical and theoretical analysis of eight distinct time stepping schemes for six different hydrological models in 13 diverse basins demonstrates several critical conclusions. (1) Unreliable time stepping schemes, in particular, fixed-step explicit methods, suffer from troublesome numerical artifacts that severely deform the objective function of the model. These deformations are not rare isolated instances but can arise in any model structure, in any catchment, and under common hydroclimatic conditions. (2) Sensitivity analysis can be severely contaminated by numerical errors, often to the extent that it becomes dominated by the sensitivity of truncation errors rather than the model equations. (3) Robust time stepping schemes generally produce "better behaved" objective functions, free of spurious local optima, and with sufficient numerical continuity to permit parameter optimization using efficient quasi Newton methods. When implemented within a multistart framework, modern Newton-type optimizers are robust even when started far from the optima and provide valuable diagnostic insights not directly available from evolutionary global optimizers. (4) Unreliable time stepping schemes lead to inconsistent and biased inferences of the model parameters and internal states. (5) Even when interactions between hydrological parameters and numerical errors provide "the right result for the wrong reason" and the calibrated model performance appears adequate, unreliable

  20. Total Variation Diminishing (TVD) schemes of uniform accuracy

    NASA Technical Reports Server (NTRS)

    Hartwich, PETER-M.; Hsu, Chung-Hao; Liu, C. H.

    1988-01-01

    Explicit second-order accurate finite-difference schemes for the approximation of hyperbolic conservation laws are presented. These schemes are nonlinear even for the constant coefficient case. They are based on first-order upwind schemes. Their accuracy is enhanced by locally replacing the first-order one-sided differences with either second-order one-sided differences or central differences or a blend thereof. The appropriate local difference stencils are selected such that they give TVD schemes of uniform second-order accuracy in the scalar, or linear systems, case. Like conventional TVD schemes, the new schemes avoid a Gibbs phenomenon at discontinuities of the solution, but they do not switch back to first-order accuracy, in the sense of truncation error, at extrema of the solution. The performance of the new schemes is demonstrated in several numerical tests.

  1. Interface- and discontinuity-aware numerical schemes for plasma 3-T radiation diffusion in two and three dimensions

    DOE Office of Scientific and Technical Information (OSTI.GOV)

    Dai, William W., E-mail: dai@lanl.gov; Scannapieco, Anthony J.

    2015-11-01

    A set of numerical schemes is developed for two- and three-dimensional time-dependent 3-T radiation diffusion equations in systems involving multi-materials. To resolve sub-cell structure, interface reconstruction is implemented within any cell that has more than one material. Therefore, the system of 3-T radiation diffusion equations is solved on two- and three-dimensional polyhedral meshes. The focus of the development is on the fully coupling between radiation and material, the treatment of nonlinearity in the equations, i.e., in the diffusion terms and source terms, treatment of the discontinuity across cell interfaces in material properties, the formulations for both transient and steady states,more » the property for large time steps, and second order accuracy in both space and time. The discontinuity of material properties between different materials is correctly treated based on the governing physics principle for general polyhedral meshes and full nonlinearity. The treatment is exact for arbitrarily strong discontinuity. The scheme is fully nonlinear for the full nonlinearity in the 3-T diffusion equations. Three temperatures are fully coupled and are updated simultaneously. The scheme is general in two and three dimensions on general polyhedral meshes. The features of the scheme are demonstrated through numerical examples for transient problems and steady states. The effects of some simplifications of numerical schemes are also shown through numerical examples, such as linearization, simple average of diffusion coefficient, and approximate treatment for the coupling between radiation and material.« less

  2. From stochastic processes to numerical methods: A new scheme for solving reaction subdiffusion fractional partial differential equations

    DOE Office of Scientific and Technical Information (OSTI.GOV)

    Angstmann, C.N.; Donnelly, I.C.; Henry, B.I., E-mail: B.Henry@unsw.edu.au

    We have introduced a new explicit numerical method, based on a discrete stochastic process, for solving a class of fractional partial differential equations that model reaction subdiffusion. The scheme is derived from the master equations for the evolution of the probability density of a sum of discrete time random walks. We show that the diffusion limit of the master equations recovers the fractional partial differential equation of interest. This limiting procedure guarantees the consistency of the numerical scheme. The positivity of the solution and stability results are simply obtained, provided that the underlying process is well posed. We also showmore » that the method can be applied to standard reaction–diffusion equations. This work highlights the broader applicability of using discrete stochastic processes to provide numerical schemes for partial differential equations, including fractional partial differential equations.« less

  3. Comparison of Several Numerical Methods for Simulation of Compressible Shear Layers

    NASA Technical Reports Server (NTRS)

    Kennedy, Christopher A.; Carpenter, Mark H.

    1997-01-01

    An investigation is conducted on several numerical schemes for use in the computation of two-dimensional, spatially evolving, laminar variable-density compressible shear layers. Schemes with various temporal accuracies and arbitrary spatial accuracy for both inviscid and viscous terms are presented and analyzed. All integration schemes use explicit or compact finite-difference derivative operators. Three classes of schemes are considered: an extension of MacCormack's original second-order temporally accurate method, a new third-order variant of the schemes proposed by Rusanov and by Kutier, Lomax, and Warming (RKLW), and third- and fourth-order Runge-Kutta schemes. In each scheme, stability and formal accuracy are considered for the interior operators on the convection-diffusion equation U(sub t) + aU(sub x) = alpha U(sub xx). Accuracy is also verified on the nonlinear problem, U(sub t) + F(sub x) = 0. Numerical treatments of various orders of accuracy are chosen and evaluated for asymptotic stability. Formally accurate boundary conditions are derived for several sixth- and eighth-order central-difference schemes. Damping of high wave-number data is accomplished with explicit filters of arbitrary order. Several schemes are used to compute variable-density compressible shear layers, where regions of large gradients exist.

  4. The upwind control volume scheme for unstructured triangular grids

    NASA Technical Reports Server (NTRS)

    Giles, Michael; Anderson, W. Kyle; Roberts, Thomas W.

    1989-01-01

    A new algorithm for the numerical solution of the Euler equations is presented. This algorithm is particularly suited to the use of unstructured triangular meshes, allowing geometric flexibility. Solutions are second-order accurate in the steady state. Implementation of the algorithm requires minimal grid connectivity information, resulting in modest storage requirements, and should enhance the implementation of the scheme on massively parallel computers. A novel form of upwind differencing is developed, and is shown to yield sharp resolution of shocks. Two new artificial viscosity models are introduced that enhance the performance of the new scheme. Numerical results for transonic airfoil flows are presented, which demonstrate the performance of the algorithm.

  5. Accurate Critical Stress Intensity Factor Griffith Crack Theory Measurements by Numerical Techniques

    PubMed Central

    Petersen, Richard C.

    2014-01-01

    Critical stress intensity factor (KIc) has been an approximation for fracture toughness using only load-cell measurements. However, artificial man-made cracks several orders of magnitude longer and wider than natural flaws have required a correction factor term (Y) that can be up to about 3 times the recorded experimental value [1-3]. In fact, over 30 years ago a National Academy of Sciences advisory board stated that empirical KIc testing was of serious concern and further requested that an accurate bulk fracture toughness method be found [4]. Now that fracture toughness can be calculated accurately by numerical integration from the load/deflection curve as resilience, work of fracture (WOF) and strain energy release (SIc) [5, 6], KIc appears to be unnecessary. However, the large body of previous KIc experimental test results found in the literature offer the opportunity for continued meta analysis with other more practical and accurate fracture toughness results using energy methods and numerical integration. Therefore, KIc is derived from the classical Griffith Crack Theory [6] to include SIc as a more accurate term for strain energy release rate (𝒢Ic), along with crack surface energy (γ), crack length (a), modulus (E), applied stress (σ), Y, crack-tip plastic zone defect region (rp) and yield strength (σys) that can all be determined from load and deflection data. Polymer matrix discontinuous quartz fiber-reinforced composites to accentuate toughness differences were prepared for flexural mechanical testing comprising of 3 mm fibers at different volume percentages from 0-54.0 vol% and at 28.2 vol% with different fiber lengths from 0.0-6.0 mm. Results provided a new correction factor and regression analyses between several numerical integration fracture toughness test methods to support KIc results. Further, bulk KIc accurate experimental values are compared with empirical test results found in literature. Also, several fracture toughness mechanisms

  6. Time-Accurate Solutions of Incompressible Navier-Stokes Equations for Potential Turbopump Applications

    NASA Technical Reports Server (NTRS)

    Kiris, Cetin; Kwak, Dochan

    2001-01-01

    Two numerical procedures, one based on artificial compressibility method and the other pressure projection method, are outlined for obtaining time-accurate solutions of the incompressible Navier-Stokes equations. The performance of the two method are compared by obtaining unsteady solutions for the evolution of twin vortices behind a at plate. Calculated results are compared with experimental and other numerical results. For an un- steady ow which requires small physical time step, pressure projection method was found to be computationally efficient since it does not require any subiterations procedure. It was observed that the artificial compressibility method requires a fast convergence scheme at each physical time step in order to satisfy incompressibility condition. This was obtained by using a GMRES-ILU(0) solver in our computations. When a line-relaxation scheme was used, the time accuracy was degraded and time-accurate computations became very expensive.

  7. AN ACCURATE AND EFFICIENT ALGORITHM FOR NUMERICAL SIMULATION OF CONDUCTION-TYPE PROBLEMS. (R824801)

    EPA Science Inventory

    Abstract

    A modification of the finite analytic numerical method for conduction-type (diffusion) problems is presented. The finite analytic discretization scheme is derived by means of the Fourier series expansion for the most general case of nonuniform grid and variabl...

  8. Analysis and design of numerical schemes for gas dynamics. 2: Artificial diffusion and discrete shock structure

    NASA Technical Reports Server (NTRS)

    Jameson, Antony

    1994-01-01

    The effect of artificial diffusion on discrete shock structures is examined for a family of schemes which includes scalar diffusion, convective upwind and split pressure (CUSP) schemes, and upwind schemes with characteristics splitting. The analysis leads to conditions on the diffusive flux such that stationary discrete shocks can contain a single interior point. The simplest formulation which meets these conditions is a CUSP scheme in which the coefficients of the pressure differences is fully determined by the coefficient of convective diffusion. It is also shown how both the characteristic and CUSP schemes can be modified to preserve constant stagnation enthalpy in steady flow, leading to four variants, the E and H-characteristic schemes, and the E and H-CUSP schemes. Numerical results are presented which confirm the properties of these schemes.

  9. The alpha(3) Scheme - A Fourth-Order Neutrally Stable CESE Solver

    NASA Technical Reports Server (NTRS)

    Chang, Sin-Chung

    2007-01-01

    The conservation element and solution element (CESE) development is driven by a belief that a solver should (i) enforce conservation laws in both space and time, and (ii) be built from a non-dissipative (i.e., neutrally stable) core scheme so that the numerical dissipation can be controlled effectively. To provide a solid foundation for a systematic CESE development of high order schemes, in this paper we describe a new 4th-order neutrally stable CESE solver of the advection equation Theta u/Theta + alpha Theta u/Theta x = 0. The space-time stencil of this two-level explicit scheme is formed by one point at the upper time level and three points at the lower time level. Because it is associated with three independent mesh variables u(sup n) (sub j), (u(sub x))(sup n) (sub j) , and (uxz)(sup n) (sub j) (the numerical analogues of u, Theta u/Theta x, and Theta(exp 2)u/Theta x(exp 2), respectively) and four equations per mesh point, the new scheme is referred to as the alpha(3) scheme. As in the case of other similar CESE neutrally stable solvers, the alpha(3) scheme enforces conservation laws in space-time locally and globally, and it has the basic, forward marching, and backward marching forms. These forms are equivalent and satisfy a space-time inversion (STI) invariant property which is shared by the advection equation. Based on the concept of STI invariance, a set of algebraic relations is developed and used to prove that the alpha(3) scheme must be neutrally stable when it is stable. Moreover it is proved rigorously that all three amplification factors of the alpha(3) scheme are of unit magnitude for all phase angles if |v| <= 1/2 (v = alpha delta t/delta x). This theoretical result is consistent with the numerical stability condition |v| <= 1/2. Through numerical experiments, it is established that the alpha(3) scheme generally is (i) 4th-order accurate for the mesh variables u(sup n) (sub j) and (ux)(sup n) (sub j); and 2nd-order accurate for (uxx)(sup n) (sub

  10. Numerical integration for ab initio many-electron self energy calculations within the GW approximation

    DOE Office of Scientific and Technical Information (OSTI.GOV)

    Liu, Fang, E-mail: fliu@lsec.cc.ac.cn; Lin, Lin, E-mail: linlin@math.berkeley.edu; Computational Research Division, Lawrence Berkeley National Laboratory, Berkeley, CA 94720

    We present a numerical integration scheme for evaluating the convolution of a Green's function with a screened Coulomb potential on the real axis in the GW approximation of the self energy. Our scheme takes the zero broadening limit in Green's function first, replaces the numerator of the integrand with a piecewise polynomial approximation, and performs principal value integration on subintervals analytically. We give the error bound of our numerical integration scheme and show by numerical examples that it is more reliable and accurate than the standard quadrature rules such as the composite trapezoidal rule. We also discuss the benefit ofmore » using different self energy expressions to perform the numerical convolution at different frequencies.« less

  11. Can numerical simulations accurately predict hydrodynamic instabilities in liquid films?

    NASA Astrophysics Data System (ADS)

    Denner, Fabian; Charogiannis, Alexandros; Pradas, Marc; van Wachem, Berend G. M.; Markides, Christos N.; Kalliadasis, Serafim

    2014-11-01

    Understanding the dynamics of hydrodynamic instabilities in liquid film flows is an active field of research in fluid dynamics and non-linear science in general. Numerical simulations offer a powerful tool to study hydrodynamic instabilities in film flows and can provide deep insights into the underlying physical phenomena. However, the direct comparison of numerical results and experimental results is often hampered by several reasons. For instance, in numerical simulations the interface representation is problematic and the governing equations and boundary conditions may be oversimplified, whereas in experiments it is often difficult to extract accurate information on the fluid and its behavior, e.g. determine the fluid properties when the liquid contains particles for PIV measurements. In this contribution we present the latest results of our on-going, extensive study on hydrodynamic instabilities in liquid film flows, which includes direct numerical simulations, low-dimensional modelling as well as experiments. The major focus is on wave regimes, wave height and wave celerity as a function of Reynolds number and forcing frequency of a falling liquid film. Specific attention is paid to the differences in numerical and experimental results and the reasons for these differences. The authors are grateful to the EPSRC for their financial support (Grant EP/K008595/1).

  12. Multi-Dimensional Asymptotically Stable 4th Order Accurate Schemes for the Diffusion Equation

    NASA Technical Reports Server (NTRS)

    Abarbanel, Saul; Ditkowski, Adi

    1996-01-01

    An algorithm is presented which solves the multi-dimensional diffusion equation on co mplex shapes to 4th-order accuracy and is asymptotically stable in time. This bounded-error result is achieved by constructing, on a rectangular grid, a differentiation matrix whose symmetric part is negative definite. The differentiation matrix accounts for the Dirichlet boundary condition by imposing penalty like terms. Numerical examples in 2-D show that the method is effective even where standard schemes, stable by traditional definitions fail.

  13. Some results on numerical methods for hyperbolic conservation laws

    DOE Office of Scientific and Technical Information (OSTI.GOV)

    Yang Huanan.

    1989-01-01

    This dissertation contains some results on the numerical solutions of hyperbolic conservation laws. (1) The author introduced an artificial compression method as a correction to the basic ENO schemes. The method successfully prevents contact discontinuities from being smeared. This is achieved by increasing the slopes of the ENO reconstructions in such a way that the essentially non-oscillatory property of the schemes is kept. He analyzes the non-oscillatory property of the new artificial compression method by applying it to the UNO scheme which is a second order accurate ENO scheme, and proves that the resulting scheme is indeed non-oscillatory. Extensive 1-Dmore » numerical results and some preliminary 2-D ones are provided to show the strong performance of the method. (2) He combines the ENO schemes and the centered difference schemes into self-adjusting hybrid schemes which will be called the localized ENO schemes. At or near the jumps, he uses the ENO schemes with the field by field decompositions, otherwise he simply uses the centered difference schemes without the field by field decompositions. The method involves a new interpolation analysis. In the numerical experiments on several standard test problems, the quality of the numerical results of this method is close to that of the pure ENO results. The localized ENO schemes can be equipped with the above artificial compression method. In this way, he dramatically improves the resolutions of the contact discontinuities at very little additional costs. (3) He introduces a space-time mesh refinement method for time dependent problems.« less

  14. An explicit mixed numerical method for mesoscale model

    NASA Technical Reports Server (NTRS)

    Hsu, H.-M.

    1981-01-01

    A mixed numerical method has been developed for mesoscale models. The technique consists of a forward difference scheme for time tendency terms, an upstream scheme for advective terms, and a central scheme for the other terms in a physical system. It is shown that the mixed method is conditionally stable and highly accurate for approximating the system of either shallow-water equations in one dimension or primitive equations in three dimensions. Since the technique is explicit and two time level, it conserves computer and programming resources.

  15. Development of highly accurate approximate scheme for computing the charge transfer integral

    DOE Office of Scientific and Technical Information (OSTI.GOV)

    Pershin, Anton; Szalay, Péter G.

    The charge transfer integral is a key parameter required by various theoretical models to describe charge transport properties, e.g., in organic semiconductors. The accuracy of this important property depends on several factors, which include the level of electronic structure theory and internal simplifications of the applied formalism. The goal of this paper is to identify the performance of various approximate approaches of the latter category, while using the high level equation-of-motion coupled cluster theory for the electronic structure. The calculations have been performed on the ethylene dimer as one of the simplest model systems. By studying different spatial perturbations, itmore » was shown that while both energy split in dimer and fragment charge difference methods are equivalent with the exact formulation for symmetrical displacements, they are less efficient when describing transfer integral along the asymmetric alteration coordinate. Since the “exact” scheme was found computationally expensive, we examine the possibility to obtain the asymmetric fluctuation of the transfer integral by a Taylor expansion along the coordinate space. By exploring the efficiency of this novel approach, we show that the Taylor expansion scheme represents an attractive alternative to the “exact” calculations due to a substantial reduction of computational costs, when a considerably large region of the potential energy surface is of interest. Moreover, we show that the Taylor expansion scheme, irrespective of the dimer symmetry, is very accurate for the entire range of geometry fluctuations that cover the space the molecule accesses at room temperature.« less

  16. Uniformly high-order accurate non-oscillatory schemes, 1

    NASA Technical Reports Server (NTRS)

    Harten, A.; Osher, S.

    1985-01-01

    The construction and the analysis of nonoscillatory shock capturing methods for the approximation of hyperbolic conservation laws was begun. These schemes share many desirable properties with total variation diminishing schemes (TVD), but TVD schemes have at most first order accuracy, in the sense of truncation error, at extreme of the solution. A uniformly second order approximation was constucted, which is nonoscillatory in the sense that the number of extrema of the discrete solution is not increasing in time. This is achieved via a nonoscillatory piecewise linear reconstruction of the solution from its cell averages, time evolution through an approximate solution of the resulting initial value problem, and averaging of this approximate solution over each cell.

  17. Trajectory errors of different numerical integration schemes diagnosed with the MPTRAC advection module driven by ECMWF operational analyses

    NASA Astrophysics Data System (ADS)

    Rößler, Thomas; Stein, Olaf; Heng, Yi; Baumeister, Paul; Hoffmann, Lars

    2018-02-01

    The accuracy of trajectory calculations performed by Lagrangian particle dispersion models (LPDMs) depends on various factors. The optimization of numerical integration schemes used to solve the trajectory equation helps to maximize the computational efficiency of large-scale LPDM simulations. We analyzed global truncation errors of six explicit integration schemes of the Runge-Kutta family, which we implemented in the Massive-Parallel Trajectory Calculations (MPTRAC) advection module. The simulations were driven by wind fields from operational analysis and forecasts of the European Centre for Medium-Range Weather Forecasts (ECMWF) at T1279L137 spatial resolution and 3 h temporal sampling. We defined separate test cases for 15 distinct regions of the atmosphere, covering the polar regions, the midlatitudes, and the tropics in the free troposphere, in the upper troposphere and lower stratosphere (UT/LS) region, and in the middle stratosphere. In total, more than 5000 different transport simulations were performed, covering the months of January, April, July, and October for the years 2014 and 2015. We quantified the accuracy of the trajectories by calculating transport deviations with respect to reference simulations using a fourth-order Runge-Kutta integration scheme with a sufficiently fine time step. Transport deviations were assessed with respect to error limits based on turbulent diffusion. Independent of the numerical scheme, the global truncation errors vary significantly between the different regions. Horizontal transport deviations in the stratosphere are typically an order of magnitude smaller compared with the free troposphere. We found that the truncation errors of the six numerical schemes fall into three distinct groups, which mostly depend on the numerical order of the scheme. Schemes of the same order differ little in accuracy, but some methods need less computational time, which gives them an advantage in efficiency. The selection of the integration

  18. Numerical applications of the advective-diffusive codes for the inner magnetosphere

    NASA Astrophysics Data System (ADS)

    Aseev, N. A.; Shprits, Y. Y.; Drozdov, A. Y.; Kellerman, A. C.

    2016-11-01

    In this study we present analytical solutions for convection and diffusion equations. We gather here the analytical solutions for the one-dimensional convection equation, the two-dimensional convection problem, and the one- and two-dimensional diffusion equations. Using obtained analytical solutions, we test the four-dimensional Versatile Electron Radiation Belt code (the VERB-4D code), which solves the modified Fokker-Planck equation with additional convection terms. The ninth-order upwind numerical scheme for the one-dimensional convection equation shows much more accurate results than the results obtained with the third-order scheme. The universal limiter eliminates unphysical oscillations generated by high-order linear upwind schemes. Decrease in the space step leads to convergence of a numerical solution of the two-dimensional diffusion equation with mixed terms to the analytical solution. We compare the results of the third- and ninth-order schemes applied to magnetospheric convection modeling. The results show significant differences in electron fluxes near geostationary orbit when different numerical schemes are used.

  19. Numerical viscosity and resolution of high-order weighted essentially nonoscillatory schemes for compressible flows with high Reynolds numbers.

    PubMed

    Zhang, Yong-Tao; Shi, Jing; Shu, Chi-Wang; Zhou, Ye

    2003-10-01

    A quantitative study is carried out in this paper to investigate the size of numerical viscosities and the resolution power of high-order weighted essentially nonoscillatory (WENO) schemes for solving one- and two-dimensional Navier-Stokes equations for compressible gas dynamics with high Reynolds numbers. A one-dimensional shock tube problem, a one-dimensional example with parameters motivated by supernova and laser experiments, and a two-dimensional Rayleigh-Taylor instability problem are used as numerical test problems. For the two-dimensional Rayleigh-Taylor instability problem, or similar problems with small-scale structures, the details of the small structures are determined by the physical viscosity (therefore, the Reynolds number) in the Navier-Stokes equations. Thus, to obtain faithful resolution to these small-scale structures, the numerical viscosity inherent in the scheme must be small enough so that the physical viscosity dominates. A careful mesh refinement study is performed to capture the threshold mesh for full resolution, for specific Reynolds numbers, when WENO schemes of different orders of accuracy are used. It is demonstrated that high-order WENO schemes are more CPU time efficient to reach the same resolution, both for the one-dimensional and two-dimensional test problems.

  20. The construction of high-accuracy schemes for acoustic equations

    NASA Technical Reports Server (NTRS)

    Tang, Lei; Baeder, James D.

    1995-01-01

    An accuracy analysis of various high order schemes is performed from an interpolation point of view. The analysis indicates that classical high order finite difference schemes, which use polynomial interpolation, hold high accuracy only at nodes and are therefore not suitable for time-dependent problems. Thus, some schemes improve their numerical accuracy within grid cells by the near-minimax approximation method, but their practical significance is degraded by maintaining the same stencil as classical schemes. One-step methods in space discretization, which use piecewise polynomial interpolation and involve data at only two points, can generate a uniform accuracy over the whole grid cell and avoid spurious roots. As a result, they are more accurate and efficient than multistep methods. In particular, the Cubic-Interpolated Psuedoparticle (CIP) scheme is recommended for computational acoustics.

  1. Wavenumber-extended high-order oscillation control finite volume schemes for multi-dimensional aeroacoustic computations

    NASA Astrophysics Data System (ADS)

    Kim, Sungtae; Lee, Soogab; Kim, Kyu Hong

    2008-04-01

    A new numerical method toward accurate and efficient aeroacoustic computations of multi-dimensional compressible flows has been developed. The core idea of the developed scheme is to unite the advantages of the wavenumber-extended optimized scheme and M-AUSMPW+/MLP schemes by predicting a physical distribution of flow variables more accurately in multi-space dimensions. The wavenumber-extended optimization procedure for the finite volume approach based on the conservative requirement is newly proposed for accuracy enhancement, which is required to capture the acoustic portion of the solution in the smooth region. Furthermore, the new distinguishing mechanism which is based on the Gibbs phenomenon in discontinuity, between continuous and discontinuous regions is introduced to eliminate the excessive numerical dissipation in the continuous region by the restricted application of MLP according to the decision of the distinguishing function. To investigate the effectiveness of the developed method, a sequence of benchmark simulations such as spherical wave propagation, nonlinear wave propagation, shock tube problem and vortex preservation test problem are executed. Also, throughout more realistic shock-vortex interaction and muzzle blast flow problems, the utility of the new method for aeroacoustic applications is verified by comparing with the previous numerical or experimental results.

  2. A New Numerical Scheme for Cosmic-Ray Transport

    NASA Astrophysics Data System (ADS)

    Jiang, Yan-Fei; Oh, S. Peng

    2018-02-01

    Numerical solutions of the cosmic-ray (CR) magnetohydrodynamic equations are dogged by a powerful numerical instability, which arises from the constraint that CRs can only stream down their gradient. The standard cure is to regularize by adding artificial diffusion. Besides introducing ad hoc smoothing, this has a significant negative impact on either computational cost or complexity and parallel scalings. We describe a new numerical algorithm for CR transport, with close parallels to two-moment methods for radiative transfer under the reduced speed of light approximation. It stably and robustly handles CR streaming without any artificial diffusion. It allows for both isotropic and field-aligned CR streaming and diffusion, with arbitrary streaming and diffusion coefficients. CR transport is handled explicitly, while source terms are handled implicitly. The overall time step scales linearly with resolution (even when computing CR diffusion) and has a perfect parallel scaling. It is given by the standard Courant condition with respect to a constant maximum velocity over the entire simulation domain. The computational cost is comparable to that of solving the ideal MHD equation. We demonstrate the accuracy and stability of this new scheme with a wide variety of tests, including anisotropic streaming and diffusion tests, CR-modified shocks, CR-driven blast waves, and CR transport in multiphase media. The new algorithm opens doors to much more ambitious and hitherto intractable calculations of CR physics in galaxies and galaxy clusters. It can also be applied to other physical processes with similar mathematical structure, such as saturated, anisotropic heat conduction.

  3. Optimal scheme of star observation of missile-borne inertial navigation system/stellar refraction integrated navigation

    NASA Astrophysics Data System (ADS)

    Lu, Jiazhen; Yang, Lie

    2018-05-01

    To achieve accurate and completely autonomous navigation for spacecraft, inertial/celestial integrated navigation gets increasing attention. In this study, a missile-borne inertial/stellar refraction integrated navigation scheme is proposed. Position Dilution of Precision (PDOP) for stellar refraction is introduced and the corresponding equation is derived. Based on the condition when PDOP reaches the minimum value, an optimized observation scheme is proposed. To verify the feasibility of the proposed scheme, numerical simulation is conducted. The results of the Extended Kalman Filter (EKF) and Unscented Kalman Filter (UKF) are compared and impact factors of navigation accuracy are studied in the simulation. The simulation results indicated that the proposed observation scheme has an accurate positioning performance, and the results of EKF and UKF are similar.

  4. Optimal scheme of star observation of missile-borne inertial navigation system/stellar refraction integrated navigation.

    PubMed

    Lu, Jiazhen; Yang, Lie

    2018-05-01

    To achieve accurate and completely autonomous navigation for spacecraft, inertial/celestial integrated navigation gets increasing attention. In this study, a missile-borne inertial/stellar refraction integrated navigation scheme is proposed. Position Dilution of Precision (PDOP) for stellar refraction is introduced and the corresponding equation is derived. Based on the condition when PDOP reaches the minimum value, an optimized observation scheme is proposed. To verify the feasibility of the proposed scheme, numerical simulation is conducted. The results of the Extended Kalman Filter (EKF) and Unscented Kalman Filter (UKF) are compared and impact factors of navigation accuracy are studied in the simulation. The simulation results indicated that the proposed observation scheme has an accurate positioning performance, and the results of EKF and UKF are similar.

  5. Accurate thermoelastic tensor and acoustic velocities of NaCl

    DOE Office of Scientific and Technical Information (OSTI.GOV)

    Marcondes, Michel L., E-mail: michel@if.usp.br; Chemical Engineering and Material Science, University of Minnesota, Minneapolis, 55455; Shukla, Gaurav, E-mail: shukla@physics.umn.edu

    Despite the importance of thermoelastic properties of minerals in geology and geophysics, their measurement at high pressures and temperatures are still challenging. Thus, ab initio calculations are an essential tool for predicting these properties at extreme conditions. Owing to the approximate description of the exchange-correlation energy, approximations used in calculations of vibrational effects, and numerical/methodological approximations, these methods produce systematic deviations. Hybrid schemes combining experimental data and theoretical results have emerged as a way to reconcile available information and offer more reliable predictions at experimentally inaccessible thermodynamics conditions. Here we introduce a method to improve the calculated thermoelastic tensor bymore » using highly accurate thermal equation of state (EoS). The corrective scheme is general, applicable to crystalline solids with any symmetry, and can produce accurate results at conditions where experimental data may not exist. We apply it to rock-salt-type NaCl, a material whose structural properties have been challenging to describe accurately by standard ab initio methods and whose acoustic/seismic properties are important for the gas and oil industry.« less

  6. Multigrid solutions to quasi-elliptic schemes

    NASA Technical Reports Server (NTRS)

    Brandt, A.; Taasan, S.

    1985-01-01

    Quasi-elliptic schemes arise from central differencing or finite element discretization of elliptic systems with odd order derivatives on non-staggered grids. They are somewhat unstable and less accurate then corresponding staggered-grid schemes. When usual multigrid solvers are applied to them, the asymptotic algebraic convergence is necessarily slow. Nevertheless, it is shown by mode analyses and numerical experiments that the usual FMG algorithm is very efficient in solving quasi-elliptic equations to the level of truncation errors. Also, a new type of multigrid algorithm is presented, mode analyzed and tested, for which even the asymptotic algebraic convergence is fast. The essence of that algorithm is applicable to other kinds of problems, including highly indefinite ones.

  7. Multigrid solutions to quasi-elliptic schemes

    NASA Technical Reports Server (NTRS)

    Brandt, A.; Taasan, S.

    1985-01-01

    Quasi-elliptic schemes arise from central differencing or finite element discretization of elliptic systems with odd order derivatives on non-staggered grids. They are somewhat unstable and less accurate than corresponding staggered-grid schemes. When usual multigrid solvers are applied to them, the asymptotic algebraic convergence is necessarily slow. Nevertheless, it is shown by mode analyses and numerical experiments that the usual FMG algorithm is very efficient in solving quasi-elliptic equations to the level of truncation errors. Also, a new type of multigrid algorithm is presented, mode analyzed and tested, for which even the asymptotic algebraic convergence is fast. The essence of that algorithm is applicable to other kinds of problems, including highly indefinite ones.

  8. Overcoming numerical shockwave anomalies using energy balanced numerical schemes. Application to the Shallow Water Equations with discontinuous topography

    NASA Astrophysics Data System (ADS)

    Navas-Montilla, A.; Murillo, J.

    2017-07-01

    When designing a numerical scheme for the resolution of conservation laws, the selection of a particular source term discretization (STD) may seem irrelevant whenever it ensures convergence with mesh refinement, but it has a decisive impact on the solution. In the framework of the Shallow Water Equations (SWE), well-balanced STD based on quiescent equilibrium are unable to converge to physically based solutions, which can be constructed considering energy arguments. Energy based discretizations can be designed assuming dissipation or conservation, but in any case, the STD procedure required should not be merely based on ad hoc approximations. The STD proposed in this work is derived from the Generalized Hugoniot Locus obtained from the Generalized Rankine Hugoniot conditions and the Integral Curve across the contact wave associated to the bed step. In any case, the STD must allow energy-dissipative solutions: steady and unsteady hydraulic jumps, for which some numerical anomalies have been documented in the literature. These anomalies are the incorrect positioning of steady jumps and the presence of a spurious spike of discharge inside the cell containing the jump. The former issue can be addressed by proposing a modification of the energy-conservative STD that ensures a correct dissipation rate across the hydraulic jump, whereas the latter is of greater complexity and cannot be fixed by simply choosing a suitable STD, as there are more variables involved. The problem concerning the spike of discharge is a well-known problem in the scientific community, also known as slowly-moving shock anomaly, it is produced by a nonlinearity of the Hugoniot locus connecting the states at both sides of the jump. However, it seems that this issue is more a feature than a problem when considering steady solutions of the SWE containing hydraulic jumps. The presence of the spurious spike in the discharge has been taken for granted and has become a feature of the solution. Even though

  9. Improved numerical methods for turbulent viscous flows aerothermal modeling program, phase 2

    NASA Technical Reports Server (NTRS)

    Karki, K. C.; Patankar, S. V.; Runchal, A. K.; Mongia, H. C.

    1988-01-01

    The details of a study to develop accurate and efficient numerical schemes to predict complex flows are described. In this program, several discretization schemes were evaluated using simple test cases. This assessment led to the selection of three schemes for an in-depth evaluation based on two-dimensional flows. The scheme with the superior overall performance was incorporated in a computer program for three-dimensional flows. To improve the computational efficiency, the selected discretization scheme was combined with a direct solution approach in which the fluid flow equations are solved simultaneously rather than sequentially.

  10. A kinetic flux vector splitting scheme for shallow water equations incorporating variable bottom topography and horizontal temperature gradients.

    PubMed

    Saleem, M Rehan; Ashraf, Waqas; Zia, Saqib; Ali, Ishtiaq; Qamar, Shamsul

    2018-01-01

    This paper is concerned with the derivation of a well-balanced kinetic scheme to approximate a shallow flow model incorporating non-flat bottom topography and horizontal temperature gradients. The considered model equations, also called as Ripa system, are the non-homogeneous shallow water equations considering temperature gradients and non-uniform bottom topography. Due to the presence of temperature gradient terms, the steady state at rest is of primary interest from the physical point of view. However, capturing of this steady state is a challenging task for the applied numerical methods. The proposed well-balanced kinetic flux vector splitting (KFVS) scheme is non-oscillatory and second order accurate. The second order accuracy of the scheme is obtained by considering a MUSCL-type initial reconstruction and Runge-Kutta time stepping method. The scheme is applied to solve the model equations in one and two space dimensions. Several numerical case studies are carried out to validate the proposed numerical algorithm. The numerical results obtained are compared with those of staggered central NT scheme. The results obtained are also in good agreement with the recently published results in the literature, verifying the potential, efficiency, accuracy and robustness of the suggested numerical scheme.

  11. Improved numerical methods for turbulent viscous recirculating flows

    NASA Technical Reports Server (NTRS)

    Turan, A.

    1985-01-01

    The hybrid-upwind finite difference schemes employed in generally available combustor codes possess excessive numerical diffusion errors which preclude accurate quantative calculations. The present study has as its primary objective the identification and assessment of an improved solution algorithm as well as discretization schemes applicable to analysis of turbulent viscous recirculating flows. The assessment is carried out primarily in two dimensional/axisymetric geometries with a view to identifying an appropriate technique to be incorporated in a three-dimensional code.

  12. A numerical spectral approach to solve the dislocation density transport equation

    NASA Astrophysics Data System (ADS)

    Djaka, K. S.; Taupin, V.; Berbenni, S.; Fressengeas, C.

    2015-09-01

    A numerical spectral approach is developed to solve in a fast, stable and accurate fashion, the quasi-linear hyperbolic transport equation governing the spatio-temporal evolution of the dislocation density tensor in the mechanics of dislocation fields. The approach relies on using the Fast Fourier Transform algorithm. Low-pass spectral filters are employed to control both the high frequency Gibbs oscillations inherent to the Fourier method and the fast-growing numerical instabilities resulting from the hyperbolic nature of the transport equation. The numerical scheme is validated by comparison with an exact solution in the 1D case corresponding to dislocation dipole annihilation. The expansion and annihilation of dislocation loops in 2D and 3D settings are also produced and compared with finite element approximations. The spectral solutions are shown to be stable, more accurate for low Courant numbers and much less computation time-consuming than the finite element technique based on an explicit Galerkin-least squares scheme.

  13. Runge-Kutta methods combined with compact difference schemes for the unsteady Euler equations

    NASA Technical Reports Server (NTRS)

    Yu, Sheng-Tao

    1992-01-01

    Recent development using compact difference schemes to solve the Navier-Stokes equations show spectral-like accuracy. A study was made of the numerical characteristics of various combinations of the Runge-Kutta (RK) methods and compact difference schemes to calculate the unsteady Euler equations. The accuracy of finite difference schemes is assessed based on the evaluations of dissipative error. The objectives are reducing the numerical damping and, at the same time, preserving numerical stability. While this approach has tremendous success solving steady flows, numerical characteristics of unsteady calculations remain largely unclear. For unsteady flows, in addition to the dissipative errors, phase velocity and harmonic content of the numerical results are of concern. As a result of the discretization procedure, the simulated unsteady flow motions actually propagate in a dispersive numerical medium. Consequently, the dispersion characteristics of the numerical schemes which relate the phase velocity and wave number may greatly impact the numerical accuracy. The aim is to assess the numerical accuracy of the simulated results. To this end, the Fourier analysis is to provide the dispersive correlations of various numerical schemes. First, a detailed investigation of the existing RK methods is carried out. A generalized form of an N-step RK method is derived. With this generalized form, the criteria are derived for the three and four-step RK methods to be third and fourth-order time accurate for the non-linear equations, e.g., flow equations. These criteria are then applied to commonly used RK methods such as Jameson's 3-step and 4-step schemes and Wray's algorithm to identify the accuracy of the methods. For the spatial discretization, compact difference schemes are presented. The schemes are formulated in the operator-type to render themselves suitable for the Fourier analyses. The performance of the numerical methods is shown by numerical examples. These examples

  14. Entropy Splitting for High Order Numerical Simulation of Compressible Turbulence

    NASA Technical Reports Server (NTRS)

    Sandham, N. D.; Yee, H. C.; Kwak, Dochan (Technical Monitor)

    2000-01-01

    A stable high order numerical scheme for direct numerical simulation (DNS) of shock-free compressible turbulence is presented. The method is applicable to general geometries. It contains no upwinding, artificial dissipation, or filtering. Instead the method relies on the stabilizing mechanisms of an appropriate conditioning of the governing equations and the use of compatible spatial difference operators for the interior points (interior scheme) as well as the boundary points (boundary scheme). An entropy splitting approach splits the inviscid flux derivatives into conservative and non-conservative portions. The spatial difference operators satisfy a summation by parts condition leading to a stable scheme (combined interior and boundary schemes) for the initial boundary value problem using a generalized energy estimate. A Laplacian formulation of the viscous and heat conduction terms on the right hand side of the Navier-Stokes equations is used to ensure that any tendency to odd-even decoupling associated with central schemes can be countered by the fluid viscosity. A special formulation of the continuity equation is used, based on similar arguments. The resulting methods are able to minimize spurious high frequency oscillation producing nonlinear instability associated with pure central schemes, especially for long time integration simulation such as DNS. For validation purposes, the methods are tested in a DNS of compressible turbulent plane channel flow at a friction Mach number of 0.1 where a very accurate turbulence data base exists. It is demonstrated that the methods are robust in terms of grid resolution, and in good agreement with incompressible channel data, as expected at this Mach number. Accurate turbulence statistics can be obtained with moderate grid sizes. Stability limits on the range of the splitting parameter are determined from numerical tests.

  15. Multiple-correction hybrid k-exact schemes for high-order compressible RANS-LES simulations on fully unstructured grids

    NASA Astrophysics Data System (ADS)

    Pont, Grégoire; Brenner, Pierre; Cinnella, Paola; Maugars, Bruno; Robinet, Jean-Christophe

    2017-12-01

    A Godunov's type unstructured finite volume method suitable for highly compressible turbulent scale-resolving simulations around complex geometries is constructed by using a successive correction technique. First, a family of k-exact Godunov schemes is developed by recursively correcting the truncation error of the piecewise polynomial representation of the primitive variables. The keystone of the proposed approach is a quasi-Green gradient operator which ensures consistency on general meshes. In addition, a high-order single-point quadrature formula, based on high-order approximations of the successive derivatives of the solution, is developed for flux integration along cell faces. The proposed family of schemes is compact in the algorithmic sense, since it only involves communications between direct neighbors of the mesh cells. The numerical properties of the schemes up to fifth-order are investigated, with focus on their resolvability in terms of number of mesh points required to resolve a given wavelength accurately. Afterwards, in the aim of achieving the best possible trade-off between accuracy, computational cost and robustness in view of industrial flow computations, we focus more specifically on the third-order accurate scheme of the family, and modify locally its numerical flux in order to reduce the amount of numerical dissipation in vortex-dominated regions. This is achieved by switching from the upwind scheme, mostly applied in highly compressible regions, to a fourth-order centered one in vortex-dominated regions. An analytical switch function based on the local grid Reynolds number is adopted in order to warrant numerical stability of the recentering process. Numerical applications demonstrate the accuracy and robustness of the proposed methodology for compressible scale-resolving computations. In particular, supersonic RANS/LES computations of the flow over a cavity are presented to show the capability of the scheme to predict flows with shocks

  16. An unsteady Euler scheme for the analysis of ducted propellers

    NASA Technical Reports Server (NTRS)

    Srivastava, R.

    1992-01-01

    An efficient unsteady solution procedure has been developed for analyzing inviscid unsteady flow past ducted propeller configurations. This scheme is first order accurate in time and second order accurate in space. The solution procedure has been applied to a ducted propeller consisting of an 8-bladed SR7 propeller with a duct of NACA 0003 airfoil cross section around it, operating in a steady axisymmetric flowfield. The variation of elemental blade loading with radius, compares well with other published numerical results.

  17. A Numerical Scheme for the Solution of the Space Charge Problem on a Multiply Connected Region

    NASA Astrophysics Data System (ADS)

    Budd, C. J.; Wheeler, A. A.

    1991-11-01

    In this paper we extend the work of Budd and Wheeler ( Proc. R. Soc. London A, 417, 389, 1988) , who described a new numerical scheme for the solution of the space charge equation on a simple connected domain, to multiply connected regions. The space charge equation, ▿ · ( Δ overlineϕ ▽ overlineϕ) = 0 , is a third-order nonlinear partial differential equation for the electric potential overlineϕ which models the electric field in the vicinity of a coronating conductor. Budd and Wheeler described a new way of analysing this equation by constructing an orthogonal coordinate system ( overlineϕ, overlineψ) and recasting the equation in terms of x, y, and ▽ overlineϕ as functions of ( overlineϕ, overlineψ). This transformation is singular on multiply connected regions and in this paper we show how this may be overcome to provide an efficient numerical scheme for the solution of the space charge equation. This scheme also provides a new method for the solution of Laplaces equation and the calculation of orthogonal meshes on multiply connected regions.

  18. High-resolution schemes for hyperbolic conservation laws

    NASA Technical Reports Server (NTRS)

    Harten, A.

    1982-01-01

    A class of new explicit second order accurate finite difference schemes for the computation of weak solutions of hyperbolic conservation laws is presented. These highly nonlinear schemes are obtained by applying a nonoscillatory first order accurae scheme to an appropriately modified flux function. The so derived second order accurate schemes achieve high resolution while preserving the robustness of the original nonoscillatory first order accurate scheme.

  19. Numerical investigation of a modified family of centered schemes applied to multiphase equations with nonconservative sources

    NASA Astrophysics Data System (ADS)

    Crochet, M. W.; Gonthier, K. A.

    2013-12-01

    Systems of hyperbolic partial differential equations are frequently used to model the flow of multiphase mixtures. These equations often contain sources, referred to as nozzling terms, that cannot be posed in divergence form, and have proven to be particularly challenging in the development of finite-volume methods. Upwind schemes have recently shown promise in properly resolving the steady wave solution of the associated multiphase Riemann problem. However, these methods require a full characteristic decomposition of the system eigenstructure, which may be either unavailable or computationally expensive. Central schemes, such as the Kurganov-Tadmor (KT) family of methods, require minimal characteristic information, which makes them easily applicable to systems with an arbitrary number of phases. However, the proper implementation of nozzling terms in these schemes has been mathematically ambiguous. The primary objectives of this work are twofold: first, an extension of the KT family of schemes is proposed that formally accounts for the nonconservative nozzling sources. This modification results in a semidiscrete form that retains the simplicity of its predecessor and introduces little additional computational expense. Second, this modified method is applied to multiple, but equivalent, forms of the multiphase equations to perform a numerical study by solving several one-dimensional test problems. Both ideal and Mie-Grüneisen equations of state are used, with the results compared to an analytical solution. This study demonstrates that the magnitudes of the resulting numerical errors are sensitive to the form of the equations considered, and suggests an optimal form to minimize these errors. Finally, a separate modification of the wave propagation speeds used in the KT family is also suggested that can reduce the extent of numerical diffusion in multiphase flows.

  20. A faster numerical scheme for a coupled system modeling soil erosion and sediment transport

    NASA Astrophysics Data System (ADS)

    Le, M.-H.; Cordier, S.; Lucas, C.; Cerdan, O.

    2015-02-01

    Overland flow and soil erosion play an essential role in water quality and soil degradation. Such processes, involving the interactions between water flow and the bed sediment, are classically described by a well-established system coupling the shallow water equations and the Hairsine-Rose model. Numerical approximation of this coupled system requires advanced methods to preserve some important physical and mathematical properties; in particular, the steady states and the positivity of both water depth and sediment concentration. Recently, finite volume schemes based on Roe's solver have been proposed by Heng et al. (2009) and Kim et al. (2013) for one and two-dimensional problems. In their approach, an additional and artificial restriction on the time step is required to guarantee the positivity of sediment concentration. This artificial condition can lead the computation to be costly when dealing with very shallow flow and wet/dry fronts. The main result of this paper is to propose a new and faster scheme for which only the CFL condition of the shallow water equations is sufficient to preserve the positivity of sediment concentration. In addition, the numerical procedure of the erosion part can be used with any well-balanced and positivity preserving scheme of the shallow water equations. The proposed method is tested on classical benchmarks and also on a realistic configuration.

  1. Accurate modelling of unsteady flows in collapsible tubes.

    PubMed

    Marchandise, Emilie; Flaud, Patrice

    2010-01-01

    The context of this paper is the development of a general and efficient numerical haemodynamic tool to help clinicians and researchers in understanding of physiological flow phenomena. We propose an accurate one-dimensional Runge-Kutta discontinuous Galerkin (RK-DG) method coupled with lumped parameter models for the boundary conditions. The suggested model has already been successfully applied to haemodynamics in arteries and is now extended for the flow in collapsible tubes such as veins. The main difference with cardiovascular simulations is that the flow may become supercritical and elastic jumps may appear with the numerical consequence that scheme may not remain monotone if no limiting procedure is introduced. We show that our second-order RK-DG method equipped with an approximate Roe's Riemann solver and a slope-limiting procedure allows us to capture elastic jumps accurately. Moreover, this paper demonstrates that the complex physics associated with such flows is more accurately modelled than with traditional methods such as finite difference methods or finite volumes. We present various benchmark problems that show the flexibility and applicability of the numerical method. Our solutions are compared with analytical solutions when they are available and with solutions obtained using other numerical methods. Finally, to illustrate the clinical interest, we study the emptying process in a calf vein squeezed by contracting skeletal muscle in a normal and pathological subject. We compare our results with experimental simulations and discuss the sensitivity to parameters of our model.

  2. Re-evaluation of an Optimized Second Order Backward Difference (BDF2OPT) Scheme for Unsteady Flow Applications

    NASA Technical Reports Server (NTRS)

    Vatsa, Veer N.; Carpenter, Mark H.; Lockard, David P.

    2009-01-01

    Recent experience in the application of an optimized, second-order, backward-difference (BDF2OPT) temporal scheme is reported. The primary focus of the work is on obtaining accurate solutions of the unsteady Reynolds-averaged Navier-Stokes equations over long periods of time for aerodynamic problems of interest. The baseline flow solver under consideration uses a particular BDF2OPT temporal scheme with a dual-time-stepping algorithm for advancing the flow solutions in time. Numerical difficulties are encountered with this scheme when the flow code is run for a large number of time steps, a behavior not seen with the standard second-order, backward-difference, temporal scheme. Based on a stability analysis, slight modifications to the BDF2OPT scheme are suggested. The performance and accuracy of this modified scheme is assessed by comparing the computational results with other numerical schemes and experimental data.

  3. A conservative numerical scheme for modeling nonlinear acoustic propagation in thermoviscous homogeneous media

    NASA Astrophysics Data System (ADS)

    Diaz, Manuel A.; Solovchuk, Maxim A.; Sheu, Tony W. H.

    2018-06-01

    A nonlinear system of partial differential equations capable of describing the nonlinear propagation and attenuation of finite amplitude perturbations in thermoviscous media is presented. This system constitutes a full nonlinear wave model that has been formulated in the conservation form. Initially, this model is investigated analytically in the inviscid limit where it has been found that the resulting flux function fulfills the Lax-Wendroff theorem, and the scheme can match the solutions of the Westervelt and Burgers equations numerically. Here, high-order numerical descriptions of strongly nonlinear wave propagations become of great interest. For that matter we consider finite difference formulations of the weighted essentially non-oscillatory (WENO) schemes associated with explicit strong stability preserving Runge-Kutta (SSP-RK) time integration methods. Although this strategy is known to be computationally demanding, it is found to be effective when implemented to be solved in graphical processing units (GPUs). As we consider wave propagations in unbounded domains, perfectly matching layers (PML) have been also considered in this work. The proposed system model is validated and illustrated by using one- and two-dimensional benchmark test cases proposed in the literature for nonlinear acoustic propagation in homogeneous thermoviscous media.

  4. A Time-Accurate Upwind Unstructured Finite Volume Method for Compressible Flow with Cure of Pathological Behaviors

    NASA Technical Reports Server (NTRS)

    Loh, Ching Y.; Jorgenson, Philip C. E.

    2007-01-01

    A time-accurate, upwind, finite volume method for computing compressible flows on unstructured grids is presented. The method is second order accurate in space and time and yields high resolution in the presence of discontinuities. For efficiency, the Roe approximate Riemann solver with an entropy correction is employed. In the basic Euler/Navier-Stokes scheme, many concepts of high order upwind schemes are adopted: the surface flux integrals are carefully treated, a Cauchy-Kowalewski time-stepping scheme is used in the time-marching stage, and a multidimensional limiter is applied in the reconstruction stage. However even with these up-to-date improvements, the basic upwind scheme is still plagued by the so-called "pathological behaviors," e.g., the carbuncle phenomenon, the expansion shock, etc. A solution to these limitations is presented which uses a very simple dissipation model while still preserving second order accuracy. This scheme is referred to as the enhanced time-accurate upwind (ETAU) scheme in this paper. The unstructured grid capability renders flexibility for use in complex geometry; and the present ETAU Euler/Navier-Stokes scheme is capable of handling a broad spectrum of flow regimes from high supersonic to subsonic at very low Mach number, appropriate for both CFD (computational fluid dynamics) and CAA (computational aeroacoustics). Numerous examples are included to demonstrate the robustness of the methods.

  5. Assessment of numerical methods for the solution of fluid dynamics equations for nonlinear resonance systems

    NASA Technical Reports Server (NTRS)

    Przekwas, A. J.; Yang, H. Q.

    1989-01-01

    The capability of accurate nonlinear flow analysis of resonance systems is essential in many problems, including combustion instability. Classical numerical schemes are either too diffusive or too dispersive especially for transient problems. In the last few years, significant progress has been made in the numerical methods for flows with shocks. The objective was to assess advanced shock capturing schemes on transient flows. Several numerical schemes were tested including TVD, MUSCL, ENO, FCT, and Riemann Solver Godunov type schemes. A systematic assessment was performed on scalar transport, Burgers' and gas dynamic problems. Several shock capturing schemes are compared on fast transient resonant pipe flow problems. A system of 1-D nonlinear hyperbolic gas dynamics equations is solved to predict propagation of finite amplitude waves, the wave steepening, formation, propagation, and reflection of shocks for several hundred wave cycles. It is shown that high accuracy schemes can be used for direct, exact nonlinear analysis of combustion instability problems, preserving high harmonic energy content for long periods of time.

  6. Asymptotic analysis of discrete schemes for non-equilibrium radiation diffusion

    DOE Office of Scientific and Technical Information (OSTI.GOV)

    Cui, Xia, E-mail: cui_xia@iapcm.ac.cn; Yuan, Guang-wei; Shen, Zhi-jun

    Motivated by providing well-behaved fully discrete schemes in practice, this paper extends the asymptotic analysis on time integration methods for non-equilibrium radiation diffusion in [2] to space discretizations. Therein studies were carried out on a two-temperature model with Larsen's flux-limited diffusion operator, both the implicitly balanced (IB) and linearly implicit (LI) methods were shown asymptotic-preserving. In this paper, we focus on asymptotic analysis for space discrete schemes in dimensions one and two. First, in construction of the schemes, in contrast to traditional first-order approximations, asymmetric second-order accurate spatial approximations are devised for flux-limiters on boundary, and discrete schemes with second-ordermore » accuracy on global spatial domain are acquired consequently. Then by employing formal asymptotic analysis, the first-order asymptotic-preserving property for these schemes and furthermore for the fully discrete schemes is shown. Finally, with the help of manufactured solutions, numerical tests are performed, which demonstrate quantitatively the fully discrete schemes with IB time evolution indeed have the accuracy and asymptotic convergence as theory predicts, hence are well qualified for both non-equilibrium and equilibrium radiation diffusion. - Highlights: • Provide AP fully discrete schemes for non-equilibrium radiation diffusion. • Propose second order accurate schemes by asymmetric approach for boundary flux-limiter. • Show first order AP property of spatially and fully discrete schemes with IB evolution. • Devise subtle artificial solutions; verify accuracy and AP property quantitatively. • Ideas can be generalized to 3-dimensional problems and higher order implicit schemes.« less

  7. Numerical solution of the Saint-Venant equations by an efficient hybrid finite-volume/finite-difference method

    NASA Astrophysics Data System (ADS)

    Lai, Wencong; Khan, Abdul A.

    2018-04-01

    A computationally efficient hybrid finite-volume/finite-difference method is proposed for the numerical solution of Saint-Venant equations in one-dimensional open channel flows. The method adopts a mass-conservative finite volume discretization for the continuity equation and a semi-implicit finite difference discretization for the dynamic-wave momentum equation. The spatial discretization of the convective flux term in the momentum equation employs an upwind scheme and the water-surface gradient term is discretized using three different schemes. The performance of the numerical method is investigated in terms of efficiency and accuracy using various examples, including steady flow over a bump, dam-break flow over wet and dry downstream channels, wetting and drying in a parabolic bowl, and dam-break floods in laboratory physical models. Numerical solutions from the hybrid method are compared with solutions from a finite volume method along with analytic solutions or experimental measurements. Comparisons demonstrates that the hybrid method is efficient, accurate, and robust in modeling various flow scenarios, including subcritical, supercritical, and transcritical flows. In this method, the QUICK scheme for the surface slope discretization is more accurate and less diffusive than the center difference and the weighted average schemes.

  8. Sensitivity analysis of numerical weather prediction radiative schemes to forecast direct solar radiation over Australia

    NASA Astrophysics Data System (ADS)

    Mukkavilli, S. K.; Kay, M. J.; Taylor, R.; Prasad, A. A.; Troccoli, A.

    2014-12-01

    The Australian Solar Energy Forecasting System (ASEFS) project requires forecasting timeframes which range from nowcasting to long-term forecasts (minutes to two years). As concentrating solar power (CSP) plant operators are one of the key stakeholders in the national energy market, research and development enhancements for direct normal irradiance (DNI) forecasts is a major subtask. This project involves comparing different radiative scheme codes to improve day ahead DNI forecasts on the national supercomputing infrastructure running mesoscale simulations on NOAA's Weather Research & Forecast (WRF) model. ASEFS also requires aerosol data fusion for improving accurate representation of spatio-temporally variable atmospheric aerosols to reduce DNI bias error in clear sky conditions over southern Queensland & New South Wales where solar power is vulnerable to uncertainities from frequent aerosol radiative events such as bush fires and desert dust. Initial results from thirteen years of Bureau of Meteorology's (BOM) deseasonalised DNI and MODIS NASA-Terra aerosol optical depth (AOD) anomalies demonstrated strong negative correlations in north and southeast Australia along with strong variability in AOD (~0.03-0.05). Radiative transfer schemes, DNI and AOD anomaly correlations will be discussed for the population and transmission grid centric regions where current and planned CSP plants dispatch electricity to capture peak prices in the market. Aerosol and solar irradiance datasets include satellite and ground based assimilations from the national BOM, regional aerosol researchers and agencies. The presentation will provide an overview of this ASEFS project task on WRF and results to date. The overall goal of this ASEFS subtask is to develop a hybrid numerical weather prediction (NWP) and statistical/machine learning multi-model ensemble strategy that meets future operational requirements of CSP plant operators.

  9. A kinetic flux vector splitting scheme for shallow water equations incorporating variable bottom topography and horizontal temperature gradients

    PubMed Central

    2018-01-01

    This paper is concerned with the derivation of a well-balanced kinetic scheme to approximate a shallow flow model incorporating non-flat bottom topography and horizontal temperature gradients. The considered model equations, also called as Ripa system, are the non-homogeneous shallow water equations considering temperature gradients and non-uniform bottom topography. Due to the presence of temperature gradient terms, the steady state at rest is of primary interest from the physical point of view. However, capturing of this steady state is a challenging task for the applied numerical methods. The proposed well-balanced kinetic flux vector splitting (KFVS) scheme is non-oscillatory and second order accurate. The second order accuracy of the scheme is obtained by considering a MUSCL-type initial reconstruction and Runge-Kutta time stepping method. The scheme is applied to solve the model equations in one and two space dimensions. Several numerical case studies are carried out to validate the proposed numerical algorithm. The numerical results obtained are compared with those of staggered central NT scheme. The results obtained are also in good agreement with the recently published results in the literature, verifying the potential, efficiency, accuracy and robustness of the suggested numerical scheme. PMID:29851978

  10. A numerical scheme to calculate temperature and salinity dependent air-water transfer velocities for any gas

    NASA Astrophysics Data System (ADS)

    Johnson, M. T.

    2010-10-01

    The ocean-atmosphere flux of a gas can be calculated from its measured or estimated concentration gradient across the air-sea interface and the transfer velocity (a term representing the conductivity of the layers either side of the interface with respect to the gas of interest). Traditionally the transfer velocity has been estimated from empirical relationships with wind speed, and then scaled by the Schmidt number of the gas being transferred. Complex, physically based models of transfer velocity (based on more physical forcings than wind speed alone), such as the NOAA COARE algorithm, have more recently been applied to well-studied gases such as carbon dioxide and DMS (although many studies still use the simpler approach for these gases), but there is a lack of validation of such schemes for other, more poorly studied gases. The aim of this paper is to provide a flexible numerical scheme which will allow the estimation of transfer velocity for any gas as a function of wind speed, temperature and salinity, given data on the solubility and liquid molar volume of the particular gas. New and existing parameterizations (including a novel empirical parameterization of the salinity-dependence of Henry's law solubility) are brought together into a scheme implemented as a modular, extensible program in the R computing environment which is available in the supplementary online material accompanying this paper; along with input files containing solubility and structural data for ~90 gases of general interest, enabling the calculation of their total transfer velocities and component parameters. Comparison of the scheme presented here with alternative schemes and methods for calculating air-sea flux parameters shows good agreement in general. It is intended that the various components of this numerical scheme should be applied only in the absence of experimental data providing robust values for parameters for a particular gas of interest.

  11. A modified Holly-Preissmann scheme for simulating sharp concentration fronts in streams with steep velocity gradients using RIV1Q

    NASA Astrophysics Data System (ADS)

    Liu, Zhao-wei; Zhu, De-jun; Chen, Yong-can; Wang, Zhi-gang

    2014-12-01

    RIV1Q is the stand-alone water quality program of CE-QUAL-RIV1, a hydraulic and water quality model developed by U.S. Army Corps of Engineers Waterways Experiment Station. It utilizes an operator-splitting algorithm and the advection term in governing equation is treated using the explicit two-point, fourth-order accurate, Holly-Preissmann scheme, in order to preserve numerical accuracy for advection of sharp gradients in concentration. In the scheme, the spatial derivative of the transport equation, where the derivative of velocity is included, is introduced to update the first derivative of dependent variable. In the stream with larger cross-sectional variation, steep velocity gradient can be easily found and should be estimated correctly. In the original version of RIV1Q, however, the derivative of velocity is approximated by a finite difference which is first-order accurate. Its leading truncation error leads to the numerical error of concentration which is related with the velocity and concentration gradients and increases with the decreasing Courant number. The simulation may also be unstable when a sharp velocity drop occurs. In the present paper, the derivative of velocity is estimated with a modified second-order accurate scheme and the corresponding numerical error of concentration decreases. Additionally, the stability of the simulation is improved. The modified scheme is verified with a hypothetical channel case and the results demonstrate that satisfactory accuracy and stability can be achieved even when the Courant number is very low. Finally, the applicability of the modified scheme is discussed.

  12. Hybrid Numerical-Analytical Scheme for Calculating Elastic Wave Diffraction in Locally Inhomogeneous Waveguides

    NASA Astrophysics Data System (ADS)

    Glushkov, E. V.; Glushkova, N. V.; Evdokimov, A. A.

    2018-01-01

    Numerical simulation of traveling wave excitation, propagation, and diffraction in structures with local inhomogeneities (obstacles) is computationally expensive due to the need for mesh-based approximation of extended domains with the rigorous account for the radiation conditions at infinity. Therefore, hybrid numerical-analytic approaches are being developed based on the conjugation of a numerical solution in a local vicinity of the obstacle and/or source with an explicit analytic representation in the remaining semi-infinite external domain. However, in standard finite-element software, such a coupling with the external field, moreover, in the case of multimode expansion, is generally not provided. This work proposes a hybrid computational scheme that allows realization of such a conjugation using a standard software. The latter is used to construct a set of numerical solutions used as the basis for the sought solution in the local internal domain. The unknown expansion coefficients on this basis and on normal modes in the semi-infinite external domain are then determined from the conditions of displacement and stress continuity at the boundary between the two domains. We describe the implementation of this approach in the scalar and vector cases. To evaluate the reliability of the results and the efficiency of the algorithm, we compare it with a semianalytic solution to the problem of traveling wave diffraction by a horizontal obstacle, as well as with a finite-element solution obtained for a limited domain artificially restricted using absorbing boundaries. As an example, we consider the incidence of a fundamental antisymmetric Lamb wave onto surface and partially submerged elastic obstacles. It is noted that the proposed hybrid scheme can also be used to determine the eigenfrequencies and eigenforms of resonance scattering, as well as the characteristics of traveling waves in embedded waveguides.

  13. Numerical Simulation of a High Mach Number Jet Flow

    NASA Technical Reports Server (NTRS)

    Hayder, M. Ehtesham; Turkel, Eli; Mankbadi, Reda R.

    1993-01-01

    The recent efforts to develop accurate numerical schemes for transition and turbulent flows are motivated, among other factors, by the need for accurate prediction of flow noise. The success of developing high speed civil transport plane (HSCT) is contingent upon our understanding and suppression of the jet exhaust noise. The radiated sound can be directly obtained by solving the full (time-dependent) compressible Navier-Stokes equations. However, this requires computational storage that is beyond currently available machines. This difficulty can be overcome by limiting the solution domain to the near field where the jet is nonlinear and then use acoustic analogy (e.g., Lighthill) to relate the far-field noise to the near-field sources. The later requires obtaining the time-dependent flow field. The other difficulty in aeroacoustics computations is that at high Reynolds numbers the turbulent flow has a large range of scales. Direct numerical simulations (DNS) cannot obtain all the scales of motion at high Reynolds number of technological interest. However, it is believed that the large scale structure is more efficient than the small-scale structure in radiating noise. Thus, one can model the small scales and calculate the acoustically active scales. The large scale structure in the noise-producing initial region of the jet can be viewed as a wavelike nature, the net radiated sound is the net cancellation after integration over space. As such, aeroacoustics computations are highly sensitive to errors in computing the sound sources. It is therefore essential to use a high-order numerical scheme to predict the flow field. The present paper presents the first step in a ongoing effort to predict jet noise. The emphasis here is in accurate prediction of the unsteady flow field. We solve the full time-dependent Navier-Stokes equations by a high order finite difference method. Time accurate spatial simulations of both plane and axisymmetric jet are presented. Jet Mach

  14. Comparative study of numerical schemes of TVD3, UNO3-ACM and optimized compact scheme

    NASA Technical Reports Server (NTRS)

    Lee, Duck-Joo; Hwang, Chang-Jeon; Ko, Duck-Kon; Kim, Jae-Wook

    1995-01-01

    Three different schemes are employed to solve the benchmark problem. The first one is a conventional TVD-MUSCL (Monotone Upwind Schemes for Conservation Laws) scheme. The second scheme is a UNO3-ACM (Uniformly Non-Oscillatory Artificial Compression Method) scheme. The third scheme is an optimized compact finite difference scheme modified by us: the 4th order Runge Kutta time stepping, the 4th order pentadiagonal compact spatial discretization with the maximum resolution characteristics. The problems of category 1 are solved by using the second (UNO3-ACM) and third (Optimized Compact) schemes. The problems of category 2 are solved by using the first (TVD3) and second (UNO3-ACM) schemes. The problem of category 5 is solved by using the first (TVD3) scheme. It can be concluded from the present calculations that the Optimized Compact scheme and the UN03-ACM show good resolutions for category 1 and category 2 respectively.

  15. Efficient scheme for parametric fitting of data in arbitrary dimensions.

    PubMed

    Pang, Ning-Ning; Tzeng, Wen-Jer; Kao, Hisen-Ching

    2008-07-01

    We propose an efficient scheme for parametric fitting expressed in terms of the Legendre polynomials. For continuous systems, our scheme is exact and the derived explicit expression is very helpful for further analytical studies. For discrete systems, our scheme is almost as accurate as the method of singular value decomposition. Through a few numerical examples, we show that our algorithm costs much less CPU time and memory space than the method of singular value decomposition. Thus, our algorithm is very suitable for a large amount of data fitting. In addition, the proposed scheme can also be used to extract the global structure of fluctuating systems. We then derive the exact relation between the correlation function and the detrended variance function of fluctuating systems in arbitrary dimensions and give a general scaling analysis.

  16. High-Order Multioperator Compact Schemes for Numerical Simulation of Unsteady Subsonic Airfoil Flow

    NASA Astrophysics Data System (ADS)

    Savel'ev, A. D.

    2018-02-01

    On the basis of high-order schemes, the viscous gas flow over the NACA2212 airfoil is numerically simulated at a free-stream Mach number of 0.3 and Reynolds numbers ranging from 103 to 107. Flow regimes sequentially varying due to variations in the free-stream viscosity are considered. Vortex structures developing on the airfoil surface are investigated, and a physical interpretation of this phenomenon is given.

  17. Numerical methods for the stochastic Landau-Lifshitz Navier-Stokes equations.

    PubMed

    Bell, John B; Garcia, Alejandro L; Williams, Sarah A

    2007-07-01

    The Landau-Lifshitz Navier-Stokes (LLNS) equations incorporate thermal fluctuations into macroscopic hydrodynamics by using stochastic fluxes. This paper examines explicit Eulerian discretizations of the full LLNS equations. Several computational fluid dynamics approaches are considered (including MacCormack's two-step Lax-Wendroff scheme and the piecewise parabolic method) and are found to give good results for the variance of momentum fluctuations. However, neither of these schemes accurately reproduces the fluctuations in energy or density. We introduce a conservative centered scheme with a third-order Runge-Kutta temporal integrator that does accurately produce fluctuations in density, energy, and momentum. A variety of numerical tests, including the random walk of a standing shock wave, are considered and results from the stochastic LLNS solver are compared with theory, when available, and with molecular simulations using a direct simulation Monte Carlo algorithm.

  18. The a(3) Scheme--A Fourth-Order Space-Time Flux-Conserving and Neutrally Stable CESE Solver

    NASA Technical Reports Server (NTRS)

    Chang, Sin-Chung

    2008-01-01

    The CESE development is driven by a belief that a solver should (i) enforce conservation laws in both space and time, and (ii) be built from a non-dissipative (i.e., neutrally stable) core scheme so that the numerical dissipation can be controlled effectively. To initiate a systematic CESE development of high order schemes, in this paper we provide a thorough discussion on the structure, consistency, stability, phase error, and accuracy of a new 4th-order space-time flux-conserving and neutrally stable CESE solver of an 1D scalar advection equation. The space-time stencil of this two-level explicit scheme is formed by one point at the upper time level and three points at the lower time level. Because it is associated with three independent mesh variables (the numerical analogues of the dependent variable and its 1st-order and 2ndorder spatial derivatives, respectively) and three equations per mesh point, the new scheme is referred to as the a(3) scheme. Through the von Neumann analysis, it is shown that the a(3) scheme is stable if and only if the Courant number is less than 0.5. Moreover, it is established numerically that the a(3) scheme is 4th-order accurate.

  19. Accurate Adaptive Level Set Method and Sharpening Technique for Three Dimensional Deforming Interfaces

    NASA Technical Reports Server (NTRS)

    Kim, Hyoungin; Liou, Meng-Sing

    2011-01-01

    In this paper, we demonstrate improved accuracy of the level set method for resolving deforming interfaces by proposing two key elements: (1) accurate level set solutions on adapted Cartesian grids by judiciously choosing interpolation polynomials in regions of different grid levels and (2) enhanced reinitialization by an interface sharpening procedure. The level set equation is solved using a fifth order WENO scheme or a second order central differencing scheme depending on availability of uniform stencils at each grid point. Grid adaptation criteria are determined so that the Hamiltonian functions at nodes adjacent to interfaces are always calculated by the fifth order WENO scheme. This selective usage between the fifth order WENO and second order central differencing schemes is confirmed to give more accurate results compared to those in literature for standard test problems. In order to further improve accuracy especially near thin filaments, we suggest an artificial sharpening method, which is in a similar form with the conventional re-initialization method but utilizes sign of curvature instead of sign of the level set function. Consequently, volume loss due to numerical dissipation on thin filaments is remarkably reduced for the test problems

  20. Numerical Simulation of Shock Interaction with Deformable Particles Using a Constrained Interface Reinitialization Scheme

    NASA Astrophysics Data System (ADS)

    Jackson, Thomas L.; Sridharan, Prashanth; Zhang, Ju; Balachandar, S.

    2015-11-01

    In this work we present axisymmetric numerical simulations of shock propagating in nitromethane over an aluminum particle for post-shock pressures up to 10 GPa. The numerical method is a finite-volume based solver on a Cartesian grid, which allows for multi-material interfaces and shocks. To preserve particle mass and volume, a novel constraint reinitialization scheme is introduced. We compute the unsteady drag coefficient as a function of post-shock pressure, and show that when normalized by post-shock conditions, the maximum drag coefficient decreases with increasing post-shock pressure. Using this information, we also present a simplified point-particle force model that can be used for mesoscale simulations.

  1. Nonequilibrium scheme for computing the flux of the convection-diffusion equation in the framework of the lattice Boltzmann method.

    PubMed

    Chai, Zhenhua; Zhao, T S

    2014-07-01

    In this paper, we propose a local nonequilibrium scheme for computing the flux of the convection-diffusion equation with a source term in the framework of the multiple-relaxation-time (MRT) lattice Boltzmann method (LBM). Both the Chapman-Enskog analysis and the numerical results show that, at the diffusive scaling, the present nonequilibrium scheme has a second-order convergence rate in space. A comparison between the nonequilibrium scheme and the conventional second-order central-difference scheme indicates that, although both schemes have a second-order convergence rate in space, the present nonequilibrium scheme is more accurate than the central-difference scheme. In addition, the flux computation rendered by the present scheme also preserves the parallel computation feature of the LBM, making the scheme more efficient than conventional finite-difference schemes in the study of large-scale problems. Finally, a comparison between the single-relaxation-time model and the MRT model is also conducted, and the results show that the MRT model is more accurate than the single-relaxation-time model, both in solving the convection-diffusion equation and in computing the flux.

  2. Numerical calculations of two dimensional, unsteady transonic flows with circulation

    NASA Technical Reports Server (NTRS)

    Beam, R. M.; Warming, R. F.

    1974-01-01

    The feasibility of obtaining two-dimensional, unsteady transonic aerodynamic data by numerically integrating the Euler equations is investigated. An explicit, third-order-accurate, noncentered, finite-difference scheme is used to compute unsteady flows about airfoils. Solutions for lifting and nonlifting airfoils are presented and compared with subsonic linear theory. The applicability and efficiency of the numerical indicial function method are outlined. Numerically computed subsonic and transonic oscillatory aerodynamic coefficients are presented and compared with those obtained from subsonic linear theory and transonic wind-tunnel data.

  3. Modelling Detailed-Chemistry Effects on Turbulent Diffusion Flames using a Parallel Solution-Adaptive Scheme

    NASA Astrophysics Data System (ADS)

    Jha, Pradeep Kumar

    Capturing the effects of detailed-chemistry on turbulent combustion processes is a central challenge faced by the numerical combustion community. However, the inherent complexity and non-linear nature of both turbulence and chemistry require that combustion models rely heavily on engineering approximations to remain computationally tractable. This thesis proposes a computationally efficient algorithm for modelling detailed-chemistry effects in turbulent diffusion flames and numerically predicting the associated flame properties. The cornerstone of this combustion modelling tool is the use of parallel Adaptive Mesh Refinement (AMR) scheme with the recently proposed Flame Prolongation of Intrinsic low-dimensional manifold (FPI) tabulated-chemistry approach for modelling complex chemistry. The effect of turbulence on the mean chemistry is incorporated using a Presumed Conditional Moment (PCM) approach based on a beta-probability density function (PDF). The two-equation k-w turbulence model is used for modelling the effects of the unresolved turbulence on the mean flow field. The finite-rate of methane-air combustion is represented here by using the GRI-Mech 3.0 scheme. This detailed mechanism is used to build the FPI tables. A state of the art numerical scheme based on a parallel block-based solution-adaptive algorithm has been developed to solve the Favre-averaged Navier-Stokes (FANS) and other governing partial-differential equations using a second-order accurate, fully-coupled finite-volume formulation on body-fitted, multi-block, quadrilateral/hexahedral mesh for two-dimensional and three-dimensional flow geometries, respectively. A standard fourth-order Runge-Kutta time-marching scheme is used for time-accurate temporal discretizations. Numerical predictions of three different diffusion flames configurations are considered in the present work: a laminar counter-flow flame; a laminar co-flow diffusion flame; and a Sydney bluff-body turbulent reacting flow

  4. First order comparison of numerical calculation and two different turtle input schemes to represent a SLC defocusing magnet

    DOE Office of Scientific and Technical Information (OSTI.GOV)

    Jaeger, J.

    1983-07-14

    Correcting the dispersion function in the SLC north arc it turned out that backleg-windings (BLW) acting horizontally as well as BLW acting vertically have to be used. In the latter case the question arose what is the best representation of a defocusing magnet with excited BLW acting in the vertical plane for the computer code TURTLE. Two different schemes, the 14.-scheme and the 20.-scheme were studied and the TURTLE output for one ray through such a magnet compared with the numerical solution of the equation of motion; only terms of first order have been taken into account.

  5. Space-time adaptive ADER-DG schemes for dissipative flows: Compressible Navier-Stokes and resistive MHD equations

    NASA Astrophysics Data System (ADS)

    Fambri, Francesco; Dumbser, Michael; Zanotti, Olindo

    2017-11-01

    This paper presents an arbitrary high-order accurate ADER Discontinuous Galerkin (DG) method on space-time adaptive meshes (AMR) for the solution of two important families of non-linear time dependent partial differential equations for compressible dissipative flows : the compressible Navier-Stokes equations and the equations of viscous and resistive magnetohydrodynamics in two and three space-dimensions. The work continues a recent series of papers concerning the development and application of a proper a posteriori subcell finite volume limiting procedure suitable for discontinuous Galerkin methods (Dumbser et al., 2014, Zanotti et al., 2015 [40,41]). It is a well known fact that a major weakness of high order DG methods lies in the difficulty of limiting discontinuous solutions, which generate spurious oscillations, namely the so-called 'Gibbs phenomenon'. In the present work, a nonlinear stabilization of the scheme is sequentially and locally introduced only for troubled cells on the basis of a novel a posteriori detection criterion, i.e. the MOOD approach. The main benefits of the MOOD paradigm, i.e. the computational robustness even in the presence of strong shocks, are preserved and the numerical diffusion is considerably reduced also for the limited cells by resorting to a proper sub-grid. In practice the method first produces a so-called candidate solution by using a high order accurate unlimited DG scheme. Then, a set of numerical and physical detection criteria is applied to the candidate solution, namely: positivity of pressure and density, absence of floating point errors and satisfaction of a discrete maximum principle in the sense of polynomials. Furthermore, in those cells where at least one of these criteria is violated the computed candidate solution is detected as troubled and is locally rejected. Subsequently, a more reliable numerical solution is recomputed a posteriori by employing a more robust but still very accurate ADER-WENO finite volume

  6. On the numerical treatment of selected oscillatory evolutionary problems

    NASA Astrophysics Data System (ADS)

    Cardone, Angelamaria; Conte, Dajana; D'Ambrosio, Raffaele; Paternoster, Beatrice

    2017-07-01

    We focus on evolutionary problems whose qualitative behaviour is known a-priori and exploited in order to provide efficient and accurate numerical schemes. For classical numerical methods, depending on constant coefficients, the required computational effort could be quite heavy, due to the necessary employ of very small stepsizes needed to accurately reproduce the qualitative behaviour of the solution. In these situations, it may be convenient to use special purpose formulae, i.e. non-polynomially fitted formulae on basis functions adapted to the problem (see [16, 17] and references therein). We show examples of special purpose strategies to solve two families of evolutionary problems exhibiting periodic solutions, i.e. partial differential equations and Volterra integral equations.

  7. Well-balanced high-order centered schemes on unstructured meshes for shallow water equations with fixed and mobile bed

    NASA Astrophysics Data System (ADS)

    Canestrelli, Alberto; Dumbser, Michael; Siviglia, Annunziato; Toro, Eleuterio F.

    2010-03-01

    In this paper, we study the numerical approximation of the two-dimensional morphodynamic model governed by the shallow water equations and bed-load transport following a coupled solution strategy. The resulting system of governing equations contains non-conservative products and it is solved simultaneously within each time step. The numerical solution is obtained using a new high-order accurate centered scheme of the finite volume type on unstructured meshes, which is an extension of the one-dimensional PRICE-C scheme recently proposed in Canestrelli et al. (2009) [5]. The resulting first-order accurate centered method is then extended to high order of accuracy in space via a high order WENO reconstruction technique and in time via a local continuous space-time Galerkin predictor method. The scheme is applied to the shallow water equations and the well-balanced properties of the method are investigated. Finally, we apply the new scheme to different test cases with both fixed and movable bed. An attractive future of the proposed method is that it is particularly suitable for engineering applications since it allows practitioners to adopt the most suitable sediment transport formula which better fits the field data.

  8. Accurate upwind methods for the Euler equations

    NASA Technical Reports Server (NTRS)

    Huynh, Hung T.

    1993-01-01

    A new class of piecewise linear methods for the numerical solution of the one-dimensional Euler equations of gas dynamics is presented. These methods are uniformly second-order accurate, and can be considered as extensions of Godunov's scheme. With an appropriate definition of monotonicity preservation for the case of linear convection, it can be shown that they preserve monotonicity. Similar to Van Leer's MUSCL scheme, they consist of two key steps: a reconstruction step followed by an upwind step. For the reconstruction step, a monotonicity constraint that preserves uniform second-order accuracy is introduced. Computational efficiency is enhanced by devising a criterion that detects the 'smooth' part of the data where the constraint is redundant. The concept and coding of the constraint are simplified by the use of the median function. A slope steepening technique, which has no effect at smooth regions and can resolve a contact discontinuity in four cells, is described. As for the upwind step, existing and new methods are applied in a manner slightly different from those in the literature. These methods are derived by approximating the Euler equations via linearization and diagonalization. At a 'smooth' interface, Harten, Lax, and Van Leer's one intermediate state model is employed. A modification for this model that can resolve contact discontinuities is presented. Near a discontinuity, either this modified model or a more accurate one, namely, Roe's flux-difference splitting. is used. The current presentation of Roe's method, via the conceptually simple flux-vector splitting, not only establishes a connection between the two splittings, but also leads to an admissibility correction with no conditional statement, and an efficient approximation to Osher's approximate Riemann solver. These reconstruction and upwind steps result in schemes that are uniformly second-order accurate and economical at smooth regions, and yield high resolution at discontinuities.

  9. Numerical Solution of Dyson Brownian Motion and a Sampling Scheme for Invariant Matrix Ensembles

    NASA Astrophysics Data System (ADS)

    Li, Xingjie Helen; Menon, Govind

    2013-12-01

    The Dyson Brownian Motion (DBM) describes the stochastic evolution of N points on the line driven by an applied potential, a Coulombic repulsion and identical, independent Brownian forcing at each point. We use an explicit tamed Euler scheme to numerically solve the Dyson Brownian motion and sample the equilibrium measure for non-quadratic potentials. The Coulomb repulsion is too singular for the SDE to satisfy the hypotheses of rigorous convergence proofs for tamed Euler schemes (Hutzenthaler et al. in Ann. Appl. Probab. 22(4):1611-1641, 2012). Nevertheless, in practice the scheme is observed to be stable for time steps of O(1/ N 2) and to relax exponentially fast to the equilibrium measure with a rate constant of O(1) independent of N. Further, this convergence rate appears to improve with N in accordance with O(1/ N) relaxation of local statistics of the Dyson Brownian motion. This allows us to use the Dyson Brownian motion to sample N× N Hermitian matrices from the invariant ensembles. The computational cost of generating M independent samples is O( MN 4) with a naive scheme, and O( MN 3log N) when a fast multipole method is used to evaluate the Coulomb interaction.

  10. Tetrahedral-Mesh Simulation of Turbulent Flows with the Space-Time Conservative Schemes

    NASA Technical Reports Server (NTRS)

    Chang, Chau-Lyan; Venkatachari, Balaji; Cheng, Gary C.

    2015-01-01

    Direct numerical simulations of turbulent flows are predominantly carried out using structured, hexahedral meshes despite decades of development in unstructured mesh methods. Tetrahedral meshes offer ease of mesh generation around complex geometries and the potential of an orientation free grid that would provide un-biased small-scale dissipation and more accurate intermediate scale solutions. However, due to the lack of consistent multi-dimensional numerical formulations in conventional schemes for triangular and tetrahedral meshes at the cell interfaces, numerical issues exist when flow discontinuities or stagnation regions are present. The space-time conservative conservation element solution element (CESE) method - due to its Riemann-solver-free shock capturing capabilities, non-dissipative baseline schemes, and flux conservation in time as well as space - has the potential to more accurately simulate turbulent flows using unstructured tetrahedral meshes. To pave the way towards accurate simulation of shock/turbulent boundary-layer interaction, a series of wave and shock interaction benchmark problems that increase in complexity, are computed in this paper with triangular/tetrahedral meshes. Preliminary computations for the normal shock/turbulence interactions are carried out with a relatively coarse mesh, by direct numerical simulations standards, in order to assess other effects such as boundary conditions and the necessity of a buffer domain. The results indicate that qualitative agreement with previous studies can be obtained for flows where, strong shocks co-exist along with unsteady waves that display a broad range of scales, with a relatively compact computational domain and less stringent requirements for grid clustering near the shock. With the space-time conservation properties, stable solutions without any spurious wave reflections can be obtained without a need for buffer domains near the outflow/farfield boundaries. Computational results for the

  11. Application of a symmetric total variation diminishing scheme to aerodynamics of rotors

    NASA Astrophysics Data System (ADS)

    Usta, Ebru

    2002-09-01

    The aerodynamics characteristics of rotors in hover have been studied on stretched non-orthogonal grids using spatially high order symmetric total variation diminishing (STVD) schemes. Several companion numerical viscosity terms have been tested. The effects of higher order metrics, higher order load integrations and turbulence effects on the rotor performance have been studied. Where possible, calculations for 1-D and 2-D benchmark problems have been done on uniform grids, and comparisons with exact solutions have been made to understand the dispersion and dissipation characteristics of these algorithms. A baseline finite volume methodology termed TURNS (Transonic Unsteady Rotor Navier-Stokes) is the starting point for this effort. The original TURNS solver solves the 3-D compressible Navier-Stokes equations in an integral form using a third order upwind scheme. It is first or second order accurate in time. In the modified solver, the inviscid flux at a cell face is decomposed into two parts. The first part of the flux is symmetric in space, while the second part consists of an upwind-biased numerical viscosity term. The symmetric part of the flux at the cell face is computed to fourth-, sixth- or eighth order accuracy in space. The numerical viscosity portion of the flux is computed using either a third order accurate MUSCL scheme or a fifth order WENO scheme. A number of results are presented for the two-bladed Caradonna-Tung rotor and for a four-bladed UH-60A rotor in hover. Comparisons with the original TURNS code, and experiments are given. Results are also presented on the effects of metrics calculations, load integration algorithms, and turbulence models on the solution accuracy. A total of 64 combinations were studied in this thesis work. For brevity, only a small subset of results highlighting the most important conclusions are presented. It should be noted that use of higher order formulations did not affect the temporal stability of the algorithm and

  12. A systematic approach for the accurate non-invasive estimation of blood glucose utilizing a novel light-tissue interaction adaptive modelling scheme

    NASA Astrophysics Data System (ADS)

    Rybynok, V. O.; Kyriacou, P. A.

    2007-10-01

    Diabetes is one of the biggest health challenges of the 21st century. The obesity epidemic, sedentary lifestyles and an ageing population mean prevalence of the condition is currently doubling every generation. Diabetes is associated with serious chronic ill health, disability and premature mortality. Long-term complications including heart disease, stroke, blindness, kidney disease and amputations, make the greatest contribution to the costs of diabetes care. Many of these long-term effects could be avoided with earlier, more effective monitoring and treatment. Currently, blood glucose can only be monitored through the use of invasive techniques. To date there is no widely accepted and readily available non-invasive monitoring technique to measure blood glucose despite the many attempts. This paper challenges one of the most difficult non-invasive monitoring techniques, that of blood glucose, and proposes a new novel approach that will enable the accurate, and calibration free estimation of glucose concentration in blood. This approach is based on spectroscopic techniques and a new adaptive modelling scheme. The theoretical implementation and the effectiveness of the adaptive modelling scheme for this application has been described and a detailed mathematical evaluation has been employed to prove that such a scheme has the capability of extracting accurately the concentration of glucose from a complex biological media.

  13. New high order schemes in BATS-R-US

    NASA Astrophysics Data System (ADS)

    Toth, G.; van der Holst, B.; Daldorff, L.; Chen, Y.; Gombosi, T. I.

    2013-12-01

    The University of Michigan global magnetohydrodynamics code BATS-R-US has long relied on the block-adaptive mesh refinement (AMR) to increase accuracy in regions of interest, and we used a second order accurate TVD scheme. While AMR can in principle produce arbitrarily accurate results, there are still practical limitations due to computational resources. To further improve the accuracy of the BATS-R-US code, recently, we have implemented a 4th order accurate finite volume scheme (McCorquodale and Colella, 2011}), the 5th order accurate Monotonicity Preserving scheme (MP5, Suresh and Huynh, 1997) and the 5th order accurate CWENO5 scheme (Capdeville, 2008). In the first implementation the high order accuracy is achieved in the uniform parts of the Cartesian grids, and we still use the second order TVD scheme at resolution changes. For spherical grids the new schemes are only second order accurate so far, but still much less diffusive than the TVD scheme. We show a few verification tests that demonstrate the order of accuracy as well as challenging space physics applications. The high order schemes are less robust than the TVD scheme, and it requires some tricks and effort to make the code work. When the high order scheme works, however, we find that in most cases it can obtain similar or better results than the TVD scheme on twice finer grids. For three dimensional time dependent simulations this means that the high order scheme is almost 10 times faster requires 8 times less storage than the second order method.

  14. A generic efficient adaptive grid scheme for rocket propulsion modeling

    NASA Technical Reports Server (NTRS)

    Mo, J. D.; Chow, Alan S.

    1993-01-01

    The objective of this research is to develop an efficient, time-accurate numerical algorithm to discretize the Navier-Stokes equations for the predictions of internal one-, two-dimensional and axisymmetric flows. A generic, efficient, elliptic adaptive grid generator is implicitly coupled with the Lower-Upper factorization scheme in the development of ALUNS computer code. The calculations of one-dimensional shock tube wave propagation and two-dimensional shock wave capture, wave-wave interactions, shock wave-boundary interactions show that the developed scheme is stable, accurate and extremely robust. The adaptive grid generator produced a very favorable grid network by a grid speed technique. This generic adaptive grid generator is also applied in the PARC and FDNS codes and the computational results for solid rocket nozzle flowfield and crystal growth modeling by those codes will be presented in the conference, too. This research work is being supported by NASA/MSFC.

  15. A Fixed-point Scheme for the Numerical Construction of Magnetohydrostatic Atmospheres in Three Dimensions

    NASA Astrophysics Data System (ADS)

    Gilchrist, S. A.; Braun, D. C.; Barnes, G.

    2016-12-01

    Magnetohydrostatic models of the solar atmosphere are often based on idealized analytic solutions because the underlying equations are too difficult to solve in full generality. Numerical approaches, too, are often limited in scope and have tended to focus on the two-dimensional problem. In this article we develop a numerical method for solving the nonlinear magnetohydrostatic equations in three dimensions. Our method is a fixed-point iteration scheme that extends the method of Grad and Rubin ( Proc. 2nd Int. Conf. on Peaceful Uses of Atomic Energy 31, 190, 1958) to include a finite gravity force. We apply the method to a test case to demonstrate the method in general and our implementation in code in particular.

  16. A New Framework to Compare Mass-Flux Schemes Within the AROME Numerical Weather Prediction Model

    NASA Astrophysics Data System (ADS)

    Riette, Sébastien; Lac, Christine

    2016-08-01

    In the Application of Research to Operations at Mesoscale (AROME) numerical weather forecast model used in operations at Météo-France, five mass-flux schemes are available to parametrize shallow convection at kilometre resolution. All but one are based on the eddy-diffusivity-mass-flux approach, and differ in entrainment/detrainment, the updraft vertical velocity equation and the closure assumption. The fifth is based on a more classical mass-flux approach. Screen-level scores obtained with these schemes show few discrepancies and are not sufficient to highlight behaviour differences. Here, we describe and use a new experimental framework, able to compare and discriminate among different schemes. For a year, daily forecast experiments were conducted over small domains centred on the five French metropolitan radio-sounding locations. Cloud base, planetary boundary-layer height and normalized vertical profiles of specific humidity, potential temperature, wind speed and cloud condensate were compared with observations, and with each other. The framework allowed the behaviour of the different schemes in and above the boundary layer to be characterized. In particular, the impact of the entrainment/detrainment formulation, closure assumption and cloud scheme were clearly visible. Differences mainly concerned the transport intensity thus allowing schemes to be separated into two groups, with stronger or weaker updrafts. In the AROME model (with all interactions and the possible existence of compensating errors), evaluation diagnostics gave the advantage to the first group.

  17. Parallel solution of high-order numerical schemes for solving incompressible flows

    NASA Technical Reports Server (NTRS)

    Milner, Edward J.; Lin, Avi; Liou, May-Fun; Blech, Richard A.

    1993-01-01

    A new parallel numerical scheme for solving incompressible steady-state flows is presented. The algorithm uses a finite-difference approach to solving the Navier-Stokes equations. The algorithms are scalable and expandable. They may be used with only two processors or with as many processors as are available. The code is general and expandable. Any size grid may be used. Four processors of the NASA LeRC Hypercluster were used to solve for steady-state flow in a driven square cavity. The Hypercluster was configured in a distributed-memory, hypercube-like architecture. By using a 50-by-50 finite-difference solution grid, an efficiency of 74 percent (a speedup of 2.96) was obtained.

  18. Error analysis of finite difference schemes applied to hyperbolic initial boundary value problems

    NASA Technical Reports Server (NTRS)

    Skollermo, G.

    1979-01-01

    Finite difference methods for the numerical solution of mixed initial boundary value problems for hyperbolic equations are studied. The reported investigation has the objective to develop a technique for the total error analysis of a finite difference scheme, taking into account initial approximations, boundary conditions, and interior approximation. Attention is given to the Cauchy problem and the initial approximation, the homogeneous problem in an infinite strip with inhomogeneous boundary data, the reflection of errors in the boundaries, and two different boundary approximations for the leapfrog scheme with a fourth order accurate difference operator in space.

  19. An Improved Transformation and Optimized Sampling Scheme for the Numerical Evaluation of Singular and Near-Singular Potentials

    NASA Technical Reports Server (NTRS)

    Khayat, Michael A.; Wilton, Donald R.; Fink, Patrick W.

    2007-01-01

    Simple and efficient numerical procedures using singularity cancellation methods are presented for evaluating singular and near-singular potential integrals. Four different transformations are compared and the advantages of the Radial-angular transform are demonstrated. A method is then described for optimizing this integration scheme.

  20. Time domain numerical calculations of unsteady vortical flows about a flat plate airfoil

    NASA Technical Reports Server (NTRS)

    Hariharan, S. I.; Yu, Ping; Scott, J. R.

    1989-01-01

    A time domain numerical scheme is developed to solve for the unsteady flow about a flat plate airfoil due to imposed upstream, small amplitude, transverse velocity perturbations. The governing equation for the resulting unsteady potential is a homogeneous, constant coefficient, convective wave equation. Accurate solution of the problem requires the development of approximate boundary conditions which correctly model the physics of the unsteady flow in the far field. A uniformly valid far field boundary condition is developed, and numerical results are presented using this condition. The stability of the scheme is discussed, and the stability restriction for the scheme is established as a function of the Mach number. Finally, comparisons are made with the frequency domain calculation by Scott and Atassi, and the relative strengths and weaknesses of each approach are assessed.

  1. A second-order cell-centered Lagrangian ADER-MOOD finite volume scheme on multidimensional unstructured meshes for hydrodynamics

    NASA Astrophysics Data System (ADS)

    Boscheri, Walter; Dumbser, Michael; Loubère, Raphaël; Maire, Pierre-Henri

    2018-04-01

    In this paper we develop a conservative cell-centered Lagrangian finite volume scheme for the solution of the hydrodynamics equations on unstructured multidimensional grids. The method is derived from the Eucclhyd scheme discussed in [47,43,45]. It is second-order accurate in space and is combined with the a posteriori Multidimensional Optimal Order Detection (MOOD) limiting strategy to ensure robustness and stability at shock waves. Second-order of accuracy in time is achieved via the ADER (Arbitrary high order schemes using DERivatives) approach. A large set of numerical test cases is proposed to assess the ability of the method to achieve effective second order of accuracy on smooth flows, maintaining an essentially non-oscillatory behavior on discontinuous profiles, general robustness ensuring physical admissibility of the numerical solution, and precision where appropriate.

  2. Positivity-preserving numerical schemes for multidimensional advection

    NASA Technical Reports Server (NTRS)

    Leonard, B. P.; Macvean, M. K.; Lock, A. P.

    1993-01-01

    This report describes the construction of an explicit, single time-step, conservative, finite-volume method for multidimensional advective flow, based on a uniformly third-order polynomial interpolation algorithm (UTOPIA). Particular attention is paid to the problem of flow-to-grid angle-dependent, anisotropic distortion typical of one-dimensional schemes used component-wise. The third-order multidimensional scheme automatically includes certain cross-difference terms that guarantee good isotropy (and stability). However, above first-order, polynomial-based advection schemes do not preserve positivity (the multidimensional analogue of monotonicity). For this reason, a multidimensional generalization of the first author's universal flux-limiter is sought. This is a very challenging problem. A simple flux-limiter can be found; but this introduces strong anisotropic distortion. A more sophisticated technique, limiting part of the flux and then restoring the isotropy-maintaining cross-terms afterwards, gives more satisfactory results. Test cases are confined to two dimensions; three-dimensional extensions are briefly discussed.

  3. Non-hydrostatic semi-elastic hybrid-coordinate SISL extension of HIRLAM. Part I: numerical scheme

    NASA Astrophysics Data System (ADS)

    Rõõm, Rein; Männik, Aarne; Luhamaa, Andres

    2007-10-01

    Two-time-level, semi-implicit, semi-Lagrangian (SISL) scheme is applied to the non-hydrostatic pressure coordinate equations, constituting a modified Miller-Pearce-White model, in hybrid-coordinate framework. Neutral background is subtracted in the initial continuous dynamics, yielding modified equations for geopotential, temperature and logarithmic surface pressure fluctuation. Implicit Lagrangian marching formulae for single time-step are derived. A disclosure scheme is presented, which results in an uncoupled diagnostic system, consisting of 3-D Poisson equation for omega velocity and 2-D Helmholtz equation for logarithmic pressure fluctuation. The model is discretized to create a non-hydrostatic extension to numerical weather prediction model HIRLAM. The discretization schemes, trajectory computation algorithms and interpolation routines, as well as the physical parametrization package are maintained from parent hydrostatic HIRLAM. For stability investigation, the derived SISL model is linearized with respect to the initial, thermally non-equilibrium resting state. Explicit residuals of the linear model prove to be sensitive to the relative departures of temperature and static stability from the reference state. Relayed on the stability study, the semi-implicit term in the vertical momentum equation is replaced to the implicit term, which results in stability increase of the model.

  4. Numerically pricing American options under the generalized mixed fractional Brownian motion model

    NASA Astrophysics Data System (ADS)

    Chen, Wenting; Yan, Bowen; Lian, Guanghua; Zhang, Ying

    2016-06-01

    In this paper, we introduce a robust numerical method, based on the upwind scheme, for the pricing of American puts under the generalized mixed fractional Brownian motion (GMFBM) model. By using portfolio analysis and applying the Wick-Itô formula, a partial differential equation (PDE) governing the prices of vanilla options under the GMFBM is successfully derived for the first time. Based on this, we formulate the pricing of American puts under the current model as a linear complementarity problem (LCP). Unlike the classical Black-Scholes (B-S) model or the generalized B-S model discussed in Cen and Le (2011), the newly obtained LCP under the GMFBM model is difficult to be solved accurately because of the numerical instability which results from the degeneration of the governing PDE as time approaches zero. To overcome this difficulty, a numerical approach based on the upwind scheme is adopted. It is shown that the coefficient matrix of the current method is an M-matrix, which ensures its stability in the maximum-norm sense. Remarkably, we have managed to provide a sharp theoretic error estimate for the current method, which is further verified numerically. The results of various numerical experiments also suggest that this new approach is quite accurate, and can be easily extended to price other types of financial derivatives with an American-style exercise feature under the GMFBM model.

  5. Numerical algorithm comparison for the accurate and efficient computation of high-incidence vortical flow

    NASA Technical Reports Server (NTRS)

    Chaderjian, Neal M.

    1991-01-01

    Computations from two Navier-Stokes codes, NSS and F3D, are presented for a tangent-ogive-cylinder body at high angle of attack. Features of this steady flow include a pair of primary vortices on the leeward side of the body as well as secondary vortices. The topological and physical plausibility of this vortical structure is discussed. The accuracy of these codes are assessed by comparison of the numerical solutions with experimental data. The effects of turbulence model, numerical dissipation, and grid refinement are presented. The overall efficiency of these codes are also assessed by examining their convergence rates, computational time per time step, and maximum allowable time step for time-accurate computations. Overall, the numerical results from both codes compared equally well with experimental data, however, the NSS code was found to be significantly more efficient than the F3D code.

  6. Variationally consistent discretization schemes and numerical algorithms for contact problems

    NASA Astrophysics Data System (ADS)

    Wohlmuth, Barbara

    We consider variationally consistent discretization schemes for mechanical contact problems. Most of the results can also be applied to other variational inequalities, such as those for phase transition problems in porous media, for plasticity or for option pricing applications from finance. The starting point is to weakly incorporate the constraint into the setting and to reformulate the inequality in the displacement in terms of a saddle-point problem. Here, the Lagrange multiplier represents the surface forces, and the constraints are restricted to the boundary of the simulation domain. Having a uniform inf-sup bound, one can then establish optimal low-order a priori convergence rates for the discretization error in the primal and dual variables. In addition to the abstract framework of linear saddle-point theory, complementarity terms have to be taken into account. The resulting inequality system is solved by rewriting it equivalently by means of the non-linear complementarity function as a system of equations. Although it is not differentiable in the classical sense, semi-smooth Newton methods, yielding super-linear convergence rates, can be applied and easily implemented in terms of a primal-dual active set strategy. Quite often the solution of contact problems has a low regularity, and the efficiency of the approach can be improved by using adaptive refinement techniques. Different standard types, such as residual- and equilibrated-based a posteriori error estimators, can be designed based on the interpretation of the dual variable as Neumann boundary condition. For the fully dynamic setting it is of interest to apply energy-preserving time-integration schemes. However, the differential algebraic character of the system can result in high oscillations if standard methods are applied. A possible remedy is to modify the fully discretized system by a local redistribution of the mass. Numerical results in two and three dimensions illustrate the wide range of

  7. Spatial eigensolution analysis of energy-stable flux reconstruction schemes and influence of the numerical flux on accuracy and robustness

    NASA Astrophysics Data System (ADS)

    Mengaldo, Gianmarco; De Grazia, Daniele; Moura, Rodrigo C.; Sherwin, Spencer J.

    2018-04-01

    This study focuses on the dispersion and diffusion characteristics of high-order energy-stable flux reconstruction (ESFR) schemes via the spatial eigensolution analysis framework proposed in [1]. The analysis is performed for five ESFR schemes, where the parameter 'c' dictating the properties of the specific scheme recovered is chosen such that it spans the entire class of ESFR methods, also referred to as VCJH schemes, proposed in [2]. In particular, we used five values of 'c', two that correspond to its lower and upper bounds and the others that identify three schemes that are linked to common high-order methods, namely the ESFR recovering two versions of discontinuous Galerkin methods and one recovering the spectral difference scheme. The performance of each scheme is assessed when using different numerical intercell fluxes (e.g. different levels of upwinding), ranging from "under-" to "over-upwinding". In contrast to the more common temporal analysis, the spatial eigensolution analysis framework adopted here allows one to grasp crucial insights into the diffusion and dispersion properties of FR schemes for problems involving non-periodic boundary conditions, typically found in open-flow problems, including turbulence, unsteady aerodynamics and aeroacoustics.

  8. Numerical Speed of Sound and its Application to Schemes for all Speeds

    NASA Technical Reports Server (NTRS)

    Liou, Meng-Sing; Edwards, Jack R.

    1999-01-01

    The concept of "numerical speed of sound" is proposed in the construction of numerical flux. It is shown that this variable is responsible for the accurate resolution of' discontinuities, such as contacts and shocks. Moreover, this concept can he readily extended to deal with low speed and multiphase flows. As a results, the numerical dissipation for low speed flows is scaled with the local fluid speed, rather than the sound speed. Hence, the accuracy is enhanced the correct solution recovered, and the convergence rate improved. We also emphasize the role of mass flux and analyze the behavior of this flux. Study of mass flux is important because the numerical diffusivity introduced in it can be identified. In addition, it is the term common to all conservation equations. We show calculated results for a wide variety of flows to validate the effectiveness of using the numerical speed of sound concept in constructing the numerical flux. We especially aim at achieving these two goals: (1) improving accuracy and (2) gaining convergence rates for all speed ranges. We find that while the performance at high speed range is maintained, the flux now has the capability of performing well even with the low: speed flows. Thanks to the new numerical speed of sound, the convergence is even enhanced for the flows outside of the low speed range. To realize the usefulness of the proposed method in engineering problems, we have also performed calculations for complex 3D turbulent flows and the results are in excellent agreement with data.

  9. Final Report for''Numerical Methods and Studies of High-Speed Reactive and Non-Reactive Flows''

    DOE Office of Scientific and Technical Information (OSTI.GOV)

    Schwendeman, D W

    2002-11-20

    The work carried out under this subcontract involved the development and use of an adaptive numerical method for the accurate calculation of high-speed reactive flows on overlapping grids. The flow is modeled by the reactive Euler equations with an assumed equation of state and with various reaction rate models. A numerical method has been developed to solve the nonlinear hyperbolic partial differential equations in the model. The method uses an unsplit, shock-capturing scheme, and uses a Godunov-type scheme to compute fluxes and a Runge-Kutta error control scheme to compute the source term modeling the chemical reactions. An adaptive mesh refinementmore » (AMR) scheme has been implemented in order to locally increase grid resolution. The numerical method uses composite overlapping grids to handle complex flow geometries. The code is part of the ''Overture-OverBlown'' framework of object-oriented codes [1, 2], and the development has occurred in close collaboration with Bill Henshaw and David Brown, and other members of the Overture team within CASC. During the period of this subcontract, a number of tasks were accomplished, including: (1) an extension of the numerical method to handle ''ignition and grow'' reaction models and a JWL equations of state; (2) an improvement in the efficiency of the AMR scheme and the error estimator; (3) an addition of a scheme of numerical dissipation designed to suppress numerical oscillations/instabilities near expanding detonations and along grid overlaps; and (4) an exploration of the evolution to detonation in an annulus and of detonation failure in an expanding channel.« less

  10. Comparison of the AUSM(+) and H-CUSP Schemes for Turbomachinery Applications

    NASA Technical Reports Server (NTRS)

    Chima, Rodrick V.; Liou, Meng-Sing

    2003-01-01

    Many turbomachinery CFD codes use second-order central-difference (C-D) schemes with artificial viscosity to control point decoupling and to capture shocks. While C-D schemes generally give accurate results, they can also exhibit minor numerical problems including overshoots at shocks and at the edges of viscous layers, and smearing of shocks and other flow features. In an effort to improve predictive capability for turbomachinery problems, two C-D codes developed by Chima, RVCQ3D and Swift, were modified by the addition of two upwind schemes: the AUSM+ scheme developed by Liou, et al., and the H-CUSP scheme developed by Tatsumi, et al. Details of the C-D scheme and the two upwind schemes are described, and results of three test cases are shown. Results for a 2-D transonic turbine vane showed that the upwind schemes eliminated viscous layer overshoots. Results for a 3-D turbine vane showed that the upwind schemes gave improved predictions of exit flow angles and losses, although the HCUSP scheme predicted slightly higher losses than the other schemes. Results for a 3-D supersonic compressor (NASA rotor 37) showed that the AUSM+ scheme predicted exit distributions of total pressure and temperature that are not generally captured by C-D codes. All schemes showed similar convergence rates, but the upwind schemes required considerably more CPU time per iteration.

  11. A new hybrid-Lagrangian numerical scheme for gyrokinetic simulation of tokamak edge plasma

    DOE PAGES

    Ku, S.; Hager, R.; Chang, C. S.; ...

    2016-04-01

    In order to enable kinetic simulation of non-thermal edge plasmas at a reduced computational cost, a new hybrid-Lagrangian δf scheme has been developed that utilizes the phase space grid in addition to the usual marker particles, taking advantage of the computational strengths from both sides. The new scheme splits the particle distribution function of a kinetic equation into two parts. Marker particles contain the fast space-time varying, δf, part of the distribution function and the coarse-grained phase-space grid contains the slow space-time varying part. The coarse-grained phase-space grid reduces the memory-requirement and the computing cost, while the marker particles providemore » scalable computing ability for the fine-grained physics. Weights of the marker particles are determined by a direct weight evolution equation instead of the differential form weight evolution equations that the conventional delta-f schemes use. The particle weight can be slowly transferred to the phase space grid, thereby reducing the growth of the particle weights. The non-Lagrangian part of the kinetic equation – e.g., collision operation, ionization, charge exchange, heat-source, radiative cooling, and others – can be operated directly on the phase space grid. Deviation of the particle distribution function on the velocity grid from a Maxwellian distribution function – driven by ionization, charge exchange and wall loss – is allowed to be arbitrarily large. In conclusion, the numerical scheme is implemented in the gyrokinetic particle code XGC1, which specializes in simulating the tokamak edge plasma that crosses the magnetic separatrix and is in contact with the material wall.« less

  12. A new hybrid-Lagrangian numerical scheme for gyrokinetic simulation of tokamak edge plasma

    DOE Office of Scientific and Technical Information (OSTI.GOV)

    Ku, S.; Hager, R.; Chang, C. S.

    In order to enable kinetic simulation of non-thermal edge plasmas at a reduced computational cost, a new hybrid-Lagrangian δf scheme has been developed that utilizes the phase space grid in addition to the usual marker particles, taking advantage of the computational strengths from both sides. The new scheme splits the particle distribution function of a kinetic equation into two parts. Marker particles contain the fast space-time varying, δf, part of the distribution function and the coarse-grained phase-space grid contains the slow space-time varying part. The coarse-grained phase-space grid reduces the memory-requirement and the computing cost, while the marker particles providemore » scalable computing ability for the fine-grained physics. Weights of the marker particles are determined by a direct weight evolution equation instead of the differential form weight evolution equations that the conventional delta-f schemes use. The particle weight can be slowly transferred to the phase space grid, thereby reducing the growth of the particle weights. The non-Lagrangian part of the kinetic equation – e.g., collision operation, ionization, charge exchange, heat-source, radiative cooling, and others – can be operated directly on the phase space grid. Deviation of the particle distribution function on the velocity grid from a Maxwellian distribution function – driven by ionization, charge exchange and wall loss – is allowed to be arbitrarily large. In conclusion, the numerical scheme is implemented in the gyrokinetic particle code XGC1, which specializes in simulating the tokamak edge plasma that crosses the magnetic separatrix and is in contact with the material wall.« less

  13. A new hybrid-Lagrangian numerical scheme for gyrokinetic simulation of tokamak edge plasma

    DOE Office of Scientific and Technical Information (OSTI.GOV)

    Ku, S., E-mail: sku@pppl.gov; Hager, R.; Chang, C.S.

    In order to enable kinetic simulation of non-thermal edge plasmas at a reduced computational cost, a new hybrid-Lagrangian δf scheme has been developed that utilizes the phase space grid in addition to the usual marker particles, taking advantage of the computational strengths from both sides. The new scheme splits the particle distribution function of a kinetic equation into two parts. Marker particles contain the fast space-time varying, δf, part of the distribution function and the coarse-grained phase-space grid contains the slow space-time varying part. The coarse-grained phase-space grid reduces the memory-requirement and the computing cost, while the marker particles providemore » scalable computing ability for the fine-grained physics. Weights of the marker particles are determined by a direct weight evolution equation instead of the differential form weight evolution equations that the conventional delta-f schemes use. The particle weight can be slowly transferred to the phase space grid, thereby reducing the growth of the particle weights. The non-Lagrangian part of the kinetic equation – e.g., collision operation, ionization, charge exchange, heat-source, radiative cooling, and others – can be operated directly on the phase space grid. Deviation of the particle distribution function on the velocity grid from a Maxwellian distribution function – driven by ionization, charge exchange and wall loss – is allowed to be arbitrarily large. The numerical scheme is implemented in the gyrokinetic particle code XGC1, which specializes in simulating the tokamak edge plasma that crosses the magnetic separatrix and is in contact with the material wall.« less

  14. Numerical simulation of steady and unsteady viscous flow in turbomachinery using pressure based algorithm

    NASA Astrophysics Data System (ADS)

    Lakshminarayana, B.; Ho, Y.; Basson, A.

    1993-07-01

    The objective of this research is to simulate steady and unsteady viscous flows, including rotor/stator interaction and tip clearance effects in turbomachinery. The numerical formulation for steady flow developed here includes an efficient grid generation scheme, particularly suited to computational grids for the analysis of turbulent turbomachinery flows and tip clearance flows, and a semi-implicit, pressure-based computational fluid dynamics scheme that directly includes artificial dissipation, and is applicable to both viscous and inviscid flows. The values of these artificial dissipation is optimized to achieve accuracy and convergency in the solution. The numerical model is used to investigate the structure of tip clearance flows in a turbine nozzle. The structure of leakage flow is captured accurately, including blade-to-blade variation of all three velocity components, pitch and yaw angles, losses and blade static pressures in the tip clearance region. The simulation also includes evaluation of such quantities of leakage mass flow, vortex strength, losses, dominant leakage flow regions and the spanwise extent affected by the leakage flow. It is demonstrated, through optimization of grid size and artificial dissipation, that the tip clearance flow field can be captured accurately. The above numerical formulation was modified to incorporate time accurate solutions. An inner loop iteration scheme is used at each time step to account for the non-linear effects. The computation of unsteady flow through a flat plate cascade subjected to a transverse gust reveals that the choice of grid spacing and the amount of artificial dissipation is critical for accurate prediction of unsteady phenomena. The rotor-stator interaction problem is simulated by starting the computation upstream of the stator, and the upstream rotor wake is specified from the experimental data. The results show that the stator potential effects have appreciable influence on the upstream rotor wake

  15. Performance of Low Dissipative High Order Shock-Capturing Schemes for Shock-Turbulence Interactions

    NASA Technical Reports Server (NTRS)

    Sandham, N. D.; Yee, H. C.

    1998-01-01

    Accurate and efficient direct numerical simulation of turbulence in the presence of shock waves represents a significant challenge for numerical methods. The objective of this paper is to evaluate the performance of high order compact and non-compact central spatial differencing employing total variation diminishing (TVD) shock-capturing dissipations as characteristic based filters for two model problems combining shock wave and shear layer phenomena. A vortex pairing model evaluates the ability of the schemes to cope with shear layer instability and eddy shock waves, while a shock wave impingement on a spatially-evolving mixing layer model studies the accuracy of computation of vortices passing through a sequence of shock and expansion waves. A drastic increase in accuracy is observed if a suitable artificial compression formulation is applied to the TVD dissipations. With this modification to the filter step the fourth-order non-compact scheme shows improved results in comparison to second-order methods, while retaining the good shock resolution of the basic TVD scheme. For this characteristic based filter approach, however, the benefits of compact schemes or schemes with higher than fourth order are not sufficient to justify the higher complexity near the boundary and/or the additional computational cost.

  16. A numerical scheme to solve unstable boundary value problems

    NASA Technical Reports Server (NTRS)

    Kalnay Derivas, E.

    1975-01-01

    A new iterative scheme for solving boundary value problems is presented. It consists of the introduction of an artificial time dependence into a modified version of the system of equations. Then explicit forward integrations in time are followed by explicit integrations backwards in time. The method converges under much more general conditions than schemes based in forward time integrations (false transient schemes). In particular it can attain a steady state solution of an elliptical system of equations even if the solution is unstable, in which case other iterative schemes fail to converge. The simplicity of its use makes it attractive for solving large systems of nonlinear equations.

  17. Recommendations for Achieving Accurate Numerical Simulation of Tip Clearance Flows in Transonic Compressor Rotors

    NASA Technical Reports Server (NTRS)

    VanZante, Dale E.; Strazisar, Anthony J.; Wood, Jerry R,; Hathaway, Michael D.; Okiishi, Theodore H.

    2000-01-01

    The tip clearance flows of transonic compressor rotors are important because they have a significant impact on rotor and stage performance. While numerical simulations of these flows are quite sophisticated. they are seldom verified through rigorous comparisons of numerical and measured data because these kinds of measurements are rare in the detail necessary to be useful in high-speed machines. In this paper we compare measured tip clearance flow details (e.g. trajectory and radial extent) with corresponding data obtained from a numerical simulation. Recommendations for achieving accurate numerical simulation of tip clearance flows are presented based on this comparison. Laser Doppler Velocimeter (LDV) measurements acquired in a transonic compressor rotor, NASA Rotor 35, are used. The tip clearance flow field of this transonic rotor was simulated using a Navier-Stokes turbomachinery solver that incorporates an advanced k-epsilon turbulence model derived for flows that are not in local equilibrium. Comparison between measured and simulated results indicates that simulation accuracy is primarily dependent upon the ability of the numerical code to resolve important details of a wall-bounded shear layer formed by the relative motion between the over-tip leakage flow and the shroud wall. A simple method is presented for determining the strength of this shear layer.

  18. Protostellar hydrodynamics: Constructing and testing a spacially and temporally second-order accurate method. 2: Cartesian coordinates

    NASA Technical Reports Server (NTRS)

    Myhill, Elizabeth A.; Boss, Alan P.

    1993-01-01

    In Boss & Myhill (1992) we described the derivation and testing of a spherical coordinate-based scheme for solving the hydrodynamic equations governing the gravitational collapse of nonisothermal, nonmagnetic, inviscid, radiative, three-dimensional protostellar clouds. Here we discuss a Cartesian coordinate-based scheme based on the same set of hydrodynamic equations. As with the spherical coorrdinate-based code, the Cartesian coordinate-based scheme employs explicit Eulerian methods which are both spatially and temporally second-order accurate. We begin by describing the hydrodynamic equations in Cartesian coordinates and the numerical methods used in this particular code. Following Finn & Hawley (1989), we pay special attention to the proper implementations of high-order accuracy, finite difference methods. We evaluate the ability of the Cartesian scheme to handle shock propagation problems, and through convergence testing, we show that the code is indeed second-order accurate. To compare the Cartesian scheme discussed here with the spherical coordinate-based scheme discussed in Boss & Myhill (1992), the two codes are used to calculate the standard isothermal collapse test case described by Bodenheimer & Boss (1981). We find that with the improved codes, the intermediate bar-configuration found previously disappears, and the cloud fragments directly into a binary protostellar system. Finally, we present the results from both codes of a new test for nonisothermal protostellar collapse.

  19. Local finite element enrichment strategies for 2D contact computations and a corresponding post-processing scheme

    NASA Astrophysics Data System (ADS)

    Sauer, Roger A.

    2013-08-01

    Recently an enriched contact finite element formulation has been developed that substantially increases the accuracy of contact computations while keeping the additional numerical effort at a minimum reported by Sauer (Int J Numer Meth Eng, 87: 593-616, 2011). Two enrich-ment strategies were proposed, one based on local p-refinement using Lagrange interpolation and one based on Hermite interpolation that produces C 1-smoothness on the contact surface. Both classes, which were initially considered for the frictionless Signorini problem, are extended here to friction and contact between deformable bodies. For this, a symmetric contact formulation is used that allows the unbiased treatment of both contact partners. This paper also proposes a post-processing scheme for contact quantities like the contact pressure. The scheme, which provides a more accurate representation than the raw data, is based on an averaging procedure that is inspired by mortar formulations. The properties of the enrichment strategies and the corresponding post-processing scheme are illustrated by several numerical examples considering sliding and peeling contact in the presence of large deformations.

  20. High-Order Hyperbolic Residual-Distribution Schemes on Arbitrary Triangular Grids

    NASA Technical Reports Server (NTRS)

    Mazaheri, Alireza; Nishikawa, Hiroaki

    2015-01-01

    In this paper, we construct high-order hyperbolic residual-distribution schemes for general advection-diffusion problems on arbitrary triangular grids. We demonstrate that the second-order accuracy of the hyperbolic schemes can be greatly improved by requiring the scheme to preserve exact quadratic solutions. We also show that the improved second-order scheme can be easily extended to third-order by further requiring the exactness for cubic solutions. We construct these schemes based on the LDA and the SUPG methodology formulated in the framework of the residual-distribution method. For both second- and third-order-schemes, we construct a fully implicit solver by the exact residual Jacobian of the second-order scheme, and demonstrate rapid convergence of 10-15 iterations to reduce the residuals by 10 orders of magnitude. We demonstrate also that these schemes can be constructed based on a separate treatment of the advective and diffusive terms, which paves the way for the construction of hyperbolic residual-distribution schemes for the compressible Navier-Stokes equations. Numerical results show that these schemes produce exceptionally accurate and smooth solution gradients on highly skewed and anisotropic triangular grids, including curved boundary problems, using linear elements. We also present Fourier analysis performed on the constructed linear system and show that an under-relaxation parameter is needed for stabilization of Gauss-Seidel relaxation.

  1. Given a one-step numerical scheme, on which ordinary differential equations is it exact?

    NASA Astrophysics Data System (ADS)

    Villatoro, Francisco R.

    2009-01-01

    A necessary condition for a (non-autonomous) ordinary differential equation to be exactly solved by a one-step, finite difference method is that the principal term of its local truncation error be null. A procedure to determine some ordinary differential equations exactly solved by a given numerical scheme is developed. Examples of differential equations exactly solved by the explicit Euler, implicit Euler, trapezoidal rule, second-order Taylor, third-order Taylor, van Niekerk's second-order rational, and van Niekerk's third-order rational methods are presented.

  2. A third-order moving mesh cell-centered scheme for one-dimensional elastic-plastic flows

    NASA Astrophysics Data System (ADS)

    Cheng, Jun-Bo; Huang, Weizhang; Jiang, Song; Tian, Baolin

    2017-11-01

    A third-order moving mesh cell-centered scheme without the remapping of physical variables is developed for the numerical solution of one-dimensional elastic-plastic flows with the Mie-Grüneisen equation of state, the Wilkins constitutive model, and the von Mises yielding criterion. The scheme combines the Lagrangian method with the MMPDE moving mesh method and adaptively moves the mesh to better resolve shock and other types of waves while preventing the mesh from crossing and tangling. It can be viewed as a direct arbitrarily Lagrangian-Eulerian method but can also be degenerated to a purely Lagrangian scheme. It treats the relative velocity of the fluid with respect to the mesh as constant in time between time steps, which allows high-order approximation of free boundaries. A time dependent scaling is used in the monitor function to avoid possible sudden movement of the mesh points due to the creation or diminishing of shock and rarefaction waves or the steepening of those waves. A two-rarefaction Riemann solver with elastic waves is employed to compute the Godunov values of the density, pressure, velocity, and deviatoric stress at cell interfaces. Numerical results are presented for three examples. The third-order convergence of the scheme and its ability to concentrate mesh points around shock and elastic rarefaction waves are demonstrated. The obtained numerical results are in good agreement with those in literature. The new scheme is also shown to be more accurate in resolving shock and rarefaction waves than an existing third-order cell-centered Lagrangian scheme.

  3. An improved bounded semi-Lagrangian scheme for the turbulent transport of passive scalars

    NASA Astrophysics Data System (ADS)

    Verma, Siddhartha; Xuan, Y.; Blanquart, G.

    2014-09-01

    An improved bounded semi-Lagrangian scalar transport scheme based on cubic Hermite polynomial reconstruction is proposed in this paper. Boundedness of the scalar being transported is ensured by applying derivative limiting techniques. Single sub-cell extrema are allowed to exist as they are often physical, and help minimize numerical dissipation. This treatment is distinct from enforcing strict monotonicity as done by D.L. Williamson and P.J. Rasch [5], and allows better preservation of small scale structures in turbulent simulations. The proposed bounding algorithm, although a seemingly subtle difference from strict monotonicity enforcement, is shown to result in significant performance gain in laminar cases, and in three-dimensional turbulent mixing layers. The scheme satisfies several important properties, including boundedness, low numerical diffusion, and high accuracy. Performance gain in the turbulent case is assessed by comparing scalar energy and dissipation spectra produced by several bounded and unbounded schemes. The results indicate that the proposed scheme is capable of furnishing extremely accurate results, with less severe resolution requirements than all the other bounded schemes tested. Additional simulations in homogeneous isotropic turbulence, with scalar timestep size unconstrained by the CFL number, show good agreement with spectral scheme results available in the literature. Detailed analytical examination of gain and phase error characteristics of the original cubic Hermite polynomial is also included, and points to dissipation and dispersion characteristics comparable to, or better than, those of a fifth order upwind Eulerian scheme.

  4. A numerical scheme for singularly perturbed reaction-diffusion problems with a negative shift via numerov method

    NASA Astrophysics Data System (ADS)

    Dinesh Kumar, S.; Nageshwar Rao, R.; Pramod Chakravarthy, P.

    2017-11-01

    In this paper, we consider a boundary value problem for a singularly perturbed delay differential equation of reaction-diffusion type. We construct an exponentially fitted numerical method using Numerov finite difference scheme, which resolves not only the boundary layers but also the interior layers arising from the delay term. An extensive amount of computational work has been carried out to demonstrate the applicability of the proposed method.

  5. Incorporation of a Cumulus Fraction Scheme in the GRAPES_Meso and Evaluation of Its Performance

    NASA Astrophysics Data System (ADS)

    Zheng, X.

    2016-12-01

    Accurate simulation of cloud cover fraction is a key and difficult issue in numerical modeling studies. Preliminary evaluations have indicated that cloud fraction is generally underestimated in GRAPES_Meso simulations, while the cloud fraction scheme (CFS) of ECMWF can provide more realistic results. Therefore, the ECMWF cumulus fraction scheme is introduced into GRAPES_Meso to replace the original CFS, and the model performance with the new CFS is evaluated based on simulated three-dimensional cloud fractions and surface temperature. Results indicate that the simulated cloud fractions increase and become more accurate with the new CFS; the simulation for vertical cloud structure has improved too; errors in surface temperature simulation have decreased. The above analysis and results suggest that the new CFS has a positive impact on cloud fraction and surface temperature simulation.

  6. A simple algorithm to improve the performance of the WENO scheme on non-uniform grids

    NASA Astrophysics Data System (ADS)

    Huang, Wen-Feng; Ren, Yu-Xin; Jiang, Xiong

    2018-02-01

    This paper presents a simple approach for improving the performance of the weighted essentially non-oscillatory (WENO) finite volume scheme on non-uniform grids. This technique relies on the reformulation of the fifth-order WENO-JS (WENO scheme presented by Jiang and Shu in J. Comput. Phys. 126:202-228, 1995) scheme designed on uniform grids in terms of one cell-averaged value and its left and/or right interfacial values of the dependent variable. The effect of grid non-uniformity is taken into consideration by a proper interpolation of the interfacial values. On non-uniform grids, the proposed scheme is much more accurate than the original WENO-JS scheme, which was designed for uniform grids. When the grid is uniform, the resulting scheme reduces to the original WENO-JS scheme. In the meantime, the proposed scheme is computationally much more efficient than the fifth-order WENO scheme designed specifically for the non-uniform grids. A number of numerical test cases are simulated to verify the performance of the present scheme.

  7. LES of Temporally Evolving Mixing Layers by Three High Order Schemes

    NASA Astrophysics Data System (ADS)

    Yee, H.; Sjögreen, B.; Hadjadj, A.

    2011-10-01

    The performance of three high order shock-capturing schemes is compared for large eddy simulations (LES) of temporally evolving mixing layers for different convective Mach number (Mc) ranging from the quasi-incompressible regime to highly compressible supersonic regime. The considered high order schemes are fifth-order WENO (WENO5), seventh-order WENO (WENO7), and the associated eighth-order central spatial base scheme with the dissipative portion of WENO7 as a nonlinear post-processing filter step (WENO7fi). This high order nonlinear filter method (Yee & Sjögreen 2009) is designed for accurate and efficient simulations of shock-free compressible turbulence, turbulence with shocklets and turbulence with strong shocks with minimum tuning of scheme parameters. The LES results by WENO7fi using the same scheme parameter agree well with experimental results of Barone et al. (2006), and published direct numerical simulations (DNS) by Rogers & Moser (1994) and Pantano & Sarkar (2002), whereas results by WENO5 and WENO7 compare poorly with experimental data and DNS computations.

  8. HARM: A Numerical Scheme for General Relativistic Magnetohydrodynamics

    NASA Astrophysics Data System (ADS)

    Gammie, Charles, F.; McKinney, Jonathan C.; Tóth, Gábor

    2012-09-01

    HARM uses a conservative, shock-capturing scheme for evolving the equations of general relativistic magnetohydrodynamics. The fluxes are calculated using the Harten, Lax, & van Leer scheme. A variant of constrained transport, proposed earlier by Tóth, is used to maintain a divergence-free magnetic field. Only the covariant form of the metric in a coordinate basis is required to specify the geometry. On smooth flows HARM converges at second order.

  9. A numerical scheme to solve unstable boundary value problems

    NASA Technical Reports Server (NTRS)

    Kalnay-Rivas, E.

    1977-01-01

    The considered scheme makes it possible to determine an unstable steady state solution in cases in which, because of lack of symmetry, such a solution cannot be obtained analytically, and other time integration or relaxation schemes, because of instability, fail to converge. The iterative solution of a single complex equation is discussed and a nonlinear system of equations is considered. Described applications of the scheme are related to a steady state solution with shear instability, an unstable nonlinear Ekman boundary layer, and the steady state solution of a baroclinic atmosphere with asymmetric forcing. The scheme makes use of forward and backward time integrations of the original spatial differential operators and of an approximation of the adjoint operators. Only two computations of the time derivative per iteration are required.

  10. Stability of finite difference numerical simulations of acoustic logging-while-drilling with different perfectly matched layer schemes

    NASA Astrophysics Data System (ADS)

    Wang, Hua; Tao, Guo; Shang, Xue-Feng; Fang, Xin-Ding; Burns, Daniel R.

    2013-12-01

    In acoustic logging-while-drilling (ALWD) finite difference in time domain (FDTD) simulations, large drill collar occupies, most of the fluid-filled borehole and divides the borehole fluid into two thin fluid columns (radius ˜27 mm). Fine grids and large computational models are required to model the thin fluid region between the tool and the formation. As a result, small time step and more iterations are needed, which increases the cumulative numerical error. Furthermore, due to high impedance contrast between the drill collar and fluid in the borehole (the difference is >30 times), the stability and efficiency of the perfectly matched layer (PML) scheme is critical to simulate complicated wave modes accurately. In this paper, we compared four different PML implementations in a staggered grid finite difference in time domain (FDTD) in the ALWD simulation, including field-splitting PML (SPML), multiaxial PML(MPML), non-splitting PML (NPML), and complex frequency-shifted PML (CFS-PML). The comparison indicated that NPML and CFS-PML can absorb the guided wave reflection from the computational boundaries more efficiently than SPML and M-PML. For large simulation time, SPML, M-PML, and NPML are numerically unstable. However, the stability of M-PML can be improved further to some extent. Based on the analysis, we proposed that the CFS-PML method is used in FDTD to eliminate the numerical instability and to improve the efficiency of absorption in the PML layers for LWD modeling. The optimal values of CFS-PML parameters in the LWD simulation were investigated based on thousands of 3D simulations. For typical LWD cases, the best maximum value of the quadratic damping profile was obtained using one d 0. The optimal parameter space for the maximum value of the linear frequency-shifted factor ( α 0) and the scaling factor ( β 0) depended on the thickness of the PML layer. For typical formations, if the PML thickness is 10 grid points, the global error can be reduced to <1

  11. Advanced numerical methods for three dimensional two-phase flow calculations

    DOE Office of Scientific and Technical Information (OSTI.GOV)

    Toumi, I.; Caruge, D.

    1997-07-01

    This paper is devoted to new numerical methods developed for both one and three dimensional two-phase flow calculations. These methods are finite volume numerical methods and are based on the use of Approximate Riemann Solvers concepts to define convective fluxes versus mean cell quantities. The first part of the paper presents the numerical method for a one dimensional hyperbolic two-fluid model including differential terms as added mass and interface pressure. This numerical solution scheme makes use of the Riemann problem solution to define backward and forward differencing to approximate spatial derivatives. The construction of this approximate Riemann solver uses anmore » extension of Roe`s method that has been successfully used to solve gas dynamic equations. As far as the two-fluid model is hyperbolic, this numerical method seems very efficient for the numerical solution of two-phase flow problems. The scheme was applied both to shock tube problems and to standard tests for two-fluid computer codes. The second part describes the numerical method in the three dimensional case. The authors discuss also some improvements performed to obtain a fully implicit solution method that provides fast running steady state calculations. Such a scheme is not implemented in a thermal-hydraulic computer code devoted to 3-D steady-state and transient computations. Some results obtained for Pressurised Water Reactors concerning upper plenum calculations and a steady state flow in the core with rod bow effect evaluation are presented. In practice these new numerical methods have proved to be stable on non staggered grids and capable of generating accurate non oscillating solutions for two-phase flow calculations.« less

  12. Comparison of in situ microstructure measurements to different turbulence closure schemes in a 3-D numerical ocean circulation model

    NASA Astrophysics Data System (ADS)

    Costa, Andrea; Doglioli, Andrea M.; Marsaleix, Patrick; Petrenko, Anne A.

    2017-12-01

    In situ measurements of kinetic energy dissipation rate ε and estimates of eddy viscosity KZ from the Gulf of Lion (NW Mediterranean Sea) are used to assess the ability of k - ɛ and k - ℓ closure schemes to predict microscale turbulence in a 3-D numerical ocean circulation model. Two different surface boundary conditions are considered in order to investigate their influence on each closure schemes' performance. The effect of two types of stability functions and optical schemes on the k - ɛ scheme is also explored. Overall, the 3-D model predictions are much closer to the in situ data in the surface mixed layer as opposed to below it. Above the mixed layer depth, we identify one model's configuration that outperforms all the other ones. Such a configuration employs a k - ɛ scheme with Canuto A stability functions, surface boundary conditions parameterizing wave breaking and an appropriate photosynthetically available radiation attenuation length. Below the mixed layer depth, reliability is limited by the model's resolution and the specification of a hard threshold on the minimum turbulent kinetic energy.

  13. Numerically accurate computational techniques for optimal estimator analyses of multi-parameter models

    NASA Astrophysics Data System (ADS)

    Berger, Lukas; Kleinheinz, Konstantin; Attili, Antonio; Bisetti, Fabrizio; Pitsch, Heinz; Mueller, Michael E.

    2018-05-01

    Modelling unclosed terms in partial differential equations typically involves two steps: First, a set of known quantities needs to be specified as input parameters for a model, and second, a specific functional form needs to be defined to model the unclosed terms by the input parameters. Both steps involve a certain modelling error, with the former known as the irreducible error and the latter referred to as the functional error. Typically, only the total modelling error, which is the sum of functional and irreducible error, is assessed, but the concept of the optimal estimator enables the separate analysis of the total and the irreducible errors, yielding a systematic modelling error decomposition. In this work, attention is paid to the techniques themselves required for the practical computation of irreducible errors. Typically, histograms are used for optimal estimator analyses, but this technique is found to add a non-negligible spurious contribution to the irreducible error if models with multiple input parameters are assessed. Thus, the error decomposition of an optimal estimator analysis becomes inaccurate, and misleading conclusions concerning modelling errors may be drawn. In this work, numerically accurate techniques for optimal estimator analyses are identified and a suitable evaluation of irreducible errors is presented. Four different computational techniques are considered: a histogram technique, artificial neural networks, multivariate adaptive regression splines, and an additive model based on a kernel method. For multiple input parameter models, only artificial neural networks and multivariate adaptive regression splines are found to yield satisfactorily accurate results. Beyond a certain number of input parameters, the assessment of models in an optimal estimator analysis even becomes practically infeasible if histograms are used. The optimal estimator analysis in this paper is applied to modelling the filtered soot intermittency in large eddy

  14. A low diffusive Lagrange-remap scheme for the simulation of violent air-water free-surface flows

    NASA Astrophysics Data System (ADS)

    Bernard-Champmartin, Aude; De Vuyst, Florian

    2014-10-01

    In 2002, Després and Lagoutière [17] proposed a low-diffusive advection scheme for pure transport equation problems, which is particularly accurate for step-shaped solutions, and thus suited for interface tracking procedure by a color function. This has been extended by Kokh and Lagoutière [28] in the context of compressible multifluid flows using a five-equation model. In this paper, we explore a simplified variant approach for gas-liquid three-equation models. The Eulerian numerical scheme has two ingredients: a robust remapped Lagrange solver for the solution of the volume-averaged equations, and a low diffusive compressive scheme for the advection of the gas mass fraction. Numerical experiments show the performance of the computational approach on various flow reference problems: dam break, sloshing of a tank filled with water, water-water impact and finally a case of Rayleigh-Taylor instability. One of the advantages of the present interface capturing solver is its natural implementation on parallel processors or computers.

  15. Single-cone finite-difference schemes for the (2+1)-dimensional Dirac equation in general electromagnetic textures

    NASA Astrophysics Data System (ADS)

    Pötz, Walter

    2017-11-01

    A single-cone finite-difference lattice scheme is developed for the (2+1)-dimensional Dirac equation in presence of general electromagnetic textures. The latter is represented on a (2+1)-dimensional staggered grid using a second-order-accurate finite difference scheme. A Peierls-Schwinger substitution to the wave function is used to introduce the electromagnetic (vector) potential into the Dirac equation. Thereby, the single-cone energy dispersion and gauge invariance are carried over from the continuum to the lattice formulation. Conservation laws and stability properties of the formal scheme are identified by comparison with the scheme for zero vector potential. The placement of magnetization terms is inferred from consistency with the one for the vector potential. Based on this formal scheme, several numerical schemes are proposed and tested. Elementary examples for single-fermion transport in the presence of in-plane magnetization are given, using material parameters typical for topological insulator surfaces.

  16. Numerical Boundary Conditions for Computational Aeroacoustics Benchmark Problems

    NASA Technical Reports Server (NTRS)

    Tam, Chritsopher K. W.; Kurbatskii, Konstantin A.; Fang, Jun

    1997-01-01

    Category 1, Problems 1 and 2, Category 2, Problem 2, and Category 3, Problem 2 are solved computationally using the Dispersion-Relation-Preserving (DRP) scheme. All these problems are governed by the linearized Euler equations. The resolution requirements of the DRP scheme for maintaining low numerical dispersion and dissipation as well as accurate wave speeds in solving the linearized Euler equations are now well understood. As long as 8 or more mesh points per wavelength is employed in the numerical computation, high quality results are assured. For the first three categories of benchmark problems, therefore, the real challenge is to develop high quality numerical boundary conditions. For Category 1, Problems 1 and 2, it is the curved wall boundary conditions. For Category 2, Problem 2, it is the internal radiation boundary conditions inside the duct. For Category 3, Problem 2, they are the inflow and outflow boundary conditions upstream and downstream of the blade row. These are the foci of the present investigation. Special nonhomogeneous radiation boundary conditions that generate the incoming disturbances and at the same time allow the outgoing reflected or scattered acoustic disturbances to leave the computation domain without significant reflection are developed. Numerical results based on these boundary conditions are provided.

  17. Development of a discrete gas-kinetic scheme for simulation of two-dimensional viscous incompressible and compressible flows.

    PubMed

    Yang, L M; Shu, C; Wang, Y

    2016-03-01

    In this work, a discrete gas-kinetic scheme (DGKS) is presented for simulation of two-dimensional viscous incompressible and compressible flows. This scheme is developed from the circular function-based GKS, which was recently proposed by Shu and his co-workers [L. M. Yang, C. Shu, and J. Wu, J. Comput. Phys. 274, 611 (2014)]. For the circular function-based GKS, the integrals for conservation forms of moments in the infinity domain for the Maxwellian function-based GKS are simplified to those integrals along the circle. As a result, the explicit formulations of conservative variables and fluxes are derived. However, these explicit formulations of circular function-based GKS for viscous flows are still complicated, which may not be easy for the application by new users. By using certain discrete points to represent the circle in the phase velocity space, the complicated formulations can be replaced by a simple solution process. The basic requirement is that the conservation forms of moments for the circular function-based GKS can be accurately satisfied by weighted summation of distribution functions at discrete points. In this work, it is shown that integral quadrature by four discrete points on the circle, which forms the D2Q4 discrete velocity model, can exactly match the integrals. Numerical results showed that the present scheme can provide accurate numerical results for incompressible and compressible viscous flows with roughly the same computational cost as that needed by the Roe scheme.

  18. Numerical Schemes and Computational Studies for Dynamically Orthogonal Equations (Multidisciplinary Simulation, Estimation, and Assimilation Systems: Reports in Ocean Science and Engineering)

    DTIC Science & Technology

    2011-08-01

    heat transfers [49, 52]. However, the DO method has not yet been applied to Boussinesq flows, and the numerical challenges of the DO decomposition for...used a PCE scheme to study mixing in a two-dimensional (2D) microchannel and improved the efficiency of their solution scheme by decoupling the...to several Navier-Stokes flows and their stochastic dynamics has been studied, including mean-mode and mode-mode energy transfers for 2D flows and

  19. Finite-volume WENO scheme for viscous compressible multicomponent flows

    PubMed Central

    Coralic, Vedran; Colonius, Tim

    2014-01-01

    We develop a shock- and interface-capturing numerical method that is suitable for the simulation of multicomponent flows governed by the compressible Navier-Stokes equations. The numerical method is high-order accurate in smooth regions of the flow, discretely conserves the mass of each component, as well as the total momentum and energy, and is oscillation-free, i.e. it does not introduce spurious oscillations at the locations of shockwaves and/or material interfaces. The method is of Godunov-type and utilizes a fifth-order, finite-volume, weighted essentially non-oscillatory (WENO) scheme for the spatial reconstruction and a Harten-Lax-van Leer contact (HLLC) approximate Riemann solver to upwind the fluxes. A third-order total variation diminishing (TVD) Runge-Kutta (RK) algorithm is employed to march the solution in time. The derivation is generalized to three dimensions and nonuniform Cartesian grids. A two-point, fourth-order, Gaussian quadrature rule is utilized to build the spatial averages of the reconstructed variables inside the cells, as well as at cell boundaries. The algorithm is therefore fourth-order accurate in space and third-order accurate in time in smooth regions of the flow. We corroborate the properties of our numerical method by considering several challenging one-, two- and three-dimensional test cases, the most complex of which is the asymmetric collapse of an air bubble submerged in a cylindrical water cavity that is embedded in 10% gelatin. PMID:25110358

  20. Finite-volume WENO scheme for viscous compressible multicomponent flows.

    PubMed

    Coralic, Vedran; Colonius, Tim

    2014-10-01

    We develop a shock- and interface-capturing numerical method that is suitable for the simulation of multicomponent flows governed by the compressible Navier-Stokes equations. The numerical method is high-order accurate in smooth regions of the flow, discretely conserves the mass of each component, as well as the total momentum and energy, and is oscillation-free, i.e. it does not introduce spurious oscillations at the locations of shockwaves and/or material interfaces. The method is of Godunov-type and utilizes a fifth-order, finite-volume, weighted essentially non-oscillatory (WENO) scheme for the spatial reconstruction and a Harten-Lax-van Leer contact (HLLC) approximate Riemann solver to upwind the fluxes. A third-order total variation diminishing (TVD) Runge-Kutta (RK) algorithm is employed to march the solution in time. The derivation is generalized to three dimensions and nonuniform Cartesian grids. A two-point, fourth-order, Gaussian quadrature rule is utilized to build the spatial averages of the reconstructed variables inside the cells, as well as at cell boundaries. The algorithm is therefore fourth-order accurate in space and third-order accurate in time in smooth regions of the flow. We corroborate the properties of our numerical method by considering several challenging one-, two- and three-dimensional test cases, the most complex of which is the asymmetric collapse of an air bubble submerged in a cylindrical water cavity that is embedded in 10% gelatin.

  1. Field Dislocation Mechanics for heterogeneous elastic materials: A numerical spectral approach

    DOE Office of Scientific and Technical Information (OSTI.GOV)

    Djaka, Komlan Senam; Villani, Aurelien; Taupin, Vincent

    Spectral methods using Fast Fourier Transform (FFT) algorithms have recently seen a surge in interest in the mechanics of materials community. The present work addresses the critical question of determining accurate local mechanical fields using FFT methods without artificial fluctuations arising from materials and defects induced discontinuities. Precisely, this work introduces a numerical approach based on intrinsic discrete Fourier transforms for the simultaneous treatment of material discontinuities arising from the presence of dislocations and from elastic stiffness heterogeneities. To this end, the elasto-static equations of the field dislocation mechanics theory for periodic heterogeneous materials are numerically solved with FFT inmore » the case of dislocations in proximity of inclusions of varying stiffness. An optimal intrinsic discrete Fourier transform method is sought based on two distinct schemes. A centered finite difference scheme for differential rules are used for numerically solving the Poisson-type equation in the Fourier space, while centered finite differences on a rotated grid is chosen for the computation of the modified Fourier–Green’s operator associated with the Lippmann–Schwinger-type equation. By comparing different methods with analytical solutions for an edge dislocation in a composite material, it is found that the present spectral method is accurate, devoid of any numerical oscillation, and efficient even for an infinite phase elastic contrast like a hole embedded in a matrix containing a dislocation. The present FFT method is then used to simulate physical cases such as the elastic fields of dislocation dipoles located near the matrix/inclusion interface in a 2D composite material and the ones due to dislocation loop distributions surrounding cubic inclusions in 3D composite material. In these configurations, the spectral method allows investigating accurately the elastic interactions and image stresses due to dislocation

  2. Field Dislocation Mechanics for heterogeneous elastic materials: A numerical spectral approach

    DOE PAGES

    Djaka, Komlan Senam; Villani, Aurelien; Taupin, Vincent; ...

    2017-03-01

    Spectral methods using Fast Fourier Transform (FFT) algorithms have recently seen a surge in interest in the mechanics of materials community. The present work addresses the critical question of determining accurate local mechanical fields using FFT methods without artificial fluctuations arising from materials and defects induced discontinuities. Precisely, this work introduces a numerical approach based on intrinsic discrete Fourier transforms for the simultaneous treatment of material discontinuities arising from the presence of dislocations and from elastic stiffness heterogeneities. To this end, the elasto-static equations of the field dislocation mechanics theory for periodic heterogeneous materials are numerically solved with FFT inmore » the case of dislocations in proximity of inclusions of varying stiffness. An optimal intrinsic discrete Fourier transform method is sought based on two distinct schemes. A centered finite difference scheme for differential rules are used for numerically solving the Poisson-type equation in the Fourier space, while centered finite differences on a rotated grid is chosen for the computation of the modified Fourier–Green’s operator associated with the Lippmann–Schwinger-type equation. By comparing different methods with analytical solutions for an edge dislocation in a composite material, it is found that the present spectral method is accurate, devoid of any numerical oscillation, and efficient even for an infinite phase elastic contrast like a hole embedded in a matrix containing a dislocation. The present FFT method is then used to simulate physical cases such as the elastic fields of dislocation dipoles located near the matrix/inclusion interface in a 2D composite material and the ones due to dislocation loop distributions surrounding cubic inclusions in 3D composite material. In these configurations, the spectral method allows investigating accurately the elastic interactions and image stresses due to dislocation

  3. A New Cell-Centered Implicit Numerical Scheme for Ions in the 2-D Axisymmetric Code Hall2de

    NASA Technical Reports Server (NTRS)

    Lopez Ortega, Alejandro; Mikellides, Ioannis G.

    2014-01-01

    We present a new algorithm in the Hall2De code to simulate the ion hydrodynamics in the acceleration channel and near plume regions of Hall-effect thrusters. This implementation constitutes an upgrade of the capabilities built in the Hall2De code. The equations of mass conservation and momentum for unmagnetized ions are solved using a conservative, finite-volume, cell-centered scheme on a magnetic-field-aligned grid. Major computational savings are achieved by making use of an implicit predictor/multi-corrector algorithm for time evolution. Inaccuracies in the prediction of the motion of low-energy ions in the near plume in hydrodynamics approaches are addressed by implementing a multi-fluid algorithm that tracks ions of different energies separately. A wide range of comparisons with measurements are performed to validate the new ion algorithms. Several numerical experiments with the location and value of the anomalous collision frequency are also presented. Differences in the plasma properties in the near-plume between the single fluid and multi-fluid approaches are discussed. We complete our validation by comparing predicted erosion rates at the channel walls of the thruster with measurements. Erosion rates predicted by the plasma properties obtained from simulations replicate accurately measured rates of erosion within the uncertainty range of the sputtering models employed.

  4. Numerical simulation of flood inundation using a well-balanced kinetic scheme for the shallow water equations with bulk recharge and discharge

    NASA Astrophysics Data System (ADS)

    Ersoy, Mehmet; Lakkis, Omar; Townsend, Philip

    2016-04-01

    The flow of water in rivers and oceans can, under general assumptions, be efficiently modelled using Saint-Venant's shallow water system of equations (SWE). SWE is a hyperbolic system of conservation laws (HSCL) which can be derived from a starting point of incompressible Navier-Stokes. A common difficulty in the numerical simulation of HSCLs is the conservation of physical entropy. Work by Audusse, Bristeau, Perthame (2000) and Perthame, Simeoni (2001), proposed numerical SWE solvers known as kinetic schemes (KSs), which can be shown to have desirable entropy-consistent properties, and are thus called well-balanced schemes. A KS is derived from kinetic equations that can be integrated into the SWE. In flood risk assessment models the SWE must be coupled with other equations describing interacting meteorological and hydrogeological phenomena such as rain and groundwater flows. The SWE must therefore be appropriately modified to accommodate source and sink terms, so kinetic schemes are no longer valid. While modifications of SWE in this direction have been recently proposed, e.g., Delestre (2010), we depart from the extant literature by proposing a novel model that is "entropy-consistent" and naturally extends the SWE by respecting its kinetic formulation connections. This allows us to derive a system of partial differential equations modelling flow of a one-dimensional river with both a precipitation term and a groundwater flow model to account for potential infiltration and recharge. We exhibit numerical simulations of the corresponding kinetic schemes. These simulations can be applied to both real world flood prediction and the tackling of wider issues on how climate and societal change are affecting flood risk.

  5. TTLEM: Open access tool for building numerically accurate landscape evolution models in MATLAB

    NASA Astrophysics Data System (ADS)

    Campforts, Benjamin; Schwanghart, Wolfgang; Govers, Gerard

    2017-04-01

    Despite a growing interest in LEMs, accuracy assessment of the numerical methods they are based on has received little attention. Here, we present TTLEM which is an open access landscape evolution package designed to develop and test your own scenarios and hypothesises. TTLEM uses a higher order flux-limiting finite-volume method to simulate river incision and tectonic displacement. We show that this scheme significantly influences the evolution of simulated landscapes and the spatial and temporal variability of erosion rates. Moreover, it allows the simulation of lateral tectonic displacement on a fixed grid. Through the use of a simple GUI the software produces visible output of evolving landscapes through model run time. In this contribution, we illustrate numerical landscape evolution through a set of movies spanning different spatial and temporal scales. We focus on the erosional domain and use both spatially constant and variable input values for uplift, lateral tectonic shortening, erodibility and precipitation. Moreover, we illustrate the relevance of a stochastic approach for realistic hillslope response modelling. TTLEM is a fully open source software package, written in MATLAB and based on the TopoToolbox platform (topotoolbox.wordpress.com). Installation instructions can be found on this website and the therefore designed GitHub repository.

  6. Numerical simulation of supersonic and hypersonic inlet flow fields

    NASA Technical Reports Server (NTRS)

    Mcrae, D. Scott; Kontinos, Dean A.

    1995-01-01

    This report summarizes the research performed by North Carolina State University and NASA Ames Research Center under Cooperative Agreement NCA2-719, 'Numerical Simulation of Supersonic and Hypersonic Inlet Flow Fields". Four distinct rotated upwind schemes were developed and investigated to determine accuracy and practicality. The scheme found to have the best combination of attributes, including reduction to grid alignment with no rotation, was the cell centered non-orthogonal (CCNO) scheme. In 2D, the CCNO scheme improved rotation when flux interpolation was extended to second order. In 3D, improvements were less dramatic in all cases, with second order flux interpolation showing the least improvement over grid aligned upwinding. The reduction in improvement is attributed to uncertainty in determining optimum rotation angle and difficulty in performing accurate and efficient interpolation of the angle in 3D. The CCNO rotational technique will prove very useful for increasing accuracy when second order interpolation is not appropriate and will materially improve inlet flow solutions.

  7. Numerical study of the small scale structures in Boussinesq convection

    NASA Technical Reports Server (NTRS)

    Weinan, E.; Shu, Chi-Wang

    1992-01-01

    Two-dimensional Boussinesq convection is studied numerically using two different methods: a filtered pseudospectral method and a high order accurate Essentially Nonoscillatory (ENO) scheme. The issue whether finite time singularity occurs for initially smooth flows is investigated. The numerical results suggest that the collapse of the bubble cap is unlikely to occur in resolved calculations. The strain rate corresponding to the intensification of the density gradient across the front saturates at the bubble cap. We also found that the cascade of energy to small scales is dominated by the formulation of thin and sharp fronts across which density jumps.

  8. Numerical simulation of three-dimensional transonic turbulent projectile aerodynamics by TVD schemes

    NASA Technical Reports Server (NTRS)

    Shiau, Nae-Haur; Hsu, Chen-Chi; Chyu, Wei-Jao

    1989-01-01

    The two-dimensional symmetric TVD scheme proposed by Yee has been extended to and investigated for three-dimensional thin-layer Navier-Stokes simulation of complex aerodynamic problems. An existing three-dimensional Navier-stokes code based on the beam and warming algorithm is modified to provide an option of using the TVD algorithm and the flow problem considered is a transonic turbulent flow past a projectile with sting at ten-degree angle of attack. Numerical experiments conducted for three flow cases, free-stream Mach numbers of 0.91, 0.96 and 1.20 show that the symmetric TVD algorithm can provide surface pressure distribution in excellent agreement with measured data; moreover, the rate of convergence to attain a steady state solution is about two times faster than the original beam and warming algorithm.

  9. Computation of Transonic Nozzle Sound Transmission and Rotor Problems by the Dispersion-Relation-Preserving Scheme

    NASA Technical Reports Server (NTRS)

    Tam, Christopher K. W.; Aganin, Alexei

    2000-01-01

    The transonic nozzle transmission problem and the open rotor noise radiation problem are solved computationally. Both are multiple length scales problems. For efficient and accurate numerical simulation, the multiple-size-mesh multiple-time-step Dispersion-Relation-Preserving scheme is used to calculate the time periodic solution. To ensure an accurate solution, high quality numerical boundary conditions are also needed. For the nozzle problem, a set of nonhomogeneous, outflow boundary conditions are required. The nonhomogeneous boundary conditions not only generate the incoming sound waves but also, at the same time, allow the reflected acoustic waves and entropy waves, if present, to exit the computation domain without reflection. For the open rotor problem, there is an apparent singularity at the axis of rotation. An analytic extension approach is developed to provide a high quality axis boundary treatment.

  10. Numerical schemes for anomalous diffusion of single-phase fluids in porous media

    NASA Astrophysics Data System (ADS)

    Awotunde, Abeeb A.; Ghanam, Ryad A.; Al-Homidan, Suliman S.; Tatar, Nasser-eddine

    2016-10-01

    Simulation of fluid flow in porous media is an indispensable part of oil and gas reservoir management. Accurate prediction of reservoir performance and profitability of investment rely on our ability to model the flow behavior of reservoir fluids. Over the years, numerical reservoir simulation models have been based mainly on solutions to the normal diffusion of fluids in the porous reservoir. Recently, however, it has been documented that fluid flow in porous media does not always follow strictly the normal diffusion process. Small deviations from normal diffusion, called anomalous diffusion, have been reported in some experimental studies. Such deviations can be caused by different factors such as the viscous state of the fluid, the fractal nature of the porous media and the pressure pulse in the system. In this work, we present explicit and implicit numerical solutions to the anomalous diffusion of single-phase fluids in heterogeneous reservoirs. An analytical solution is used to validate the numerical solution to the simple homogeneous case. The conventional wellbore flow model is modified to account for anomalous behavior. Example applications are used to show the behavior of wellbore and wellblock pressures during the single-phase anomalous flow of fluids in the reservoirs considered.

  11. A staggered conservative scheme for every Froude number in rapidly varied shallow water flows

    NASA Astrophysics Data System (ADS)

    Stelling, G. S.; Duinmeijer, S. P. A.

    2003-12-01

    This paper proposes a numerical technique that in essence is based upon the classical staggered grids and implicit numerical integration schemes, but that can be applied to problems that include rapidly varied flows as well. Rapidly varied flows occur, for instance, in hydraulic jumps and bores. Inundation of dry land implies sudden flow transitions due to obstacles such as road banks. Near such transitions the grid resolution is often low compared to the gradients of the bathymetry. In combination with the local invalidity of the hydrostatic pressure assumption, conservation properties become crucial. The scheme described here, combines the efficiency of staggered grids with conservation properties so as to ensure accurate results for rapidly varied flows, as well as in expansions as in contractions. In flow expansions, a numerical approximation is applied that is consistent with the momentum principle. In flow contractions, a numerical approximation is applied that is consistent with the Bernoulli equation. Both approximations are consistent with the shallow water equations, so under sufficiently smooth conditions they converge to the same solution. The resulting method is very efficient for the simulation of large-scale inundations.

  12. Application of Central Upwind Scheme for Solving Special Relativistic Hydrodynamic Equations

    PubMed Central

    Yousaf, Muhammad; Ghaffar, Tayabia; Qamar, Shamsul

    2015-01-01

    The accurate modeling of various features in high energy astrophysical scenarios requires the solution of the Einstein equations together with those of special relativistic hydrodynamics (SRHD). Such models are more complicated than the non-relativistic ones due to the nonlinear relations between the conserved and state variables. A high-resolution shock-capturing central upwind scheme is implemented to solve the given set of equations. The proposed technique uses the precise information of local propagation speeds to avoid the excessive numerical diffusion. The second order accuracy of the scheme is obtained with the use of MUSCL-type initial reconstruction and Runge-Kutta time stepping method. After a discussion of the equations solved and of the techniques employed, a series of one and two-dimensional test problems are carried out. To validate the method and assess its accuracy, the staggered central and the kinetic flux-vector splitting schemes are also applied to the same model. The scheme is robust and efficient. Its results are comparable to those obtained from the sophisticated algorithms, even in the case of highly relativistic two-dimensional test problems. PMID:26070067

  13. Adaptive CFD schemes for aerospace propulsion

    NASA Astrophysics Data System (ADS)

    Ferrero, A.; Larocca, F.

    2017-05-01

    The flow fields which can be observed inside several components of aerospace propulsion systems are characterised by the presence of very localised phenomena (boundary layers, shock waves,...) which can deeply influence the performances of the system. In order to accurately evaluate these effects by means of Computational Fluid Dynamics (CFD) simulations, it is necessary to locally refine the computational mesh. In this way the degrees of freedom related to the discretisation are focused in the most interesting regions and the computational cost of the simulation remains acceptable. In the present work, a discontinuous Galerkin (DG) discretisation is used to numerically solve the equations which describe the flow field. The local nature of the DG reconstruction makes it possible to efficiently exploit several adaptive schemes in which the size of the elements (h-adaptivity) and the order of reconstruction (p-adaptivity) are locally changed. After a review of the main adaptation criteria, some examples related to compressible flows in turbomachinery are presented. An hybrid hp-adaptive algorithm is also proposed and compared with a standard h-adaptive scheme in terms of computational efficiency.

  14. A new class of accurate, mesh-free hydrodynamic simulation methods

    NASA Astrophysics Data System (ADS)

    Hopkins, Philip F.

    2015-06-01

    We present two new Lagrangian methods for hydrodynamics, in a systematic comparison with moving-mesh, smoothed particle hydrodynamics (SPH), and stationary (non-moving) grid methods. The new methods are designed to simultaneously capture advantages of both SPH and grid-based/adaptive mesh refinement (AMR) schemes. They are based on a kernel discretization of the volume coupled to a high-order matrix gradient estimator and a Riemann solver acting over the volume `overlap'. We implement and test a parallel, second-order version of the method with self-gravity and cosmological integration, in the code GIZMO:1 this maintains exact mass, energy and momentum conservation; exhibits superior angular momentum conservation compared to all other methods we study; does not require `artificial diffusion' terms; and allows the fluid elements to move with the flow, so resolution is automatically adaptive. We consider a large suite of test problems, and find that on all problems the new methods appear competitive with moving-mesh schemes, with some advantages (particularly in angular momentum conservation), at the cost of enhanced noise. The new methods have many advantages versus SPH: proper convergence, good capturing of fluid-mixing instabilities, dramatically reduced `particle noise' and numerical viscosity, more accurate sub-sonic flow evolution, and sharp shock-capturing. Advantages versus non-moving meshes include: automatic adaptivity, dramatically reduced advection errors and numerical overmixing, velocity-independent errors, accurate coupling to gravity, good angular momentum conservation and elimination of `grid alignment' effects. We can, for example, follow hundreds of orbits of gaseous discs, while AMR and SPH methods break down in a few orbits. However, fixed meshes minimize `grid noise'. These differences are important for a range of astrophysical problems.

  15. Fast and high-order numerical algorithms for the solution of multidimensional nonlinear fractional Ginzburg-Landau equation

    NASA Astrophysics Data System (ADS)

    Mohebbi, Akbar

    2018-02-01

    In this paper we propose two fast and accurate numerical methods for the solution of multidimensional space fractional Ginzburg-Landau equation (FGLE). In the presented methods, to avoid solving a nonlinear system of algebraic equations and to increase the accuracy and efficiency of method, we split the complex problem into simpler sub-problems using the split-step idea. For a homogeneous FGLE, we propose a method which has fourth-order of accuracy in time component and spectral accuracy in space variable and for nonhomogeneous one, we introduce another scheme based on the Crank-Nicolson approach which has second-order of accuracy in time variable. Due to using the Fourier spectral method for fractional Laplacian operator, the resulting schemes are fully diagonal and easy to code. Numerical results are reported in terms of accuracy, computational order and CPU time to demonstrate the accuracy and efficiency of the proposed methods and to compare the results with the analytical solutions. The results show that the present methods are accurate and require low CPU time. It is illustrated that the numerical results are in good agreement with the theoretical ones.

  16. An implicit spatial and high-order temporal finite difference scheme for 2D acoustic modelling

    NASA Astrophysics Data System (ADS)

    Wang, Enjiang; Liu, Yang

    2018-01-01

    The finite difference (FD) method exhibits great superiority over other numerical methods due to its easy implementation and small computational requirement. We propose an effective FD method, characterised by implicit spatial and high-order temporal schemes, to reduce both the temporal and spatial dispersions simultaneously. For the temporal derivative, apart from the conventional second-order FD approximation, a special rhombus FD scheme is included to reach high-order accuracy in time. Compared with the Lax-Wendroff FD scheme, this scheme can achieve nearly the same temporal accuracy but requires less floating-point operation times and thus less computational cost when the same operator length is adopted. For the spatial derivatives, we adopt the implicit FD scheme to improve the spatial accuracy. Apart from the existing Taylor series expansion-based FD coefficients, we derive the least square optimisation based implicit spatial FD coefficients. Dispersion analysis and modelling examples demonstrate that, our proposed method can effectively decrease both the temporal and spatial dispersions, thus can provide more accurate wavefields.

  17. Direct Numerical Simulation of a Coolant Jet in a Periodic Crossflow

    NASA Technical Reports Server (NTRS)

    Sharma, Chirdeep; Acharya, Sumanta

    1998-01-01

    A Direct Numerical Simulation of a coolant jet injected normally into a periodic crossflow is presented. The physical situation simulated represents a periodic module in a coolant hole array with a heated crossflow. A collocated finite difference scheme is used which is fifth-order accurate spatially and second-order accurate temporally. The scheme is based on a fractional step approach and requires the solution of a pressure-Poisson equation. The simulations are obtained for a blowing ratio of 0.25 and a channel Reynolds number of 5600. The simulations reveal the dynamics of several large scale structures including the Counter-rotating Vortex Pair (CVP), the horse-shoe vortex, the shear layer vortex, the wall vortex and the wake vortex. The origins and the interactions of these vortical structures are identified and explored. Also presented are the turbulence statistics and how they relate to the flow structures.

  18. On Richardson extrapolation for low-dissipation low-dispersion diagonally implicit Runge-Kutta schemes

    NASA Astrophysics Data System (ADS)

    Havasi, Ágnes; Kazemi, Ehsan

    2018-04-01

    In the modeling of wave propagation phenomena it is necessary to use time integration methods which are not only sufficiently accurate, but also properly describe the amplitude and phase of the propagating waves. It is not clear if amending the developed schemes by extrapolation methods to obtain a high order of accuracy preserves the qualitative properties of these schemes in the perspective of dissipation, dispersion and stability analysis. It is illustrated that the combination of various optimized schemes with Richardson extrapolation is not optimal for minimal dissipation and dispersion errors. Optimized third-order and fourth-order methods are obtained, and it is shown that the proposed methods combined with Richardson extrapolation result in fourth and fifth orders of accuracy correspondingly, while preserving optimality and stability. The numerical applications include the linear wave equation, a stiff system of reaction-diffusion equations and the nonlinear Euler equations with oscillatory initial conditions. It is demonstrated that the extrapolated third-order scheme outperforms the recently developed fourth-order diagonally implicit Runge-Kutta scheme in terms of accuracy and stability.

  19. Modeling of Convective-Stratiform Precipitation Processes: Sensitivity to Partitioning Methods and Numerical Advection Schemes

    NASA Technical Reports Server (NTRS)

    Lang, Steve; Tao, W.-K.; Simpson, J.; Ferrier, B.; Einaudi, Franco (Technical Monitor)

    2001-01-01

    Six different convective-stratiform separation techniques, including a new technique that utilizes the ratio of vertical and terminal velocities, are compared and evaluated using two-dimensional numerical simulations of a tropical [Tropical Ocean Global Atmosphere Coupled Ocean-Atmosphere Response Experiment (TOGA COARE)] and midlatitude continental [Preliminary Regional Experiment for STORM-Central (PRESTORM)] squall line. The simulations are made using two different numerical advection schemes: 4th order and positive definite advection. Comparisons are made in terms of rainfall, cloud coverage, mass fluxes, apparent heating and moistening, mean hydrometeor profiles, CFADs (Contoured Frequency with Altitude Diagrams), microphysics, and latent heating retrieval. Overall, it was found that the different separation techniques produced results that qualitatively agreed. However, the quantitative differences were significant. Observational comparisons were unable to conclusively evaluate the performance of the techniques. Latent heating retrieval was shown to be sensitive to the use of separation technique mainly due to the stratiform region for methods that found very little stratiform rain. The midlatitude PRESTORM simulation was found to be nearly invariant with respect to advection type for most quantities while for TOGA COARE fourth order advection produced numerous shallow convective cores and positive definite advection fewer cells that were both broader and deeper penetrating above the freezing level.

  20. High-order accurate finite-volume formulations for the pressure gradient force in layered ocean models

    NASA Astrophysics Data System (ADS)

    Engwirda, Darren; Kelley, Maxwell; Marshall, John

    2017-08-01

    Discretisation of the horizontal pressure gradient force in layered ocean models is a challenging task, with non-trivial interactions between the thermodynamics of the fluid and the geometry of the layers often leading to numerical difficulties. We present two new finite-volume schemes for the pressure gradient operator designed to address these issues. In each case, the horizontal acceleration is computed as an integration of the contact pressure force that acts along the perimeter of an associated momentum control-volume. A pair of new schemes are developed by exploring different control-volume geometries. Non-linearities in the underlying equation-of-state definitions and thermodynamic profiles are treated using a high-order accurate numerical integration framework, designed to preserve hydrostatic balance in a non-linear manner. Numerical experiments show that the new methods achieve high levels of consistency, maintaining hydrostatic and thermobaric equilibrium in the presence of strongly-sloping layer geometries, non-linear equations-of-state and non-uniform vertical stratification profiles. These results suggest that the new pressure gradient formulations may be appropriate for general circulation models that employ hybrid vertical coordinates and/or terrain-following representations.

  1. On the validation of cloud parametrization schemes in numerical atmospheric models with satellite data from ISCCP

    NASA Astrophysics Data System (ADS)

    Meinke, I.

    2003-04-01

    A new method is presented to validate cloud parametrization schemes in numerical atmospheric models with satellite data of scanning radiometers. This method is applied to the regional atmospheric model HRM (High Resolution Regional Model) using satellite data from ISCCP (International Satellite Cloud Climatology Project). Due to the limited reliability of former validations there has been a need for developing a new validation method: Up to now differences between simulated and measured cloud properties are mostly declared as deficiencies of the cloud parametrization scheme without further investigation. Other uncertainties connected with the model or with the measurements have not been taken into account. Therefore changes in the cloud parametrization scheme based on such kind of validations might not be realistic. The new method estimates uncertainties of the model and the measurements. Criteria for comparisons of simulated and measured data are derived to localize deficiencies in the model. For a better specification of these deficiencies simulated clouds are classified regarding their parametrization. With this classification the localized model deficiencies are allocated to a certain parametrization scheme. Applying this method to the regional model HRM the quality of forecasting cloud properties is estimated in detail. The overestimation of simulated clouds in low emissivity heights especially during the night is localized as model deficiency. This is caused by subscale cloudiness. As the simulation of subscale clouds in the regional model HRM is described by a relative humidity parametrization these deficiencies are connected with this parameterization.

  2. A numerical relativity scheme for cosmological simulations

    NASA Astrophysics Data System (ADS)

    Daverio, David; Dirian, Yves; Mitsou, Ermis

    2017-12-01

    Cosmological simulations involving the fully covariant gravitational dynamics may prove relevant in understanding relativistic/non-linear features and, therefore, in taking better advantage of the upcoming large scale structure survey data. We propose a new 3  +  1 integration scheme for general relativity in the case where the matter sector contains a minimally-coupled perfect fluid field. The original feature is that we completely eliminate the fluid components through the constraint equations, thus remaining with a set of unconstrained evolution equations for the rest of the fields. This procedure does not constrain the lapse function and shift vector, so it holds in arbitrary gauge and also works for arbitrary equation of state. An important advantage of this scheme is that it allows one to define and pass an adaptation of the robustness test to the cosmological context, at least in the case of pressureless perfect fluid matter, which is the relevant one for late-time cosmology.

  3. HARM: A Numerical Scheme for General Relativistic Magnetohydrodynamics

    NASA Astrophysics Data System (ADS)

    Gammie, Charles F.; McKinney, Jonathan C.; Tóth, Gábor

    2003-05-01

    We describe a conservative, shock-capturing scheme for evolving the equations of general relativistic magnetohydrodynamics. The fluxes are calculated using the Harten, Lax, & van Leer scheme. A variant of constrained transport, proposed earlier by Tóth, is used to maintain a divergence-free magnetic field. Only the covariant form of the metric in a coordinate basis is required to specify the geometry. We describe code performance on a full suite of test problems in both special and general relativity. On smooth flows we show that it converges at second order. We conclude by showing some results from the evolution of a magnetized torus near a rotating black hole.

  4. The HIRLAM fast radiation scheme for mesoscale numerical weather prediction models

    NASA Astrophysics Data System (ADS)

    Rontu, Laura; Gleeson, Emily; Räisänen, Petri; Pagh Nielsen, Kristian; Savijärvi, Hannu; Hansen Sass, Bent

    2017-07-01

    This paper provides an overview of the HLRADIA shortwave (SW) and longwave (LW) broadband radiation schemes used in the HIRLAM numerical weather prediction (NWP) model and available in the HARMONIE-AROME mesoscale NWP model. The advantage of broadband, over spectral, schemes is that they can be called more frequently within the model, without compromising on computational efficiency. In mesoscale models fast interactions between clouds and radiation and the surface and radiation can be of greater importance than accounting for the spectral details of clear-sky radiation; thus calling the routines more frequently can be of greater benefit than the deterioration due to loss of spectral details. Fast but physically based radiation parametrizations are expected to be valuable for high-resolution ensemble forecasting, because as well as the speed of their execution, they may provide realistic physical perturbations. Results from single-column diagnostic experiments based on CIRC benchmark cases and an evaluation of 10 years of radiation output from the FMI operational archive of HIRLAM forecasts indicate that HLRADIA performs sufficiently well with respect to the clear-sky downwelling SW and longwave LW fluxes at the surface. In general, HLRADIA tends to overestimate surface fluxes, with the exception of LW fluxes under cold and dry conditions. The most obvious overestimation of the surface SW flux was seen in the cloudy cases in the 10-year comparison; this bias may be related to using a cloud inhomogeneity correction, which was too large. According to the CIRC comparisons, the outgoing LW and SW fluxes at the top of atmosphere are mostly overestimated by HLRADIA and the net LW flux is underestimated above clouds. The absorption of SW radiation by the atmosphere seems to be underestimated and LW absorption seems to be overestimated. Despite these issues, the overall results are satisfying and work on the improvement of HLRADIA for the use in HARMONIE-AROME NWP system

  5. Modified unified kinetic scheme for all flow regimes.

    PubMed

    Liu, Sha; Zhong, Chengwen

    2012-06-01

    A modified unified kinetic scheme for the prediction of fluid flow behaviors in all flow regimes is described. The time evolution of macrovariables at the cell interface is calculated with the idea that both free transport and collision mechanisms should be considered. The time evolution of macrovariables is obtained through the conservation constraints. The time evolution of local Maxwellian distribution is obtained directly through the one-to-one mapping from the evolution of macrovariables. These improvements provide more physical realities in flow behaviors and more accurate numerical results in all flow regimes especially in the complex transition flow regime. In addition, the improvement steps introduce no extra computational complexity.

  6. A time-accurate finite volume method valid at all flow velocities

    NASA Technical Reports Server (NTRS)

    Kim, S.-W.

    1993-01-01

    A finite volume method to solve the Navier-Stokes equations at all flow velocities (e.g., incompressible, subsonic, transonic, supersonic and hypersonic flows) is presented. The numerical method is based on a finite volume method that incorporates a pressure-staggered mesh and an incremental pressure equation for the conservation of mass. Comparison of three generally accepted time-advancing schemes, i.e., Simplified Marker-and-Cell (SMAC), Pressure-Implicit-Splitting of Operators (PISO), and Iterative-Time-Advancing (ITA) scheme, are made by solving a lid-driven polar cavity flow and self-sustained oscillatory flows over circular and square cylinders. Calculated results show that the ITA is the most stable numerically and yields the most accurate results. The SMAC is the most efficient computationally and is as stable as the ITA. It is shown that the PISO is the most weakly convergent and it exhibits an undesirable strong dependence on the time-step size. The degenerated numerical results obtained using the PISO are attributed to its second corrector step that cause the numerical results to deviate further from a divergence free velocity field. The accurate numerical results obtained using the ITA is attributed to its capability to resolve the nonlinearity of the Navier-Stokes equations. The present numerical method that incorporates the ITA is used to solve an unsteady transitional flow over an oscillating airfoil and a chemically reacting flow of hydrogen in a vitiated supersonic airstream. The turbulence fields in these flow cases are described using multiple-time-scale turbulence equations. For the unsteady transitional over an oscillating airfoil, the fluid flow is described using ensemble-averaged Navier-Stokes equations defined on the Lagrangian-Eulerian coordinates. It is shown that the numerical method successfully predicts the large dynamic stall vortex (DSV) and the trailing edge vortex (TEV) that are periodically generated by the oscillating airfoil

  7. A hierarchical uniformly high order DG-IMEX scheme for the 1D BGK equation

    NASA Astrophysics Data System (ADS)

    Xiong, Tao; Qiu, Jing-Mei

    2017-05-01

    A class of high order nodal discontinuous Galerkin implicit-explicit (DG-IMEX) schemes with asymptotic preserving (AP) property has been developed for the one-dimensional (1D) BGK equation in Xiong et al. (2015) [40], based on a micro-macro reformulation. The schemes are globally stiffly accurate and asymptotically consistent, and as the Knudsen number becomes small or goes to zero, they recover first the compressible Navier-Stokes (CNS) and then the Euler limit. Motivated by the recent work of Filbet and Rey (2015) [27] and the references therein, in this paper, we propose a hierarchical high order AP method, namely kinetic, CNS and Euler solvers are automatically applied in regions where their corresponding models are appropriate. The numerical solvers for different regimes are coupled naturally by interface conditions. To the best of our knowledge, the resulting scheme is the very first hierarchical one being proposed in the literature, that enjoys AP property as well as uniform high order accuracy. Numerical experiments demonstrate the efficiency and effectiveness of the proposed approach. As time evolves, three different regimes are dynamically identified and naturally coupled, leading to significant CPU time savings (more than 80% for some of our test problems).

  8. The Numerical Analysis of a Turbulent Compressible Jet. Degree awarded by Ohio State Univ., 2000

    NASA Technical Reports Server (NTRS)

    DeBonis, James R.

    2001-01-01

    A numerical method to simulate high Reynolds number jet flows was formulated and applied to gain a better understanding of the flow physics. Large-eddy simulation was chosen as the most promising approach to model the turbulent structures due to its compromise between accuracy and computational expense. The filtered Navier-Stokes equations were developed including a total energy form of the energy equation. Subgrid scale models for the momentum and energy equations were adapted from compressible forms of Smagorinsky's original model. The effect of using disparate temporal and spatial accuracy in a numerical scheme was discovered through one-dimensional model problems and a new uniformly fourth-order accurate numerical method was developed. Results from two- and three-dimensional validation exercises show that the code accurately reproduces both viscous and inviscid flows. Numerous axisymmetric jet simulations were performed to investigate the effect of grid resolution, numerical scheme, exit boundary conditions and subgrid scale modeling on the solution and the results were used to guide the three-dimensional calculations. Three-dimensional calculations of a Mach 1.4 jet showed that this LES simulation accurately captures the physics of the turbulent flow. The agreement with experimental data was relatively good and is much better than results in the current literature. Turbulent intensities indicate that the turbulent structures at this level of modeling are not isotropic and this information could lend itself to the development of improved subgrid scale models for LES and turbulence models for RANS simulations. A two point correlation technique was used to quantify the turbulent structures. Two point space correlations were used to obtain a measure of the integral length scale, which proved to be approximately 1/2 D(sub j). Two point space-time correlations were used to obtain the convection velocity for the turbulent structures. This velocity ranged from 0.57 to

  9. Comparative Study of Three High Order Schemes for LES of Temporally Evolving Mixing Layers

    NASA Technical Reports Server (NTRS)

    Yee, Helen M. C.; Sjogreen, Biorn Axel; Hadjadj, C.

    2012-01-01

    Three high order shock-capturing schemes are compared for large eddy simulations (LES) of temporally evolving mixing layers (TML) for different convective Mach numbers (Mc) ranging from the quasi-incompressible regime to highly compressible supersonic regime. The considered high order schemes are fifth-order WENO (WENO5), seventh-order WENO (WENO7) and the associated eighth-order central spatial base scheme with the dissipative portion of WENO7 as a nonlinear post-processing filter step (WENO7fi). This high order nonlinear filter method (H.C. Yee and B. Sjogreen, Proceedings of ICOSAHOM09, June 22-26, 2009, Trondheim, Norway) is designed for accurate and efficient simulations of shock-free compressible turbulence, turbulence with shocklets and turbulence with strong shocks with minimum tuning of scheme parameters. The LES results by WENO7fi using the same scheme parameter agree well with experimental results of Barone et al. (2006), and published direct numerical simulations (DNS) work of Rogers & Moser (1994) and Pantano & Sarkar (2002), whereas results by WENO5 and WENO7 compare poorly with experimental data and DNS computations.

  10. Composite scheme using localized relaxation with non-standard finite difference method for hyperbolic conservation laws

    NASA Astrophysics Data System (ADS)

    Kumar, Vivek; Raghurama Rao, S. V.

    2008-04-01

    Non-standard finite difference methods (NSFDM) introduced by Mickens [ Non-standard Finite Difference Models of Differential Equations, World Scientific, Singapore, 1994] are interesting alternatives to the traditional finite difference and finite volume methods. When applied to linear hyperbolic conservation laws, these methods reproduce exact solutions. In this paper, the NSFDM is first extended to hyperbolic systems of conservation laws, by a novel utilization of the decoupled equations using characteristic variables. In the second part of this paper, the NSFDM is studied for its efficacy in application to nonlinear scalar hyperbolic conservation laws. The original NSFDMs introduced by Mickens (1994) were not in conservation form, which is an important feature in capturing discontinuities at the right locations. Mickens [Construction and analysis of a non-standard finite difference scheme for the Burgers-Fisher equations, Journal of Sound and Vibration 257 (4) (2002) 791-797] recently introduced a NSFDM in conservative form. This method captures the shock waves exactly, without any numerical dissipation. In this paper, this algorithm is tested for the case of expansion waves with sonic points and is found to generate unphysical expansion shocks. As a remedy to this defect, we use the strategy of composite schemes [R. Liska, B. Wendroff, Composite schemes for conservation laws, SIAM Journal of Numerical Analysis 35 (6) (1998) 2250-2271] in which the accurate NSFDM is used as the basic scheme and localized relaxation NSFDM is used as the supporting scheme which acts like a filter. Relaxation schemes introduced by Jin and Xin [The relaxation schemes for systems of conservation laws in arbitrary space dimensions, Communications in Pure and Applied Mathematics 48 (1995) 235-276] are based on relaxation systems which replace the nonlinear hyperbolic conservation laws by a semi-linear system with a stiff relaxation term. The relaxation parameter ( λ) is chosen locally

  11. Transient three-dimensional thermal-hydraulic analysis of nuclear reactor fuel rod arrays: general equations and numerical scheme

    DOE Office of Scientific and Technical Information (OSTI.GOV)

    Wnek, W.J.; Ramshaw, J.D.; Trapp, J.A.

    1975-11-01

    A mathematical model and a numerical solution scheme for thermal- hydraulic analysis of fuel rod arrays are given. The model alleviates the two major deficiencies associated with existing rod array analysis models, that of a correct transverse momentum equation and the capability of handling reversing and circulatory flows. Possible applications of the model include steady state and transient subchannel calculations as well as analysis of flows in heat exchangers, other engineering equipment, and porous media. (auth)

  12. Implementation of the high-order schemes QUICK and LECUSSO in the COMMIX-1C Program

    DOE Office of Scientific and Technical Information (OSTI.GOV)

    Sakai, K.; Sun, J.G.; Sha, W.T.

    Multidimensional analysis computer programs based on the finite volume method, such as COMMIX-1C, have been commonly used to simulate thermal-hydraulic phenomena in engineering systems such as nuclear reactors. In COMMIX-1C, the first-order schemes with respect to both space and time are used. In many situations such as flow recirculations and stratifications with steep gradient of velocity and temperature fields, however, high-order difference schemes are necessary for an accurate prediction of the fields. For these reasons, two second-order finite difference numerical schemes, QUICK (Quadratic Upstream Interpolation for Convective Kinematics) and LECUSSO (Local Exact Consistent Upwind Scheme of Second Order), have beenmore » implemented in the COMMIX-1C computer code. The formulations were derived for general three-dimensional flows with nonuniform grid sizes. Numerical oscillation analyses for QUICK and LECUSSO were performed. To damp the unphysical oscillations which occur in calculations with high-order schemes at high mesh Reynolds numbers, a new FRAM (Filtering Remedy and Methodology) scheme was developed and implemented. To be consistent with the high-order schemes, the pressure equation and the boundary conditions for all the conservation equations were also modified to be of second order. The new capabilities in the code are listed. Test calculations were performed to validate the implementation of the high-order schemes. They include the test of the one-dimensional nonlinear Burgers equation, two-dimensional scalar transport in two impinging streams, von Karmann vortex shedding, shear driven cavity flow, Couette flow, and circular pipe flow. The calculated results were compared with available data; the agreement is good.« less

  13. Four-level conservative finite-difference schemes for Boussinesq paradigm equation

    NASA Astrophysics Data System (ADS)

    Kolkovska, N.

    2013-10-01

    In this paper a two-parametric family of four level conservative finite difference schemes is constructed for the multidimensional Boussinesq paradigm equation. The schemes are explicit in the sense that no inner iterations are needed for evaluation of the numerical solution. The preservation of the discrete energy with this method is proved. The schemes have been numerically tested on one soliton propagation model and two solitons interaction model. The numerical experiments demonstrate that the proposed family of schemes has second order of convergence in space and time steps in the discrete maximal norm.

  14. A soft computing scheme incorporating ANN and MOV energy in fault detection, classification and distance estimation of EHV transmission line with FSC.

    PubMed

    Khadke, Piyush; Patne, Nita; Singh, Arvind; Shinde, Gulab

    2016-01-01

    In this article, a novel and accurate scheme for fault detection, classification and fault distance estimation for a fixed series compensated transmission line is proposed. The proposed scheme is based on artificial neural network (ANN) and metal oxide varistor (MOV) energy, employing Levenberg-Marquardt training algorithm. The novelty of this scheme is the use of MOV energy signals of fixed series capacitors (FSC) as input to train the ANN. Such approach has never been used in any earlier fault analysis algorithms in the last few decades. Proposed scheme uses only single end measurement energy signals of MOV in all the 3 phases over one cycle duration from the occurrence of a fault. Thereafter, these MOV energy signals are fed as input to ANN for fault distance estimation. Feasibility and reliability of the proposed scheme have been evaluated for all ten types of fault in test power system model at different fault inception angles over numerous fault locations. Real transmission system parameters of 3-phase 400 kV Wardha-Aurangabad transmission line (400 km) with 40 % FSC at Power Grid Wardha Substation, India is considered for this research. Extensive simulation experiments show that the proposed scheme provides quite accurate results which demonstrate complete protection scheme with high accuracy, simplicity and robustness.

  15. FASTSIM2: a second-order accurate frictional rolling contact algorithm

    NASA Astrophysics Data System (ADS)

    Vollebregt, E. A. H.; Wilders, P.

    2011-01-01

    In this paper we consider the frictional (tangential) steady rolling contact problem. We confine ourselves to the simplified theory, instead of using full elastostatic theory, in order to be able to compute results fast, as needed for on-line application in vehicle system dynamics simulation packages. The FASTSIM algorithm is the leading technology in this field and is employed in all dominant railway vehicle system dynamics packages (VSD) in the world. The main contribution of this paper is a new version "FASTSIM2" of the FASTSIM algorithm, which is second-order accurate. This is relevant for VSD, because with the new algorithm 16 times less grid points are required for sufficiently accurate computations of the contact forces. The approach is based on new insights in the characteristics of the rolling contact problem when using the simplified theory, and on taking precise care of the contact conditions in the numerical integration scheme employed.

  16. Handwritten numeral databases of Indian scripts and multistage recognition of mixed numerals.

    PubMed

    Bhattacharya, Ujjwal; Chaudhuri, B B

    2009-03-01

    This article primarily concerns the problem of isolated handwritten numeral recognition of major Indian scripts. The principal contributions presented here are (a) pioneering development of two databases for handwritten numerals of two most popular Indian scripts, (b) a multistage cascaded recognition scheme using wavelet based multiresolution representations and multilayer perceptron classifiers and (c) application of (b) for the recognition of mixed handwritten numerals of three Indian scripts Devanagari, Bangla and English. The present databases include respectively 22,556 and 23,392 handwritten isolated numeral samples of Devanagari and Bangla collected from real-life situations and these can be made available free of cost to researchers of other academic Institutions. In the proposed scheme, a numeral is subjected to three multilayer perceptron classifiers corresponding to three coarse-to-fine resolution levels in a cascaded manner. If rejection occurred even at the highest resolution, another multilayer perceptron is used as the final attempt to recognize the input numeral by combining the outputs of three classifiers of the previous stages. This scheme has been extended to the situation when the script of a document is not known a priori or the numerals written on a document belong to different scripts. Handwritten numerals in mixed scripts are frequently found in Indian postal mails and table-form documents.

  17. A gas-kinetic BGK scheme for the compressible Navier-Stokes equations

    NASA Technical Reports Server (NTRS)

    Xu, Kun

    2000-01-01

    This paper presents an improved gas-kinetic scheme based on the Bhatnagar-Gross-Krook (BGK) model for the compressible Navier-Stokes equations. The current method extends the previous gas-kinetic Navier-Stokes solver developed by Xu and Prendergast by implementing a general nonequilibrium state to represent the gas distribution function at the beginning of each time step. As a result, the requirement in the previous scheme, such as the particle collision time being less than the time step for the validity of the BGK Navier-Stokes solution, is removed. Therefore, the applicable regime of the current method is much enlarged and the Navier-Stokes solution can be obtained accurately regardless of the ratio between the collision time and the time step. The gas-kinetic Navier-Stokes solver developed by Chou and Baganoff is the limiting case of the current method, and it is valid only under such a limiting condition. Also, in this paper, the appropriate implementation of boundary condition for the kinetic scheme, different kinetic limiting cases, and the Prandtl number fix are presented. The connection among artificial dissipative central schemes, Godunov-type schemes, and the gas-kinetic BGK method is discussed. Many numerical tests are included to validate the current method.

  18. Age-of-Air, Tape Recorder, and Vertical Transport Schemes

    NASA Technical Reports Server (NTRS)

    Lin, S.-J.; Einaudi, Franco (Technical Monitor)

    2000-01-01

    A numerical-analytic investigation of the impacts of vertical transport schemes on the model simulated age-of-air and the so-called 'tape recorder' will be presented using an idealized 1-D column transport model as well as a more realistic 3-D dynamical model. By comparing to the 'exact' solutions of 'age-of-air' and the 'tape recorder' obtainable in the 1-D setting, useful insight is gained on the impacts of numerical diffusion and dispersion of numerical schemes used in global models. Advantages and disadvantages of Eulerian, semi-Lagrangian, and Lagrangian transport schemes will be discussed. Vertical resolution requirement for numerical schemes as well as observing systems for capturing the fine details of the 'tape recorder' or any upward propagating wave-like structures can potentially be derived from the 1-D analytic model.

  19. A flux splitting scheme with high-resolution and robustness for discontinuities

    NASA Technical Reports Server (NTRS)

    Wada, Yasuhiro; Liou, Meng-Sing

    1994-01-01

    A flux splitting scheme is proposed for the general nonequilibrium flow equations with an aim at removing numerical dissipation of Van-Leer-type flux-vector splittings on a contact discontinuity. The scheme obtained is also recognized as an improved Advection Upwind Splitting Method (AUSM) where a slight numerical overshoot immediately behind the shock is eliminated. The proposed scheme has favorable properties: high-resolution for contact discontinuities; conservation of enthalpy for steady flows; numerical efficiency; applicability to chemically reacting flows. In fact, for a single contact discontinuity, even if it is moving, this scheme gives the numerical flux of the exact solution of the Riemann problem. Various numerical experiments including that of a thermo-chemical nonequilibrium flow were performed, which indicate no oscillation and robustness of the scheme for shock/expansion waves. A cure for carbuncle phenomenon is discussed as well.

  20. Explicit Von Neumann Stability Conditions for the c-tau Scheme: A Basic Scheme in the Development of the CE-SE Courant Number Insensitive Schemes

    NASA Technical Reports Server (NTRS)

    Chang, Sin-Chung

    2005-01-01

    As part of the continuous development of the space-time conservation element and solution element (CE-SE) method, recently a set of so call ed "Courant number insensitive schemes" has been proposed. The key advantage of these new schemes is that the numerical dissipation associa ted with them generally does not increase as the Courant number decre ases. As such, they can be applied to problems with large Courant number disparities (such as what commonly occurs in Navier-Stokes problem s) without incurring excessive numerical dissipation.

  1. A comparison of resampling schemes for estimating model observer performance with small ensembles

    NASA Astrophysics Data System (ADS)

    Elshahaby, Fatma E. A.; Jha, Abhinav K.; Ghaly, Michael; Frey, Eric C.

    2017-09-01

    In objective assessment of image quality, an ensemble of images is used to compute the 1st and 2nd order statistics of the data. Often, only a finite number of images is available, leading to the issue of statistical variability in numerical observer performance. Resampling-based strategies can help overcome this issue. In this paper, we compared different combinations of resampling schemes (the leave-one-out (LOO) and the half-train/half-test (HT/HT)) and model observers (the conventional channelized Hotelling observer (CHO), channelized linear discriminant (CLD) and channelized quadratic discriminant). Observer performance was quantified by the area under the ROC curve (AUC). For a binary classification task and for each observer, the AUC value for an ensemble size of 2000 samples per class served as a gold standard for that observer. Results indicated that each observer yielded a different performance depending on the ensemble size and the resampling scheme. For a small ensemble size, the combination [CHO, HT/HT] had more accurate rankings than the combination [CHO, LOO]. Using the LOO scheme, the CLD and CHO had similar performance for large ensembles. However, the CLD outperformed the CHO and gave more accurate rankings for smaller ensembles. As the ensemble size decreased, the performance of the [CHO, LOO] combination seriously deteriorated as opposed to the [CLD, LOO] combination. Thus, it might be desirable to use the CLD with the LOO scheme when smaller ensemble size is available.

  2. Experimental validation of convection-diffusion discretisation scheme employed for computational modelling of biological mass transport

    PubMed Central

    2010-01-01

    between the experimental results and those obtained from the First-Order Upwind and Power Law schemes, respectively. However, both the Second-Order upwind and QUICK schemes accurately predict species concentration under high Peclet number, convection-dominated flow conditions. Conclusion Convection-diffusion discretisation scheme selection has a strong influence on resultant species concentration fields, as determined by CFD. Furthermore, either the Second-Order or QUICK discretisation schemes should be implemented when numerically modelling convection-dominated mass-transport conditions. Finally, care should be taken not to utilize computationally inexpensive discretisation schemes at the cost of accuracy in resultant species concentration. PMID:20642816

  3. Finite difference elastic wave modeling with an irregular free surface using ADER scheme

    NASA Astrophysics Data System (ADS)

    Almuhaidib, Abdulaziz M.; Nafi Toksöz, M.

    2015-06-01

    In numerical modeling of seismic wave propagation in the earth, we encounter two important issues: the free surface and the topography of the surface (i.e. irregularities). In this study, we develop a 2D finite difference solver for the elastic wave equation that combines a 4th- order ADER scheme (Arbitrary high-order accuracy using DERivatives), which is widely used in aeroacoustics, with the characteristic variable method at the free surface boundary. The idea is to treat the free surface boundary explicitly by using ghost values of the solution for points beyond the free surface to impose the physical boundary condition. The method is based on the velocity-stress formulation. The ultimate goal is to develop a numerical solver for the elastic wave equation that is stable, accurate and computationally efficient. The solver treats smooth arbitrary-shaped boundaries as simple plane boundaries. The computational cost added by treating the topography is negligible compared to flat free surface because only a small number of grid points near the boundary need to be computed. In the presence of topography, using 10 grid points per shortest shear-wavelength, the solver yields accurate results. Benchmark numerical tests using several complex models that are solved by our method and other independent accurate methods show an excellent agreement, confirming the validity of the method for modeling elastic waves with an irregular free surface.

  4. Accurate ω-ψ Spectral Solution of the Singular Driven Cavity Problem

    NASA Astrophysics Data System (ADS)

    Auteri, F.; Quartapelle, L.; Vigevano, L.

    2002-08-01

    This article provides accurate spectral solutions of the driven cavity problem, calculated in the vorticity-stream function representation without smoothing the corner singularities—a prima facie impossible task. As in a recent benchmark spectral calculation by primitive variables of Botella and Peyret, closed-form contributions of the singular solution for both zero and finite Reynolds numbers are subtracted from the unknown of the problem tackled here numerically in biharmonic form. The method employed is based on a split approach to the vorticity and stream function equations, a Galerkin-Legendre approximation of the problem for the perturbation, and an evaluation of the nonlinear terms by Gauss-Legendre numerical integration. Results computed for Re=0, 100, and 1000 compare well with the benchmark steady solutions provided by the aforementioned collocation-Chebyshev projection method. The validity of the proposed singularity subtraction scheme for computing time-dependent solutions is also established.

  5. Earthquake Rupture Dynamics using Adaptive Mesh Refinement and High-Order Accurate Numerical Methods

    NASA Astrophysics Data System (ADS)

    Kozdon, J. E.; Wilcox, L.

    2013-12-01

    Our goal is to develop scalable and adaptive (spatial and temporal) numerical methods for coupled, multiphysics problems using high-order accurate numerical methods. To do so, we are developing an opensource, parallel library known as bfam (available at http://bfam.in). The first application to be developed on top of bfam is an earthquake rupture dynamics solver using high-order discontinuous Galerkin methods and summation-by-parts finite difference methods. In earthquake rupture dynamics, wave propagation in the Earth's crust is coupled to frictional sliding on fault interfaces. This coupling is two-way, required the simultaneous simulation of both processes. The use of laboratory-measured friction parameters requires near-fault resolution that is 4-5 orders of magnitude higher than that needed to resolve the frequencies of interest in the volume. This, along with earlier simulations using a low-order, finite volume based adaptive mesh refinement framework, suggest that adaptive mesh refinement is ideally suited for this problem. The use of high-order methods is motivated by the high level of resolution required off the fault in earlier the low-order finite volume simulations; we believe this need for resolution is a result of the excessive numerical dissipation of low-order methods. In bfam spatial adaptivity is handled using the p4est library and temporal adaptivity will be accomplished through local time stepping. In this presentation we will present the guiding principles behind the library as well as verification of code against the Southern California Earthquake Center dynamic rupture code validation test problems.

  6. Stabilized linear semi-implicit schemes for the nonlocal Cahn-Hilliard equation

    NASA Astrophysics Data System (ADS)

    Du, Qiang; Ju, Lili; Li, Xiao; Qiao, Zhonghua

    2018-06-01

    Comparing with the well-known classic Cahn-Hilliard equation, the nonlocal Cahn-Hilliard equation is equipped with a nonlocal diffusion operator and can describe more practical phenomena for modeling phase transitions of microstructures in materials. On the other hand, it evidently brings more computational costs in numerical simulations, thus efficient and accurate time integration schemes are highly desired. In this paper, we propose two energy-stable linear semi-implicit methods with first and second order temporal accuracies respectively for solving the nonlocal Cahn-Hilliard equation. The temporal discretization is done by using the stabilization technique with the nonlocal diffusion term treated implicitly, while the spatial discretization is carried out by the Fourier collocation method with FFT-based fast implementations. The energy stabilities are rigorously established for both methods in the fully discrete sense. Numerical experiments are conducted for a typical case involving Gaussian kernels. We test the temporal convergence rates of the proposed schemes and make a comparison of the nonlocal phase transition process with the corresponding local one. In addition, long-time simulations of the coarsening dynamics are also performed to predict the power law of the energy decay.

  7. Numerical study of radiometric forces via the direct solution of the Boltzmann kinetic equation

    NASA Astrophysics Data System (ADS)

    Anikin, Yu. A.

    2011-07-01

    The two-dimensional rarefied gas motion in a Crookes radiometer and the resulting radiometric forces are studied by numerically solving the Boltzmann kinetic equation. The collision integral is directly evaluated using a projection method, and second-order accurate TVD schemes are used to solve the advection equation. The radiometric forces are found as functions of the Knudsen number and the temperatures, and their spatial distribution is analyzed.

  8. The effect of numerical methods on the simulation of mid-ocean ridge hydrothermal models

    NASA Astrophysics Data System (ADS)

    Carpio, J.; Braack, M.

    2012-01-01

    This work considers the effect of the numerical method on the simulation of a 2D model of hydrothermal systems located in the high-permeability axial plane of mid-ocean ridges. The behavior of hot plumes, formed in a porous medium between volcanic lava and the ocean floor, is very irregular due to convective instabilities. Therefore, we discuss and compare two different numerical methods for solving the mathematical model of this system. In concrete, we consider two ways to treat the temperature equation of the model: a semi-Lagrangian formulation of the advective terms in combination with a Galerkin finite element method for the parabolic part of the equations and a stabilized finite element scheme. Both methods are very robust and accurate. However, due to physical instabilities in the system at high Rayleigh number, the effect of the numerical method is significant with regard to the temperature distribution at a certain time instant. The good news is that relevant statistical quantities remain relatively stable and coincide for the two numerical schemes. The agreement is larger in the case of a mathematical model with constant water properties. In the case of a model with nonlinear dependence of the water properties on the temperature and pressure, the agreement in the statistics is clearly less pronounced. Hence, the presented work accentuates the need for a strengthened validation of the compatibility between numerical scheme (accuracy/resolution) and complex (realistic/nonlinear) models.

  9. Very high order PNPM schemes on unstructured meshes for the resistive relativistic MHD equations

    NASA Astrophysics Data System (ADS)

    Dumbser, Michael; Zanotti, Olindo

    2009-10-01

    In this paper we propose the first better than second order accurate method in space and time for the numerical solution of the resistive relativistic magnetohydrodynamics (RRMHD) equations on unstructured meshes in multiple space dimensions. The nonlinear system under consideration is purely hyperbolic and contains a source term, the one for the evolution of the electric field, that becomes stiff for low values of the resistivity. For the spatial discretization we propose to use high order PNPM schemes as introduced in Dumbser et al. [M. Dumbser, D. Balsara, E.F. Toro, C.D. Munz, A unified framework for the construction of one-step finite volume and discontinuous Galerkin schemes, Journal of Computational Physics 227 (2008) 8209-8253] for hyperbolic conservation laws and a high order accurate unsplit time-discretization is achieved using the element-local space-time discontinuous Galerkin approach proposed in Dumbser et al. [M. Dumbser, C. Enaux, E.F. Toro, Finite volume schemes of very high order of accuracy for stiff hyperbolic balance laws, Journal of Computational Physics 227 (2008) 3971-4001] for one-dimensional balance laws with stiff source terms. The divergence-free character of the magnetic field is accounted for through the divergence cleaning procedure of Dedner et al. [A. Dedner, F. Kemm, D. Kröner, C.-D. Munz, T. Schnitzer, M. Wesenberg, Hyperbolic divergence cleaning for the MHD equations, Journal of Computational Physics 175 (2002) 645-673]. To validate our high order method we first solve some numerical test cases for which exact analytical reference solutions are known and we also show numerical convergence studies in the stiff limit of the RRMHD equations using PNPM schemes from third to fifth order of accuracy in space and time. We also present some applications with shock waves such as a classical shock tube problem with different values for the conductivity as well as a relativistic MHD rotor problem and the relativistic equivalent of the

  10. Multiscale solutions of radiative heat transfer by the discrete unified gas kinetic scheme

    NASA Astrophysics Data System (ADS)

    Luo, Xiao-Ping; Wang, Cun-Hai; Zhang, Yong; Yi, Hong-Liang; Tan, He-Ping

    2018-06-01

    The radiative transfer equation (RTE) has two asymptotic regimes characterized by the optical thickness, namely, optically thin and optically thick regimes. In the optically thin regime, a ballistic or kinetic transport is dominant. In the optically thick regime, energy transport is totally dominated by multiple collisions between photons; that is, the photons propagate by means of diffusion. To obtain convergent solutions to the RTE, conventional numerical schemes have a strong dependence on the number of spatial grids, which leads to a serious computational inefficiency in the regime where the diffusion is predominant. In this work, a discrete unified gas kinetic scheme (DUGKS) is developed to predict radiative heat transfer in participating media. Numerical performances of the DUGKS are compared in detail with conventional methods through three cases including one-dimensional transient radiative heat transfer, two-dimensional steady radiative heat transfer, and three-dimensional multiscale radiative heat transfer. Due to the asymptotic preserving property, the present method with relatively coarse grids gives accurate and reliable numerical solutions for large, small, and in-between values of optical thickness, and, especially in the optically thick regime, the DUGKS demonstrates a pronounced computational efficiency advantage over the conventional numerical models. In addition, the DUGKS has a promising potential in the study of multiscale radiative heat transfer inside the participating medium with a transition from optically thin to optically thick regimes.

  11. Reliable numerical computation in an optimal output-feedback design

    NASA Technical Reports Server (NTRS)

    Vansteenwyk, Brett; Ly, Uy-Loi

    1991-01-01

    A reliable algorithm is presented for the evaluation of a quadratic performance index and its gradients with respect to the controller design parameters. The algorithm is a part of a design algorithm for optimal linear dynamic output-feedback controller that minimizes a finite-time quadratic performance index. The numerical scheme is particularly robust when it is applied to the control-law synthesis for systems with densely packed modes and where there is a high likelihood of encountering degeneracies in the closed-loop eigensystem. This approach through the use of an accurate Pade series approximation does not require the closed-loop system matrix to be diagonalizable. The algorithm was included in a control design package for optimal robust low-order controllers. Usefulness of the proposed numerical algorithm was demonstrated using numerous practical design cases where degeneracies occur frequently in the closed-loop system under an arbitrary controller design initialization and during the numerical search.

  12. An implicit numerical scheme for the simulation of internal viscous flows on unstructured grids

    NASA Technical Reports Server (NTRS)

    Jorgenson, Philip C. E.; Pletcher, Richard H.

    1994-01-01

    The Navier-Stokes equations are solved numerically for two-dimensional steady viscous laminar flows. The grids are generated based on the method of Delaunay triangulation. A finite-volume approach is used to discretize the conservation law form of the compressible flow equations written in terms of primitive variables. A preconditioning matrix is added to the equations so that low Mach number flows can be solved economically. The equations are time marched using either an implicit Gauss-Seidel iterative procedure or a solver based on a conjugate gradient like method. A four color scheme is employed to vectorize the block Gauss-Seidel relaxation procedure. This increases the memory requirements minimally and decreases the computer time spent solving the resulting system of equations substantially. A factor of 7.6 speed up in the matrix solver is typical for the viscous equations. Numerical results are obtained for inviscid flow over a bump in a channel at subsonic and transonic conditions for validation with structured solvers. Viscous results are computed for developing flow in a channel, a symmetric sudden expansion, periodic tandem cylinders in a cross-flow, and a four-port valve. Comparisons are made with available results obtained by other investigators.

  13. A NUMERICAL SCHEME FOR SPECIAL RELATIVISTIC RADIATION MAGNETOHYDRODYNAMICS BASED ON SOLVING THE TIME-DEPENDENT RADIATIVE TRANSFER EQUATION

    DOE Office of Scientific and Technical Information (OSTI.GOV)

    Ohsuga, Ken; Takahashi, Hiroyuki R.

    2016-02-20

    We develop a numerical scheme for solving the equations of fully special relativistic, radiation magnetohydrodynamics (MHDs), in which the frequency-integrated, time-dependent radiation transfer equation is solved to calculate the specific intensity. The radiation energy density, the radiation flux, and the radiation stress tensor are obtained by the angular quadrature of the intensity. In the present method, conservation of total mass, momentum, and energy of the radiation magnetofluids is guaranteed. We treat not only the isotropic scattering but also the Thomson scattering. The numerical method of MHDs is the same as that of our previous work. The advection terms are explicitlymore » solved, and the source terms, which describe the gas–radiation interaction, are implicitly integrated. Our code is suitable for massive parallel computing. We present that our code shows reasonable results in some numerical tests for propagating radiation and radiation hydrodynamics. Particularly, the correct solution is given even in the optically very thin or moderately thin regimes, and the special relativistic effects are nicely reproduced.« less

  14. A well-balanced finite volume scheme for the Euler equations with gravitation. The exact preservation of hydrostatic equilibrium with arbitrary entropy stratification

    NASA Astrophysics Data System (ADS)

    Käppeli, R.; Mishra, S.

    2016-03-01

    Context. Many problems in astrophysics feature flows which are close to hydrostatic equilibrium. However, standard numerical schemes for compressible hydrodynamics may be deficient in approximating this stationary state, where the pressure gradient is nearly balanced by gravitational forces. Aims: We aim to develop a second-order well-balanced scheme for the Euler equations. The scheme is designed to mimic a discrete version of the hydrostatic balance. It therefore can resolve a discrete hydrostatic equilibrium exactly (up to machine precision) and propagate perturbations, on top of this equilibrium, very accurately. Methods: A local second-order hydrostatic equilibrium preserving pressure reconstruction is developed. Combined with a standard central gravitational source term discretization and numerical fluxes that resolve stationary contact discontinuities exactly, the well-balanced property is achieved. Results: The resulting well-balanced scheme is robust and simple enough to be very easily implemented within any existing computer code that solves time explicitly or implicitly the compressible hydrodynamics equations. We demonstrate the performance of the well-balanced scheme for several astrophysically relevant applications: wave propagation in stellar atmospheres, a toy model for core-collapse supernovae, convection in carbon shell burning, and a realistic proto-neutron star.

  15. An efficient and stable hydrodynamic model with novel source term discretization schemes for overland flow and flood simulations

    NASA Astrophysics Data System (ADS)

    Xia, Xilin; Liang, Qiuhua; Ming, Xiaodong; Hou, Jingming

    2017-05-01

    Numerical models solving the full 2-D shallow water equations (SWEs) have been increasingly used to simulate overland flows and better understand the transient flow dynamics of flash floods in a catchment. However, there still exist key challenges that have not yet been resolved for the development of fully dynamic overland flow models, related to (1) the difficulty of maintaining numerical stability and accuracy in the limit of disappearing water depth and (2) inaccurate estimation of velocities and discharges on slopes as a result of strong nonlinearity of friction terms. This paper aims to tackle these key research challenges and present a new numerical scheme for accurately and efficiently modeling large-scale transient overland flows over complex terrains. The proposed scheme features a novel surface reconstruction method (SRM) to correctly compute slope source terms and maintain numerical stability at small water depth, and a new implicit discretization method to handle the highly nonlinear friction terms. The resulting shallow water overland flow model is first validated against analytical and experimental test cases and then applied to simulate a hypothetic rainfall event in the 42 km2 Haltwhistle Burn, UK.

  16. Truncation effect on Taylor-Aris dispersion in lattice Boltzmann schemes: Accuracy towards stability

    NASA Astrophysics Data System (ADS)

    Ginzburg, Irina; Roux, Laetitia

    2015-10-01

    The Taylor dispersion in parabolic velocity field provides a well-known benchmark for advection-diffusion (ADE) schemes and serves as a first step towards accurate modeling of the high-order non-Gaussian effects in heterogeneous flow. While applying the Lattice Boltzmann ADE two-relaxation-times (TRT) scheme for a transport with given Péclet number (Pe) one should select six free-tunable parameters, namely, (i) molecular-diffusion-scale, equilibrium parameter; (ii) three families of equilibrium weights, assigned to the terms of mass, velocity and numerical-diffusion-correction, and (iii) two relaxation rates. We analytically and numerically investigate the respective roles of all these degrees of freedom in the accuracy and stability in the evolution of a Gaussian plume. For this purpose, the third- and fourth-order transient multi-dimensional analysis of the recurrence equations of the TRT ADE scheme is extended for a spatially-variable velocity field. The key point is in the coupling of the truncation and Taylor dispersion analysis which allows us to identify the second-order numerical correction δkT to Taylor dispersivity coefficient kT. The procedure is exemplified for a straight Poiseuille flow where δkT is given in a closed analytical form in equilibrium and relaxation parameter spaces. The predicted longitudinal dispersivity is in excellent agreement with the numerical experiments over a wide parameter range. In relatively small Pe-range, the relative dispersion error increases with Péclet number. This deficiency reduces in the intermediate and high Pe-range where it becomes Pe-independent and velocity-amplitude independent. Eliminating δkT by a proper parameter choice and employing specular reflection for zero flux condition on solid boundaries, the d2Q9 TRT ADE scheme may reproduce the Taylor-Aris result quasi-exactly, from very coarse to fine grids, and from very small to arbitrarily high Péclet numbers. Since free-tunable product of two

  17. Development of a new flux splitting scheme

    NASA Technical Reports Server (NTRS)

    Liou, Meng-Sing; Steffen, Christopher J., Jr.

    1991-01-01

    The use of a new splitting scheme, the advection upstream splitting method, for model aerodynamic problems where Van Leer and Roe schemes had failed previously is discussed. The present scheme is based on splitting in which the convective and pressure terms are separated and treated differently depending on the underlying physical conditions. The present method is found to be both simple and accurate.

  18. Numerical Hydrodynamics in General Relativity.

    PubMed

    Font, José A

    2003-01-01

    The current status of numerical solutions for the equations of ideal general relativistic hydrodynamics is reviewed. With respect to an earlier version of the article, the present update provides additional information on numerical schemes, and extends the discussion of astrophysical simulations in general relativistic hydrodynamics. Different formulations of the equations are presented, with special mention of conservative and hyperbolic formulations well-adapted to advanced numerical methods. A large sample of available numerical schemes is discussed, paying particular attention to solution procedures based on schemes exploiting the characteristic structure of the equations through linearized Riemann solvers. A comprehensive summary of astrophysical simulations in strong gravitational fields is presented. These include gravitational collapse, accretion onto black holes, and hydrodynamical evolutions of neutron stars. The material contained in these sections highlights the numerical challenges of various representative simulations. It also follows, to some extent, the chronological development of the field, concerning advances on the formulation of the gravitational field and hydrodynamic equations and the numerical methodology designed to solve them. Supplementary material is available for this article at 10.12942/lrr-2003-4.

  19. A consistent spatial differencing scheme for the transonic full-potential equation in three dimensions

    NASA Technical Reports Server (NTRS)

    Thomas, S. D.; Holst, T. L.

    1985-01-01

    A full-potential steady transonic wing flow solver has been modified so that freestream density and residual are captured in regions of constant velocity. This numerically precise freestream consistency is obtained by slightly altering the differencing scheme without affecting the implicit solution algorithm. The changes chiefly affect the fifteen metrics per grid point, which are computed once and stored. With this new method, the outer boundary condition is captured accurately, and the smoothness of the solution is especially improved near regions of grid discontinuity.

  20. Designs and numerical calculations for echo-enabled harmonic generation at very high harmonics

    NASA Astrophysics Data System (ADS)

    Penn, G.; Reinsch, M.

    2011-09-01

    The echo-enabled harmonic generation (EEHG) scheme for driving an FEL using two seeded energy modulations at much longer wavelengths than the output wavelength is a promising concept for future seeded FELs. There are many competing requirements in the design of an EEHG beamline which need careful optimization. Furthermore, revised simulation tools and methods are necessary because of both the high harmonic numbers simulated and the complicated nature of the phase space manipulations which are intrinsic to the scheme. This paper explores the constraints on performance and the required tolerances for reaching wavelengths well below 1/100th of that of the seed lasers, and describes some of the methodology for designing such a beamline. Numerical tools, developed both for the GENESIS and GINGER FEL codes, are presented and used here for more accurate study of the scheme beyond a time-averaged model. In particular, the impact of the local structure in peak current and bunching, which is an inherent part of the EEHG scheme, is evaluated.

  1. A positive and entropy-satisfying finite volume scheme for the Baer-Nunziato model

    NASA Astrophysics Data System (ADS)

    Coquel, Frédéric; Hérard, Jean-Marc; Saleh, Khaled

    2017-02-01

    We present a relaxation scheme for approximating the entropy dissipating weak solutions of the Baer-Nunziato two-phase flow model. This relaxation scheme is straightforwardly obtained as an extension of the relaxation scheme designed in [16] for the isentropic Baer-Nunziato model and consequently inherits its main properties. To our knowledge, this is the only existing scheme for which the approximated phase fractions, phase densities and phase internal energies are proven to remain positive without any restrictive condition other than a classical fully computable CFL condition. For ideal gas and stiffened gas equations of state, real values of the phasic speeds of sound are also proven to be maintained by the numerical scheme. It is also the only scheme for which a discrete entropy inequality is proven, under a CFL condition derived from the natural sub-characteristic condition associated with the relaxation approximation. This last property, which ensures the non-linear stability of the numerical method, is satisfied for any admissible equation of state. We provide a numerical study for the convergence of the approximate solutions towards some exact Riemann solutions. The numerical simulations show that the relaxation scheme compares well with two of the most popular existing schemes available for the Baer-Nunziato model, namely Schwendeman-Wahle-Kapila's Godunov-type scheme [39] and Tokareva-Toro's HLLC scheme [44]. The relaxation scheme also shows a higher precision and a lower computational cost (for comparable accuracy) than a standard numerical scheme used in the nuclear industry, namely Rusanov's scheme. Finally, we assess the good behavior of the scheme when approximating vanishing phase solutions.

  2. New, Improved Bulk-microphysical Schemes for Studying Precipitation Processes in WRF. Part 1; Comparisons with Other Schemes

    NASA Technical Reports Server (NTRS)

    Tao, W.-K.; Shi, J.; Chen, S. S> ; Lang, S.; Hong, S.-Y.; Thompson, G.; Peters-Lidard, C.; Hou, A.; Braun, S.; hide

    2007-01-01

    Advances in computing power allow atmospheric prediction models to be mn at progressively finer scales of resolution, using increasingly more sophisticated physical parameterizations and numerical methods. The representation of cloud microphysical processes is a key component of these models, over the past decade both research and operational numerical weather prediction models have started using more complex microphysical schemes that were originally developed for high-resolution cloud-resolving models (CRMs). A recent report to the United States Weather Research Program (USWRP) Science Steering Committee specifically calls for the replacement of implicit cumulus parameterization schemes with explicit bulk schemes in numerical weather prediction (NWP) as part of a community effort to improve quantitative precipitation forecasts (QPF). An improved Goddard bulk microphysical parameterization is implemented into a state-of the-art of next generation of Weather Research and Forecasting (WRF) model. High-resolution model simulations are conducted to examine the impact of microphysical schemes on two different weather events (a midlatitude linear convective system and an Atllan"ic hurricane). The results suggest that microphysics has a major impact on the organization and precipitation processes associated with a summer midlatitude convective line system. The 31CE scheme with a cloud ice-snow-hail configuration led to a better agreement with observation in terms of simulated narrow convective line and rainfall intensity. This is because the 3ICE-hail scheme includes dense ice precipitating (hail) particle with very fast fall speed (over 10 m/s). For an Atlantic hurricane case, varying the microphysical schemes had no significant impact on the track forecast but did affect the intensity (important for air-sea interaction)

  3. Development of a new flux splitting scheme

    NASA Technical Reports Server (NTRS)

    Liou, Meng-Sing; Steffen, Christopher J., Jr.

    1991-01-01

    The successful use of a novel splitting scheme, the advection upstream splitting method, for model aerodynamic problems where Van Leer and Roe schemes had failed previously is discussed. The present scheme is based on splitting in which the convective and pressure terms are separated and treated differently depending on the underlying physical conditions. The present method is found to be both simple and accurate.

  4. On the dynamics of some grid adaption schemes

    NASA Technical Reports Server (NTRS)

    Sweby, Peter K.; Yee, Helen C.

    1994-01-01

    The dynamics of a one-parameter family of mesh equidistribution schemes coupled with finite difference discretisations of linear and nonlinear convection-diffusion model equations is studied numerically. It is shown that, when time marched to steady state, the grid adaption not only influences the stability and convergence rate of the overall scheme, but can also introduce spurious dynamics to the numerical solution procedure.

  5. A discontinuous Galerkin conservative level set scheme for interface capturing in multiphase flows

    DOE Office of Scientific and Technical Information (OSTI.GOV)

    Owkes, Mark, E-mail: mfc86@cornell.edu; Desjardins, Olivier

    2013-09-15

    The accurate conservative level set (ACLS) method of Desjardins et al. [O. Desjardins, V. Moureau, H. Pitsch, An accurate conservative level set/ghost fluid method for simulating turbulent atomization, J. Comput. Phys. 227 (18) (2008) 8395–8416] is extended by using a discontinuous Galerkin (DG) discretization. DG allows for the scheme to have an arbitrarily high order of accuracy with the smallest possible computational stencil resulting in an accurate method with good parallel scaling. This work includes a DG implementation of the level set transport equation, which moves the level set with the flow field velocity, and a DG implementation of themore » reinitialization equation, which is used to maintain the shape of the level set profile to promote good mass conservation. A near second order converging interface curvature is obtained by following a height function methodology (common amongst volume of fluid schemes) in the context of the conservative level set. Various numerical experiments are conducted to test the properties of the method and show excellent results, even on coarse meshes. The tests include Zalesak’s disk, two-dimensional deformation of a circle, time evolution of a standing wave, and a study of the Kelvin–Helmholtz instability. Finally, this novel methodology is employed to simulate the break-up of a turbulent liquid jet.« less

  6. PolyPole-1: An accurate numerical algorithm for intra-granular fission gas release

    DOE Office of Scientific and Technical Information (OSTI.GOV)

    Pizzocri, D.; Rabiti, C.; Luzzi, L.

    2016-09-01

    This paper describes the development of a new numerical algorithm (called PolyPole-1) to efficiently solve the equation for intra-granular fission gas release in nuclear fuel. The work was carried out in collaboration with Politecnico di Milano and Institute for Transuranium Elements. The PolyPole-1 algorithms is being implemented in INL's fuels code BISON code as part of BISON's fission gas release model. The transport of fission gas from within the fuel grains to the grain boundaries (intra-granular fission gas release) is a fundamental controlling mechanism of fission gas release and gaseous swelling in nuclear fuel. Hence, accurate numerical solution of themore » corresponding mathematical problem needs to be included in fission gas behaviour models used in fuel performance codes. Under the assumption of equilibrium between trapping and resolution, the process can be described mathematically by a single diffusion equation for the gas atom concentration in a grain. In this work, we propose a new numerical algorithm (PolyPole-1) to efficiently solve the fission gas diffusion equation in time-varying conditions. The PolyPole-1 algorithm is based on the analytic modal solution of the diffusion equation for constant conditions, with the addition of polynomial corrective terms that embody the information on the deviation from constant conditions. The new algorithm is verified by comparing the results to a finite difference solution over a large number of randomly generated operation histories. Furthermore, comparison to state-of-the-art algorithms used in fuel performance codes demonstrates that the accuracy of the PolyPole-1 solution is superior to other algorithms, with similar computational effort. Finally, the concept of PolyPole-1 may be extended to the solution of the general problem of intra-granular fission gas diffusion during non-equilibrium trapping and resolution, which will be the subject of future work.« less

  7. An asymptotic preserving unified gas kinetic scheme for gray radiative transfer equations

    DOE Office of Scientific and Technical Information (OSTI.GOV)

    Sun, Wenjun, E-mail: sun_wenjun@iapcm.ac.cn; Jiang, Song, E-mail: jiang@iapcm.ac.cn; Xu, Kun, E-mail: makxu@ust.hk

    The solutions of radiative transport equations can cover both optical thin and optical thick regimes due to the large variation of photon's mean-free path and its interaction with the material. In the small mean free path limit, the nonlinear time-dependent radiative transfer equations can converge to an equilibrium diffusion equation due to the intensive interaction between radiation and material. In the optical thin limit, the photon free transport mechanism will emerge. In this paper, we are going to develop an accurate and robust asymptotic preserving unified gas kinetic scheme (AP-UGKS) for the gray radiative transfer equations, where the radiation transportmore » equation is coupled with the material thermal energy equation. The current work is based on the UGKS framework for the rarefied gas dynamics [14], and is an extension of a recent work [12] from a one-dimensional linear radiation transport equation to a nonlinear two-dimensional gray radiative system. The newly developed scheme has the asymptotic preserving (AP) property in the optically thick regime in the capturing of diffusive solution without using a cell size being smaller than the photon's mean free path and time step being less than the photon collision time. Besides the diffusion limit, the scheme can capture the exact solution in the optical thin regime as well. The current scheme is a finite volume method. Due to the direct modeling for the time evolution solution of the interface radiative intensity, a smooth transition of the transport physics from optical thin to optical thick can be accurately recovered. Many numerical examples are included to validate the current approach.« less

  8. The Space-Time Conservation Element and Solution Element Method-A New High-Resolution and Genuinely Multidimensional Paradigm for Solving Conservation Laws. 2; Numerical Simulation of Shock Waves and Contact Discontinuities

    NASA Technical Reports Server (NTRS)

    Wang, Xiao-Yen; Chow, Chuen-Yen; Chang, Sin-Chung

    1998-01-01

    Without resorting to special treatment for each individual test case, the 1D and 2D CE/SE shock-capturing schemes described previously (in Part I) are used to simulate flows involving phenomena such as shock waves, contact discontinuities, expansion waves and their interactions. Five 1D and six 2D problems are considered to examine the capability and robustness of these schemes. Despite their simple logical structures and low computational cost (for the 2D CE/SE shock-capturing scheme, the CPU time is about 2 micro-secs per mesh point per marching step on a Cray C90 machine), the numerical results, when compared with experimental data, exact solutions or numerical solutions by other methods, indicate that these schemes can accurately resolve shock and contact discontinuities consistently.

  9. Numerical simulation of conservation laws

    NASA Technical Reports Server (NTRS)

    Chang, Sin-Chung; To, Wai-Ming

    1992-01-01

    A new numerical framework for solving conservation laws is being developed. This new approach differs substantially from the well established methods, i.e., finite difference, finite volume, finite element and spectral methods, in both concept and methodology. The key features of the current scheme include: (1) direct discretization of the integral forms of conservation laws, (2) treating space and time on the same footing, (3) flux conservation in space and time, and (4) unified treatment of the convection and diffusion fluxes. The model equation considered in the initial study is the standard one dimensional unsteady constant-coefficient convection-diffusion equation. In a stability study, it is shown that the principal and spurious amplification factors of the current scheme, respectively, are structurally similar to those of the leapfrog/DuFort-Frankel scheme. As a result, the current scheme has no numerical diffusion in the special case of pure convection and is unconditionally stable in the special case of pure diffusion. Assuming smooth initial data, it will be shown theoretically and numerically that, by using an easily determined optimal time step, the accuracy of the current scheme may reach a level which is several orders of magnitude higher than that of the MacCormack scheme, with virtually identical operation count.

  10. A modified symplectic PRK scheme for seismic wave modeling

    NASA Astrophysics Data System (ADS)

    Liu, Shaolin; Yang, Dinghui; Ma, Jian

    2017-02-01

    A new scheme for the temporal discretization of the seismic wave equation is constructed based on symplectic geometric theory and a modified strategy. The ordinary differential equation in terms of time, which is obtained after spatial discretization via the spectral-element method, is transformed into a Hamiltonian system. A symplectic partitioned Runge-Kutta (PRK) scheme is used to solve the Hamiltonian system. A term related to the multiplication of the spatial discretization operator with the seismic wave velocity vector is added into the symplectic PRK scheme to create a modified symplectic PRK scheme. The symplectic coefficients of the new scheme are determined via Taylor series expansion. The positive coefficients of the scheme indicate that its long-term computational capability is more powerful than that of conventional symplectic schemes. An exhaustive theoretical analysis reveals that the new scheme is highly stable and has low numerical dispersion. The results of three numerical experiments demonstrate the high efficiency of this method for seismic wave modeling.

  11. A Numerical Model for Trickle Bed Reactors

    NASA Astrophysics Data System (ADS)

    Propp, Richard M.; Colella, Phillip; Crutchfield, William Y.; Day, Marcus S.

    2000-12-01

    Trickle bed reactors are governed by equations of flow in porous media such as Darcy's law and the conservation of mass. Our numerical method for solving these equations is based on a total-velocity splitting, sequential formulation which leads to an implicit pressure equation and a semi-implicit mass conservation equation. We use high-resolution finite-difference methods to discretize these equations. Our solution scheme extends previous work in modeling porous media flows in two ways. First, we incorporate physical effects due to capillary pressure, a nonlinear inlet boundary condition, spatial porosity variations, and inertial effects on phase mobilities. In particular, capillary forces introduce a parabolic component into the recast evolution equation, and the inertial effects give rise to hyperbolic nonconvexity. Second, we introduce a modification of the slope-limiting algorithm to prevent our numerical method from producing spurious shocks. We present a numerical algorithm for accommodating these difficulties, show the algorithm is second-order accurate, and demonstrate its performance on a number of simplified problems relevant to trickle bed reactor modeling.

  12. Fast and Accurate Prediction of Numerical Relativity Waveforms from Binary Black Hole Coalescences Using Surrogate Models

    NASA Astrophysics Data System (ADS)

    Blackman, Jonathan; Field, Scott E.; Galley, Chad R.; Szilágyi, Béla; Scheel, Mark A.; Tiglio, Manuel; Hemberger, Daniel A.

    2015-09-01

    Simulating a binary black hole coalescence by solving Einstein's equations is computationally expensive, requiring days to months of supercomputing time. Using reduced order modeling techniques, we construct an accurate surrogate model, which is evaluated in a millisecond to a second, for numerical relativity (NR) waveforms from nonspinning binary black hole coalescences with mass ratios in [1, 10] and durations corresponding to about 15 orbits before merger. We assess the model's uncertainty and show that our modeling strategy predicts NR waveforms not used for the surrogate's training with errors nearly as small as the numerical error of the NR code. Our model includes all spherical-harmonic -2Yℓm waveform modes resolved by the NR code up to ℓ=8 . We compare our surrogate model to effective one body waveforms from 50 M⊙ to 300 M⊙ for advanced LIGO detectors and find that the surrogate is always more faithful (by at least an order of magnitude in most cases).

  13. Fast and Accurate Prediction of Numerical Relativity Waveforms from Binary Black Hole Coalescences Using Surrogate Models.

    PubMed

    Blackman, Jonathan; Field, Scott E; Galley, Chad R; Szilágyi, Béla; Scheel, Mark A; Tiglio, Manuel; Hemberger, Daniel A

    2015-09-18

    Simulating a binary black hole coalescence by solving Einstein's equations is computationally expensive, requiring days to months of supercomputing time. Using reduced order modeling techniques, we construct an accurate surrogate model, which is evaluated in a millisecond to a second, for numerical relativity (NR) waveforms from nonspinning binary black hole coalescences with mass ratios in [1, 10] and durations corresponding to about 15 orbits before merger. We assess the model's uncertainty and show that our modeling strategy predicts NR waveforms not used for the surrogate's training with errors nearly as small as the numerical error of the NR code. Our model includes all spherical-harmonic _{-2}Y_{ℓm} waveform modes resolved by the NR code up to ℓ=8. We compare our surrogate model to effective one body waveforms from 50M_{⊙} to 300M_{⊙} for advanced LIGO detectors and find that the surrogate is always more faithful (by at least an order of magnitude in most cases).

  14. A positive and entropy-satisfying finite volume scheme for the Baer–Nunziato model

    DOE Office of Scientific and Technical Information (OSTI.GOV)

    Coquel, Frédéric, E-mail: frederic.coquel@cmap.polytechnique.fr; Hérard, Jean-Marc, E-mail: jean-marc.herard@edf.fr; Saleh, Khaled, E-mail: saleh@math.univ-lyon1.fr

    We present a relaxation scheme for approximating the entropy dissipating weak solutions of the Baer–Nunziato two-phase flow model. This relaxation scheme is straightforwardly obtained as an extension of the relaxation scheme designed in for the isentropic Baer–Nunziato model and consequently inherits its main properties. To our knowledge, this is the only existing scheme for which the approximated phase fractions, phase densities and phase internal energies are proven to remain positive without any restrictive condition other than a classical fully computable CFL condition. For ideal gas and stiffened gas equations of state, real values of the phasic speeds of sound aremore » also proven to be maintained by the numerical scheme. It is also the only scheme for which a discrete entropy inequality is proven, under a CFL condition derived from the natural sub-characteristic condition associated with the relaxation approximation. This last property, which ensures the non-linear stability of the numerical method, is satisfied for any admissible equation of state. We provide a numerical study for the convergence of the approximate solutions towards some exact Riemann solutions. The numerical simulations show that the relaxation scheme compares well with two of the most popular existing schemes available for the Baer–Nunziato model, namely Schwendeman–Wahle–Kapila's Godunov-type scheme and Tokareva–Toro's HLLC scheme . The relaxation scheme also shows a higher precision and a lower computational cost (for comparable accuracy) than a standard numerical scheme used in the nuclear industry, namely Rusanov's scheme. Finally, we assess the good behavior of the scheme when approximating vanishing phase solutions.« less

  15. Solutions of the benchmark problems by the dispersion-relation-preserving scheme

    NASA Technical Reports Server (NTRS)

    Tam, Christopher K. W.; Shen, H.; Kurbatskii, K. A.; Auriault, L.

    1995-01-01

    The 7-point stencil Dispersion-Relation-Preserving scheme of Tam and Webb is used to solve all the six categories of the CAA benchmark problems. The purpose is to show that the scheme is capable of solving linear, as well as nonlinear aeroacoustics problems accurately. Nonlinearities, inevitably, lead to the generation of spurious short wave length numerical waves. Often, these spurious waves would overwhelm the entire numerical solution. In this work, the spurious waves are removed by the addition of artificial selective damping terms to the discretized equations. Category 3 problems are for testing radiation and outflow boundary conditions. In solving these problems, the radiation and outflow boundary conditions of Tam and Webb are used. These conditions are derived from the asymptotic solutions of the linearized Euler equations. Category 4 problems involved solid walls. Here, the wall boundary conditions for high-order schemes of Tam and Dong are employed. These conditions require the use of one ghost value per boundary point per physical boundary condition. In the second problem of this category, the governing equations, when written in cylindrical coordinates, are singular along the axis of the radial coordinate. The proper boundary conditions at the axis are derived by applying the limiting process of r approaches 0 to the governing equations. The Category 5 problem deals with the numerical noise issue. In the present approach, the time-independent mean flow solution is computed first. Once the residual drops to the machine noise level, the incident sound wave is turned on gradually. The solution is marched in time until a time-periodic state is reached. No exact solution is known for the Category 6 problem. Because of this, the problem is formulated in two totally different ways, first as a scattering problem then as a direct simulation problem. There is good agreement between the two numerical solutions. This offers confidence in the computed results. Both

  16. Convergence Acceleration for Multistage Time-Stepping Schemes

    NASA Technical Reports Server (NTRS)

    Swanson, R. C.; Turkel, Eli L.; Rossow, C-C; Vasta, V. N.

    2006-01-01

    The convergence of a Runge-Kutta (RK) scheme with multigrid is accelerated by preconditioning with a fully implicit operator. With the extended stability of the Runge-Kutta scheme, CFL numbers as high as 1000 could be used. The implicit preconditioner addresses the stiffness in the discrete equations associated with stretched meshes. Numerical dissipation operators (based on the Roe scheme, a matrix formulation, and the CUSP scheme) as well as the number of RK stages are considered in evaluating the RK/implicit scheme. Both the numerical and computational efficiency of the scheme with the different dissipation operators are discussed. The RK/implicit scheme is used to solve the two-dimensional (2-D) and three-dimensional (3-D) compressible, Reynolds-averaged Navier-Stokes equations. In two dimensions, turbulent flows over an airfoil at subsonic and transonic conditions are computed. The effects of mesh cell aspect ratio on convergence are investigated for Reynolds numbers between 5.7 x 10(exp 6) and 100.0 x 10(exp 6). Results are also obtained for a transonic wing flow. For both 2-D and 3-D problems, the computational time of a well-tuned standard RK scheme is reduced at least a factor of four.

  17. Boosting flood warning schemes with fast emulator of detailed hydrodynamic models

    NASA Astrophysics Data System (ADS)

    Bellos, V.; Carbajal, J. P.; Leitao, J. P.

    2017-12-01

    Floods are among the most destructive catastrophic events and their frequency has incremented over the last decades. To reduce flood impact and risks, flood warning schemes are installed in flood prone areas. Frequently, these schemes are based on numerical models which quickly provide predictions of water levels and other relevant observables. However, the high complexity of flood wave propagation in the real world and the need of accurate predictions in urban environments or in floodplains hinders the use of detailed simulators. This sets the difficulty, we need fast predictions that meet the accuracy requirements. Most physics based detailed simulators although accurate, will not fulfill the speed demand. Even if High Performance Computing techniques are used (the magnitude of required simulation time is minutes/hours). As a consequence, most flood warning schemes are based in coarse ad-hoc approximations that cannot take advantage a detailed hydrodynamic simulation. In this work, we present a methodology for developing a flood warning scheme using an Gaussian Processes based emulator of a detailed hydrodynamic model. The methodology consists of two main stages: 1) offline stage to build the emulator; 2) online stage using the emulator to predict and generate warnings. The offline stage consists of the following steps: a) definition of the critical sites of the area under study, and the specification of the observables to predict at those sites, e.g. water depth, flow velocity, etc.; b) generation of a detailed simulation dataset to train the emulator; c) calibration of the required parameters (if measurements are available). The online stage is carried on using the emulator to predict the relevant observables quickly, and the detailed simulator is used in parallel to verify key predictions of the emulator. The speed gain given by the emulator allows also to quantify uncertainty in predictions using ensemble methods. The above methodology is applied in real

  18. Numerical investigation of a jet in ground effect using the fortified Navier-Stokes scheme

    NASA Technical Reports Server (NTRS)

    Vandalsem, William R.; Steger, Joseph L.

    1988-01-01

    One of the flows inherent in VSTOL operations, the jet in ground effect with a crossflow, is studied using the Fortified Navier-Stokes (FNS) scheme. Through comparison of the simulation results and the experimental data, and through the variation of the flow parameters (in the simulation) a number of interesting characteristics of the flow have been observed. For example, it appears that the forward penetration of the ground vortex is a strong inverse function of the level of mixing in the ground vortex. Also, an effort has been made to isolate issues which require additional work in order to improve the numerical simulation of the jet in ground effect flow. The FNS approach simplifies the simulation of a single jet in ground effect, but it will be even more effective in applications to more complex topologies.

  19. Gas Evolution Dynamics in Godunov-Type Schemes and Analysis of Numerical Shock Instability

    NASA Technical Reports Server (NTRS)

    Xu, Kun

    1999-01-01

    In this paper we are going to study the gas evolution dynamics of the exact and approximate Riemann solvers, e.g., the Flux Vector Splitting (FVS) and the Flux Difference Splitting (FDS) schemes. Since the FVS scheme and the Kinetic Flux Vector Splitting (KFVS) scheme have the same physical mechanism and similar flux function, based on the analysis of the discretized KFVS scheme the weakness and advantage of the FVS scheme are closely observed. The subtle dissipative mechanism of the Godunov method in the 2D case is also analyzed, and the physical reason for shock instability, i.e., carbuncle phenomena and odd-even decoupling, is presented.

  20. Triangle based TVD schemes for hyperbolic conservation laws

    NASA Technical Reports Server (NTRS)

    Durlofsky, Louis J.; Osher, Stanley; Engquist, Bjorn

    1990-01-01

    A triangle based total variation diminishing (TVD) scheme for the numerical approximation of hyperbolic conservation laws in two space dimensions is constructed. The novelty of the scheme lies in the nature of the preprocessing of the cell averaged data, which is accomplished via a nearest neighbor linear interpolation followed by a slope limiting procedures. Two such limiting procedures are suggested. The resulting method is considerably more simple than other triangle based non-oscillatory approximations which, like this scheme, approximate the flux up to second order accuracy. Numerical results for linear advection and Burgers' equation are presented.

  1. On central-difference and upwind schemes

    NASA Technical Reports Server (NTRS)

    Swanson, R. C.; Turkel, Eli

    1990-01-01

    A class of numerical dissipation models for central-difference schemes constructed with second- and fourth-difference terms is considered. The notion of matrix dissipation associated with upwind schemes is used to establish improved shock capturing capability for these models. In addition, conditions are given that guarantee that such dissipation models produce a Total Variation Diminishing (TVD) scheme. Appropriate switches for this type of model to ensure satisfaction of the TVD property are presented. Significant improvements in the accuracy of a central-difference scheme are demonstrated by computing both inviscid and viscous transonic airfoil flows.

  2. Numerical Simulations of Reacting Flows Using Asynchrony-Tolerant Schemes for Exascale Computing

    NASA Astrophysics Data System (ADS)

    Cleary, Emmet; Konduri, Aditya; Chen, Jacqueline

    2017-11-01

    Communication and data synchronization between processing elements (PEs) are likely to pose a major challenge in scalability of solvers at the exascale. Recently developed asynchrony-tolerant (AT) finite difference schemes address this issue by relaxing communication and synchronization between PEs at a mathematical level while preserving accuracy, resulting in improved scalability. The performance of these schemes has been validated for simple linear and nonlinear homogeneous PDEs. However, many problems of practical interest are governed by highly nonlinear PDEs with source terms, whose solution may be sensitive to perturbations caused by communication asynchrony. The current work applies the AT schemes to combustion problems with chemical source terms, yielding a stiff system of PDEs with nonlinear source terms highly sensitive to temperature. Examples shown will use single-step and multi-step CH4 mechanisms for 1D premixed and nonpremixed flames. Error analysis will be discussed both in physical and spectral space. Results show that additional errors introduced by the AT schemes are negligible and the schemes preserve their accuracy. We acknowledge funding from the DOE Computational Science Graduate Fellowship administered by the Krell Institute.

  3. Analysis of sensitivity to different parameterization schemes for a subtropical cyclone

    NASA Astrophysics Data System (ADS)

    Quitián-Hernández, L.; Fernández-González, S.; González-Alemán, J. J.; Valero, F.; Martín, M. L.

    2018-05-01

    A sensitivity analysis to diverse WRF model physical parameterization schemes is carried out during the lifecycle of a Subtropical cyclone (STC). STCs are low-pressure systems that share tropical and extratropical characteristics, with hybrid thermal structures. In October 2014, a STC made landfall in the Canary Islands, causing widespread damage from strong winds and precipitation there. The system began to develop on October 18 and its effects lasted until October 21. Accurate simulation of this type of cyclone continues to be a major challenge because of its rapid intensification and unique characteristics. In the present study, several numerical simulations were performed using the WRF model to do a sensitivity analysis of its various parameterization schemes for the development and intensification of the STC. The combination of parameterization schemes that best simulated this type of phenomenon was thereby determined. In particular, the parameterization combinations that included the Tiedtke cumulus schemes had the most positive effects on model results. Moreover, concerning STC track validation, optimal results were attained when the STC was fully formed and all convective processes stabilized. Furthermore, to obtain the parameterization schemes that optimally categorize STC structure, a verification using Cyclone Phase Space is assessed. Consequently, the combination of parameterizations including the Tiedtke cumulus schemes were again the best in categorizing the cyclone's subtropical structure. For strength validation, related atmospheric variables such as wind speed and precipitable water were analyzed. Finally, the effects of using a deterministic or probabilistic approach in simulating intense convective phenomena were evaluated.

  4. Central Upwind Scheme for a Compressible Two-Phase Flow Model

    PubMed Central

    Ahmed, Munshoor; Saleem, M. Rehan; Zia, Saqib; Qamar, Shamsul

    2015-01-01

    In this article, a compressible two-phase reduced five-equation flow model is numerically investigated. The model is non-conservative and the governing equations consist of two equations describing the conservation of mass, one for overall momentum and one for total energy. The fifth equation is the energy equation for one of the two phases and it includes source term on the right-hand side which represents the energy exchange between two fluids in the form of mechanical and thermodynamical work. For the numerical approximation of the model a high resolution central upwind scheme is implemented. This is a non-oscillatory upwind biased finite volume scheme which does not require a Riemann solver at each time step. Few numerical case studies of two-phase flows are presented. For validation and comparison, the same model is also solved by using kinetic flux-vector splitting (KFVS) and staggered central schemes. It was found that central upwind scheme produces comparable results to the KFVS scheme. PMID:26039242

  5. Central upwind scheme for a compressible two-phase flow model.

    PubMed

    Ahmed, Munshoor; Saleem, M Rehan; Zia, Saqib; Qamar, Shamsul

    2015-01-01

    In this article, a compressible two-phase reduced five-equation flow model is numerically investigated. The model is non-conservative and the governing equations consist of two equations describing the conservation of mass, one for overall momentum and one for total energy. The fifth equation is the energy equation for one of the two phases and it includes source term on the right-hand side which represents the energy exchange between two fluids in the form of mechanical and thermodynamical work. For the numerical approximation of the model a high resolution central upwind scheme is implemented. This is a non-oscillatory upwind biased finite volume scheme which does not require a Riemann solver at each time step. Few numerical case studies of two-phase flows are presented. For validation and comparison, the same model is also solved by using kinetic flux-vector splitting (KFVS) and staggered central schemes. It was found that central upwind scheme produces comparable results to the KFVS scheme.

  6. Corrigendum to ;Numerical dissipation control in high order shock-capturing schemes for LES of low speed flows; [J. Comput. Phys. 307 (2016) 189-202

    NASA Astrophysics Data System (ADS)

    Kotov, D. V.; Yee, H. C.; Wray, A. A.; Sjögreen, Björn; Kritsuk, A. G.

    2018-01-01

    The authors regret for the typographic errors that were made in equation (4) and missing phrase after equation (4) in the article "Numerical dissipation control in high order shock-capturing schemes for LES of low speed flows" [J. Comput. Phys. 307 (2016) 189-202].

  7. High-order asynchrony-tolerant finite difference schemes for partial differential equations

    NASA Astrophysics Data System (ADS)

    Aditya, Konduri; Donzis, Diego A.

    2017-12-01

    Synchronizations of processing elements (PEs) in massively parallel simulations, which arise due to communication or load imbalances between PEs, significantly affect the scalability of scientific applications. We have recently proposed a method based on finite-difference schemes to solve partial differential equations in an asynchronous fashion - synchronization between PEs is relaxed at a mathematical level. While standard schemes can maintain their stability in the presence of asynchrony, their accuracy is drastically affected. In this work, we present a general methodology to derive asynchrony-tolerant (AT) finite difference schemes of arbitrary order of accuracy, which can maintain their accuracy when synchronizations are relaxed. We show that there are several choices available in selecting a stencil to derive these schemes and discuss their effect on numerical and computational performance. We provide a simple classification of schemes based on the stencil and derive schemes that are representative of different classes. Their numerical error is rigorously analyzed within a statistical framework to obtain the overall accuracy of the solution. Results from numerical experiments are used to validate the performance of the schemes.

  8. Numerical methods for incompressible viscous flows with engineering applications

    NASA Technical Reports Server (NTRS)

    Rose, M. E.; Ash, R. L.

    1988-01-01

    A numerical scheme has been developed to solve the incompressible, 3-D Navier-Stokes equations using velocity-vorticity variables. This report summarizes the development of the numerical approximation schemes for the divergence and curl of the velocity vector fields and the development of compact schemes for handling boundary and initial boundary value problems.

  9. Second order symmetry-preserving conservative Lagrangian scheme for compressible Euler equations in two-dimensional cylindrical coordinates

    DOE Office of Scientific and Technical Information (OSTI.GOV)

    Cheng, Juan, E-mail: cheng_juan@iapcm.ac.cn; Shu, Chi-Wang, E-mail: shu@dam.brown.edu

    In applications such as astrophysics and inertial confinement fusion, there are many three-dimensional cylindrical-symmetric multi-material problems which are usually simulated by Lagrangian schemes in the two-dimensional cylindrical coordinates. For this type of simulation, a critical issue for the schemes is to keep spherical symmetry in the cylindrical coordinate system if the original physical problem has this symmetry. In the past decades, several Lagrangian schemes with such symmetry property have been developed, but all of them are only first order accurate. In this paper, we develop a second order cell-centered Lagrangian scheme for solving compressible Euler equations in cylindrical coordinates, basedmore » on the control volume discretizations, which is designed to have uniformly second order accuracy and capability to preserve one-dimensional spherical symmetry in a two-dimensional cylindrical geometry when computed on an equal-angle-zoned initial grid. The scheme maintains several good properties such as conservation for mass, momentum and total energy, and the geometric conservation law. Several two-dimensional numerical examples in cylindrical coordinates are presented to demonstrate the good performance of the scheme in terms of accuracy, symmetry, non-oscillation and robustness. The advantage of higher order accuracy is demonstrated in these examples.« less

  10. Numerical solution to generalized Burgers'-Fisher equation using Exp-function method hybridized with heuristic computation.

    PubMed

    Malik, Suheel Abdullah; Qureshi, Ijaz Mansoor; Amir, Muhammad; Malik, Aqdas Naveed; Haq, Ihsanul

    2015-01-01

    In this paper, a new heuristic scheme for the approximate solution of the generalized Burgers'-Fisher equation is proposed. The scheme is based on the hybridization of Exp-function method with nature inspired algorithm. The given nonlinear partial differential equation (NPDE) through substitution is converted into a nonlinear ordinary differential equation (NODE). The travelling wave solution is approximated by the Exp-function method with unknown parameters. The unknown parameters are estimated by transforming the NODE into an equivalent global error minimization problem by using a fitness function. The popular genetic algorithm (GA) is used to solve the minimization problem, and to achieve the unknown parameters. The proposed scheme is successfully implemented to solve the generalized Burgers'-Fisher equation. The comparison of numerical results with the exact solutions, and the solutions obtained using some traditional methods, including adomian decomposition method (ADM), homotopy perturbation method (HPM), and optimal homotopy asymptotic method (OHAM), show that the suggested scheme is fairly accurate and viable for solving such problems.

  11. Numerical Solution to Generalized Burgers'-Fisher Equation Using Exp-Function Method Hybridized with Heuristic Computation

    PubMed Central

    Malik, Suheel Abdullah; Qureshi, Ijaz Mansoor; Amir, Muhammad; Malik, Aqdas Naveed; Haq, Ihsanul

    2015-01-01

    In this paper, a new heuristic scheme for the approximate solution of the generalized Burgers'-Fisher equation is proposed. The scheme is based on the hybridization of Exp-function method with nature inspired algorithm. The given nonlinear partial differential equation (NPDE) through substitution is converted into a nonlinear ordinary differential equation (NODE). The travelling wave solution is approximated by the Exp-function method with unknown parameters. The unknown parameters are estimated by transforming the NODE into an equivalent global error minimization problem by using a fitness function. The popular genetic algorithm (GA) is used to solve the minimization problem, and to achieve the unknown parameters. The proposed scheme is successfully implemented to solve the generalized Burgers'-Fisher equation. The comparison of numerical results with the exact solutions, and the solutions obtained using some traditional methods, including adomian decomposition method (ADM), homotopy perturbation method (HPM), and optimal homotopy asymptotic method (OHAM), show that the suggested scheme is fairly accurate and viable for solving such problems. PMID:25811858

  12. Improved Boundary Conditions for Cell-centered Difference Schemes

    NASA Technical Reports Server (NTRS)

    VanderWijngaart, Rob F.; Klopfer, Goetz H.; Chancellor, Marisa K. (Technical Monitor)

    1997-01-01

    Cell-centered finite-volume (CCFV) schemes have certain attractive properties for the solution of the equations governing compressible fluid flow. Among others, they provide a natural vehicle for specifying flux conditions at the boundaries of the physical domain. Unfortunately, they lead to slow convergence for numerical programs utilizing them. In this report a method for investigating and improving the convergence of CCFV schemes is presented, which focuses on the effect of the numerical boundary conditions. The key to the method is the computation of the spectral radius of the iteration matrix of the entire demoralized system of equations, not just of the interior point scheme or the boundary conditions.

  13. The space-time solution element method: A new numerical approach for the Navier-Stokes equations

    NASA Technical Reports Server (NTRS)

    Scott, James R.; Chang, Sin-Chung

    1995-01-01

    This paper is one of a series of papers describing the development of a new numerical method for the Navier-Stokes equations. Unlike conventional numerical methods, the current method concentrates on the discrete simulation of both the integral and differential forms of the Navier-Stokes equations. Conservation of mass, momentum, and energy in space-time is explicitly provided for through a rigorous enforcement of both the integral and differential forms of the governing conservation laws. Using local polynomial expansions to represent the discrete primitive variables on each cell, fluxes at cell interfaces are evaluated and balanced using exact functional expressions. No interpolation or flux limiters are required. Because of the generality of the current method, it applies equally to the steady and unsteady Navier-Stokes equations. In this paper, we generalize and extend the authors' 2-D, steady state implicit scheme. A general closure methodology is presented so that all terms up through a given order in the local expansions may be retained. The scheme is also extended to nonorthogonal Cartesian grids. Numerous flow fields are computed and results are compared with known solutions. The high accuracy of the scheme is demonstrated through its ability to accurately resolve developing boundary layers on coarse grids. Finally, we discuss applications of the current method to the unsteady Navier-Stokes equations.

  14. Upwind and symmetric shock-capturing schemes

    NASA Technical Reports Server (NTRS)

    Yee, H. C.

    1987-01-01

    The development of numerical methods for hyperbolic conservation laws has been a rapidly growing area for the last ten years. Many of the fundamental concepts and state-of-the-art developments can only be found in meeting proceedings or internal reports. This review paper attempts to give an overview and a unified formulation of a class of shock-capturing methods. Special emphasis is on the construction of the basic nonlinear scalar second-order schemes and the methods of extending these nonlinear scalar schemes to nonlinear systems via the extact Riemann solver, approximate Riemann solvers, and flux-vector splitting approaches. Generalization of these methods to efficiently include real gases and large systems of nonequilibrium flows is discussed. The performance of some of these schemes is illustrated by numerical examples for one-, two- and three-dimensional gas dynamics problems.

  15. On Spurious Numerics in Solving Reactive Equations

    NASA Technical Reports Server (NTRS)

    Kotov, D. V; Yee, H. C.; Wang, W.; Shu, C.-W.

    2013-01-01

    The objective of this study is to gain a deeper understanding of the behavior of high order shock-capturing schemes for problems with stiff source terms and discontinuities and on corresponding numerical prediction strategies. The studies by Yee et al. (2012) and Wang et al. (2012) focus only on solving the reactive system by the fractional step method using the Strang splitting (Strang 1968). It is a common practice by developers in computational physics and engineering simulations to include a cut off safeguard if densities are outside the permissible range. Here we compare the spurious behavior of the same schemes by solving the fully coupled reactive system without the Strang splitting vs. using the Strang splitting. Comparison between the two procedures and the effects of a cut off safeguard is the focus the present study. The comparison of the performance of these schemes is largely based on the degree to which each method captures the correct location of the reaction front for coarse grids. Here "coarse grids" means standard mesh density requirement for accurate simulation of typical non-reacting flows of similar problem setup. It is remarked that, in order to resolve the sharp reaction front, local refinement beyond standard mesh density is still needed.

  16. Fast and Accurate Learning When Making Discrete Numerical Estimates.

    PubMed

    Sanborn, Adam N; Beierholm, Ulrik R

    2016-04-01

    Many everyday estimation tasks have an inherently discrete nature, whether the task is counting objects (e.g., a number of paint buckets) or estimating discretized continuous variables (e.g., the number of paint buckets needed to paint a room). While Bayesian inference is often used for modeling estimates made along continuous scales, discrete numerical estimates have not received as much attention, despite their common everyday occurrence. Using two tasks, a numerosity task and an area estimation task, we invoke Bayesian decision theory to characterize how people learn discrete numerical distributions and make numerical estimates. Across three experiments with novel stimulus distributions we found that participants fell between two common decision functions for converting their uncertain representation into a response: drawing a sample from their posterior distribution and taking the maximum of their posterior distribution. While this was consistent with the decision function found in previous work using continuous estimation tasks, surprisingly the prior distributions learned by participants in our experiments were much more adaptive: When making continuous estimates, participants have required thousands of trials to learn bimodal priors, but in our tasks participants learned discrete bimodal and even discrete quadrimodal priors within a few hundred trials. This makes discrete numerical estimation tasks good testbeds for investigating how people learn and make estimates.

  17. Fast and Accurate Learning When Making Discrete Numerical Estimates

    PubMed Central

    Sanborn, Adam N.; Beierholm, Ulrik R.

    2016-01-01

    Many everyday estimation tasks have an inherently discrete nature, whether the task is counting objects (e.g., a number of paint buckets) or estimating discretized continuous variables (e.g., the number of paint buckets needed to paint a room). While Bayesian inference is often used for modeling estimates made along continuous scales, discrete numerical estimates have not received as much attention, despite their common everyday occurrence. Using two tasks, a numerosity task and an area estimation task, we invoke Bayesian decision theory to characterize how people learn discrete numerical distributions and make numerical estimates. Across three experiments with novel stimulus distributions we found that participants fell between two common decision functions for converting their uncertain representation into a response: drawing a sample from their posterior distribution and taking the maximum of their posterior distribution. While this was consistent with the decision function found in previous work using continuous estimation tasks, surprisingly the prior distributions learned by participants in our experiments were much more adaptive: When making continuous estimates, participants have required thousands of trials to learn bimodal priors, but in our tasks participants learned discrete bimodal and even discrete quadrimodal priors within a few hundred trials. This makes discrete numerical estimation tasks good testbeds for investigating how people learn and make estimates. PMID:27070155

  18. TU-EF-204-01: Accurate Prediction of CT Tube Current Modulation: Estimating Tube Current Modulation Schemes for Voxelized Patient Models Used in Monte Carlo Simulations

    DOE Office of Scientific and Technical Information (OSTI.GOV)

    McMillan, K; Bostani, M; McNitt-Gray, M

    2015-06-15

    Purpose: Most patient models used in Monte Carlo-based estimates of CT dose, including computational phantoms, do not have tube current modulation (TCM) data associated with them. While not a problem for fixed tube current simulations, this is a limitation when modeling the effects of TCM. Therefore, the purpose of this work was to develop and validate methods to estimate TCM schemes for any voxelized patient model. Methods: For 10 patients who received clinically-indicated chest (n=5) and abdomen/pelvis (n=5) scans on a Siemens CT scanner, both CT localizer radiograph (“topogram”) and image data were collected. Methods were devised to estimate themore » complete x-y-z TCM scheme using patient attenuation data: (a) available in the Siemens CT localizer radiograph/topogram itself (“actual-topo”) and (b) from a simulated topogram (“sim-topo”) derived from a projection of the image data. For comparison, the actual TCM scheme was extracted from the projection data of each patient. For validation, Monte Carlo simulations were performed using each TCM scheme to estimate dose to the lungs (chest scans) and liver (abdomen/pelvis scans). Organ doses from simulations using the actual TCM were compared to those using each of the estimated TCM methods (“actual-topo” and “sim-topo”). Results: For chest scans, the average differences between doses estimated using actual TCM schemes and estimated TCM schemes (“actual-topo” and “sim-topo”) were 3.70% and 4.98%, respectively. For abdomen/pelvis scans, the average differences were 5.55% and 6.97%, respectively. Conclusion: Strong agreement between doses estimated using actual and estimated TCM schemes validates the methods for simulating Siemens topograms and converting attenuation data into TCM schemes. This indicates that the methods developed in this work can be used to accurately estimate TCM schemes for any patient model or computational phantom, whether a CT localizer radiograph is available or

  19. A consistent and conservative scheme for MHD flows with complex boundaries on an unstructured Cartesian adaptive system

    DOE Office of Scientific and Technical Information (OSTI.GOV)

    Zhang, Jie; Ni, Ming-Jiu, E-mail: mjni@ucas.ac.cn

    2014-01-01

    The numerical simulation of Magnetohydrodynamics (MHD) flows with complex boundaries has been a topic of great interest in the development of a fusion reactor blanket for the difficulty to accurately simulate the Hartmann layers and side layers along arbitrary geometries. An adaptive version of a consistent and conservative scheme has been developed for simulating the MHD flows. Besides, the present study forms the first attempt to apply the cut-cell approach for irregular wall-bounded MHD flows, which is more flexible and conveniently implemented under adaptive mesh refinement (AMR) technique. It employs a Volume-of-Fluid (VOF) approach to represent the fluid–conducting wall interfacemore » that makes it possible to solve the fluid–solid coupling magnetic problems, emphasizing at how electric field solver is implemented when conductivity is discontinuous in cut-cell. For the irregular cut-cells, the conservative interpolation technique is applied to calculate the Lorentz force at cell-center. On the other hand, it will be shown how consistent and conservative scheme is implemented on fine/coarse mesh boundaries when using AMR technique. Then, the applied numerical schemes are validated by five test simulations and excellent agreement was obtained for all the cases considered, simultaneously showed good consistency and conservative properties.« less

  20. High Order Semi-Lagrangian Advection Scheme

    NASA Astrophysics Data System (ADS)

    Malaga, Carlos; Mandujano, Francisco; Becerra, Julian

    2014-11-01

    In most fluid phenomena, advection plays an important roll. A numerical scheme capable of making quantitative predictions and simulations must compute correctly the advection terms appearing in the equations governing fluid flow. Here we present a high order forward semi-Lagrangian numerical scheme specifically tailored to compute material derivatives. The scheme relies on the geometrical interpretation of material derivatives to compute the time evolution of fields on grids that deform with the material fluid domain, an interpolating procedure of arbitrary order that preserves the moments of the interpolated distributions, and a nonlinear mapping strategy to perform interpolations between undeformed and deformed grids. Additionally, a discontinuity criterion was implemented to deal with discontinuous fields and shocks. Tests of pure advection, shock formation and nonlinear phenomena are presented to show performance and convergence of the scheme. The high computational cost is considerably reduced when implemented on massively parallel architectures found in graphic cards. The authors acknowledge funding from Fondo Sectorial CONACYT-SENER Grant Number 42536 (DGAJ-SPI-34-170412-217).

  1. Non-linear hydrodynamical evolution of rotating relativistic stars: numerical methods and code tests

    NASA Astrophysics Data System (ADS)

    Font, José A.; Stergioulas, Nikolaos; Kokkotas, Kostas D.

    2000-04-01

    We present numerical hydrodynamical evolutions of rapidly rotating relativistic stars, using an axisymmetric, non-linear relativistic hydrodynamics code. We use four different high-resolution shock-capturing (HRSC) finite-difference schemes (based on approximate Riemann solvers) and compare their accuracy in preserving uniformly rotating stationary initial configurations in long-term evolutions. Among these four schemes, we find that the third-order piecewise parabolic method scheme is superior in maintaining the initial rotation law in long-term evolutions, especially near the surface of the star. It is further shown that HRSC schemes are suitable for the evolution of perturbed neutron stars and for the accurate identification (via Fourier transforms) of normal modes of oscillation. This is demonstrated for radial and quadrupolar pulsations in the non-rotating limit, where we find good agreement with frequencies obtained with a linear perturbation code. The code can be used for studying small-amplitude or non-linear pulsations of differentially rotating neutron stars, while our present results serve as testbed computations for three-dimensional general-relativistic evolution codes.

  2. Crank-Nicholson difference scheme for a stochastic parabolic equation with a dependent operator coefficient

    DOE Office of Scientific and Technical Information (OSTI.GOV)

    Ashyralyev, Allaberen; Okur, Ulker

    In the present paper, the Crank-Nicolson difference scheme for the numerical solution of the stochastic parabolic equation with the dependent operator coefficient is considered. Theorem on convergence estimates for the solution of this difference scheme is established. In applications, convergence estimates for the solution of difference schemes for the numerical solution of three mixed problems for parabolic equations are obtained. The numerical results are given.

  3. A SECOND-ORDER DIVERGENCE-CONSTRAINED MULTIDIMENSIONAL NUMERICAL SCHEME FOR RELATIVISTIC TWO-FLUID ELECTRODYNAMICS

    DOE Office of Scientific and Technical Information (OSTI.GOV)

    Amano, Takanobu, E-mail: amano@eps.s.u-tokyo.ac.jp

    A new multidimensional simulation code for relativistic two-fluid electrodynamics (RTFED) is described. The basic equations consist of the full set of Maxwell’s equations coupled with relativistic hydrodynamic equations for separate two charged fluids, representing the dynamics of either an electron–positron or an electron–proton plasma. It can be recognized as an extension of conventional relativistic magnetohydrodynamics (RMHD). Finite resistivity may be introduced as a friction between the two species, which reduces to resistive RMHD in the long wavelength limit without suffering from a singularity at infinite conductivity. A numerical scheme based on HLL (Harten–Lax–Van Leer) Riemann solver is proposed that exactlymore » preserves the two divergence constraints for Maxwell’s equations simultaneously. Several benchmark problems demonstrate that it is capable of describing RMHD shocks/discontinuities at long wavelength limit, as well as dispersive characteristics due to the two-fluid effect appearing at small scales. This shows that the RTFED model is a promising tool for high energy astrophysics application.« less

  4. Numerical simulation of the debris flow dynamics with an upwind scheme and specific friction treatment

    NASA Astrophysics Data System (ADS)

    Sánchez Burillo, Guillermo; Beguería, Santiago; Latorre, Borja; Burguete, Javier

    2014-05-01

    Debris flows, snow and rock avalanches, mud and earth flows are often modeled by means of a particular realization of the so called shallow water equations (SWE). Indeed, a number of simulation models have been already developed [1], [2], [3], [4], [5], [6], [7]. Debris flow equations differ from shallow water equations in two main aspects. These are (a) strong bed gradient and (b) rheology friction terms that differ from the traditional SWE. A systematic analysis of the numerical solution of the hyperbolic system of equations rising from the shallow water equations with different rheological laws has not been done. Despite great efforts have been done to deal with friction expressions common in hydraulics (such as Manning friction), landslide rheologies are characterized by more complicated expressions that may deal to unphysical solutions if not treated carefully. In this work, a software that solves the time evolution of sliding masses over complex bed configurations is presented. The set of non- linear equations is treated by means of a first order upwind explicit scheme, and the friction contribution to the dynamics is treated with a suited numerical scheme [8]. In addition, the software incorporates various rheological models to accommodate for different flow types, such as the Voellmy frictional model [9] for rock and debris avalanches, or the Herschley-Bulkley model for debris and mud flows. The aim of this contribution is to release this code as a free, open source tool for the simulation of mass movements, and to encourage the scientific community to make use of it. The code uses as input data the friction coefficients and two input files: the topography of the bed and the initial (pre-failure) position of the sliding mass. In addition, another file with the final (post-event) position of the sliding mass, if desired, can be introduced to be compared with the simulation obtained result. If the deposited mass is given, an error estimation is computed by

  5. Calculating the binding free energies of charged species based on explicit-solvent simulations employing lattice-sum methods: An accurate correction scheme for electrostatic finite-size effects

    PubMed Central

    Rocklin, Gabriel J.; Mobley, David L.; Dill, Ken A.; Hünenberger, Philippe H.

    2013-01-01

    The calculation of a protein-ligand binding free energy based on molecular dynamics (MD) simulations generally relies on a thermodynamic cycle in which the ligand is alchemically inserted into the system, both in the solvated protein and free in solution. The corresponding ligand-insertion free energies are typically calculated in nanoscale computational boxes simulated under periodic boundary conditions and considering electrostatic interactions defined by a periodic lattice-sum. This is distinct from the ideal bulk situation of a system of macroscopic size simulated under non-periodic boundary conditions with Coulombic electrostatic interactions. This discrepancy results in finite-size effects, which affect primarily the charging component of the insertion free energy, are dependent on the box size, and can be large when the ligand bears a net charge, especially if the protein is charged as well. This article investigates finite-size effects on calculated charging free energies using as a test case the binding of the ligand 2-amino-5-methylthiazole (net charge +1 e) to a mutant form of yeast cytochrome c peroxidase in water. Considering different charge isoforms of the protein (net charges −5, 0, +3, or +9 e), either in the absence or the presence of neutralizing counter-ions, and sizes of the cubic computational box (edges ranging from 7.42 to 11.02 nm), the potentially large magnitude of finite-size effects on the raw charging free energies (up to 17.1 kJ mol−1) is demonstrated. Two correction schemes are then proposed to eliminate these effects, a numerical and an analytical one. Both schemes are based on a continuum-electrostatics analysis and require performing Poisson-Boltzmann (PB) calculations on the protein-ligand system. While the numerical scheme requires PB calculations under both non-periodic and periodic boundary conditions, the latter at the box size considered in the MD simulations, the analytical scheme only requires three non-periodic PB

  6. Calculating the binding free energies of charged species based on explicit-solvent simulations employing lattice-sum methods: an accurate correction scheme for electrostatic finite-size effects.

    PubMed

    Rocklin, Gabriel J; Mobley, David L; Dill, Ken A; Hünenberger, Philippe H

    2013-11-14

    The calculation of a protein-ligand binding free energy based on molecular dynamics (MD) simulations generally relies on a thermodynamic cycle in which the ligand is alchemically inserted into the system, both in the solvated protein and free in solution. The corresponding ligand-insertion free energies are typically calculated in nanoscale computational boxes simulated under periodic boundary conditions and considering electrostatic interactions defined by a periodic lattice-sum. This is distinct from the ideal bulk situation of a system of macroscopic size simulated under non-periodic boundary conditions with Coulombic electrostatic interactions. This discrepancy results in finite-size effects, which affect primarily the charging component of the insertion free energy, are dependent on the box size, and can be large when the ligand bears a net charge, especially if the protein is charged as well. This article investigates finite-size effects on calculated charging free energies using as a test case the binding of the ligand 2-amino-5-methylthiazole (net charge +1 e) to a mutant form of yeast cytochrome c peroxidase in water. Considering different charge isoforms of the protein (net charges -5, 0, +3, or +9 e), either in the absence or the presence of neutralizing counter-ions, and sizes of the cubic computational box (edges ranging from 7.42 to 11.02 nm), the potentially large magnitude of finite-size effects on the raw charging free energies (up to 17.1 kJ mol(-1)) is demonstrated. Two correction schemes are then proposed to eliminate these effects, a numerical and an analytical one. Both schemes are based on a continuum-electrostatics analysis and require performing Poisson-Boltzmann (PB) calculations on the protein-ligand system. While the numerical scheme requires PB calculations under both non-periodic and periodic boundary conditions, the latter at the box size considered in the MD simulations, the analytical scheme only requires three non-periodic PB

  7. Calculating the binding free energies of charged species based on explicit-solvent simulations employing lattice-sum methods: An accurate correction scheme for electrostatic finite-size effects

    NASA Astrophysics Data System (ADS)

    Rocklin, Gabriel J.; Mobley, David L.; Dill, Ken A.; Hünenberger, Philippe H.

    2013-11-01

    The calculation of a protein-ligand binding free energy based on molecular dynamics (MD) simulations generally relies on a thermodynamic cycle in which the ligand is alchemically inserted into the system, both in the solvated protein and free in solution. The corresponding ligand-insertion free energies are typically calculated in nanoscale computational boxes simulated under periodic boundary conditions and considering electrostatic interactions defined by a periodic lattice-sum. This is distinct from the ideal bulk situation of a system of macroscopic size simulated under non-periodic boundary conditions with Coulombic electrostatic interactions. This discrepancy results in finite-size effects, which affect primarily the charging component of the insertion free energy, are dependent on the box size, and can be large when the ligand bears a net charge, especially if the protein is charged as well. This article investigates finite-size effects on calculated charging free energies using as a test case the binding of the ligand 2-amino-5-methylthiazole (net charge +1 e) to a mutant form of yeast cytochrome c peroxidase in water. Considering different charge isoforms of the protein (net charges -5, 0, +3, or +9 e), either in the absence or the presence of neutralizing counter-ions, and sizes of the cubic computational box (edges ranging from 7.42 to 11.02 nm), the potentially large magnitude of finite-size effects on the raw charging free energies (up to 17.1 kJ mol-1) is demonstrated. Two correction schemes are then proposed to eliminate these effects, a numerical and an analytical one. Both schemes are based on a continuum-electrostatics analysis and require performing Poisson-Boltzmann (PB) calculations on the protein-ligand system. While the numerical scheme requires PB calculations under both non-periodic and periodic boundary conditions, the latter at the box size considered in the MD simulations, the analytical scheme only requires three non-periodic PB

  8. Assessment of numerical techniques for unsteady flow calculations

    NASA Technical Reports Server (NTRS)

    Hsieh, Kwang-Chung

    1989-01-01

    The characteristics of unsteady flow motions have long been a serious concern in the study of various fluid dynamic and combustion problems. With the advancement of computer resources, numerical approaches to these problems appear to be feasible. The objective of this paper is to assess the accuracy of several numerical schemes for unsteady flow calculations. In the present study, Fourier error analysis is performed for various numerical schemes based on a two-dimensional wave equation. Four methods sieved from the error analysis are then adopted for further assessment. Model problems include unsteady quasi-one-dimensional inviscid flows, two-dimensional wave propagations, and unsteady two-dimensional inviscid flows. According to the comparison between numerical and exact solutions, although second-order upwind scheme captures the unsteady flow and wave motions quite well, it is relatively more dissipative than sixth-order central difference scheme. Among various numerical approaches tested in this paper, the best performed one is Runge-Kutta method for time integration and six-order central difference for spatial discretization.

  9. Direct numerical simulation of transitional and turbulent flow over a heated flat plate using finite-difference schemes

    NASA Technical Reports Server (NTRS)

    Madavan, Nateri K.

    1995-01-01

    This report deals with the direct numerical simulation of transitional and turbulent flow at low Mach numbers using high-order-accurate finite-difference techniques. A computation of transition to turbulence of the spatially-evolving boundary layer on a heated flat plate in the presence of relatively high freestream turbulence was performed. The geometry and flow conditions were chosen to match earlier experiments. The development of the momentum and thermal boundary layers was documented. Velocity and temperature profiles, as well as distributions of skin friction, surface heat transfer rate, Reynolds shear stress, and turbulent heat flux, were shown to compare well with experiment. The results indicate that the essential features of the transition process have been captured. The numerical method used here can be applied to complex geometries in a straightforward manner.

  10. Numerical study of the radiometric phenomenon exhibited by a rotating Crookes radiometer

    NASA Astrophysics Data System (ADS)

    Anikin, Yu. A.

    2011-11-01

    The two-dimensional rarefied gas flow around a rotating Crookes radiometer and the arising radiometric forces are studied by numerically solving the Boltzmann kinetic equation. The computations are performed in a noninertial frame of reference rotating together with the radiometer. The collision integral is directly evaluated using a projection method, while second- and third-order accurate TVD schemes are used to solve the advection equation and the equation for inertia-induced transport in the velocity space, respectively. The radiometric forces are found as functions of the rotation frequency.

  11. A moving mesh unstaggered constrained transport scheme for magnetohydrodynamics

    NASA Astrophysics Data System (ADS)

    Mocz, Philip; Pakmor, Rüdiger; Springel, Volker; Vogelsberger, Mark; Marinacci, Federico; Hernquist, Lars

    2016-11-01

    We present a constrained transport (CT) algorithm for solving the 3D ideal magnetohydrodynamic (MHD) equations on a moving mesh, which maintains the divergence-free condition on the magnetic field to machine-precision. Our CT scheme uses an unstructured representation of the magnetic vector potential, making the numerical method simple and computationally efficient. The scheme is implemented in the moving mesh code AREPO. We demonstrate the performance of the approach with simulations of driven MHD turbulence, a magnetized disc galaxy, and a cosmological volume with primordial magnetic field. We compare the outcomes of these experiments to those obtained with a previously implemented Powell divergence-cleaning scheme. While CT and the Powell technique yield similar results in idealized test problems, some differences are seen in situations more representative of astrophysical flows. In the turbulence simulations, the Powell cleaning scheme artificially grows the mean magnetic field, while CT maintains this conserved quantity of ideal MHD. In the disc simulation, CT gives slower magnetic field growth rate and saturates to equipartition between the turbulent kinetic energy and magnetic energy, whereas Powell cleaning produces a dynamically dominant magnetic field. Such difference has been observed in adaptive-mesh refinement codes with CT and smoothed-particle hydrodynamics codes with divergence-cleaning. In the cosmological simulation, both approaches give similar magnetic amplification, but Powell exhibits more cell-level noise. CT methods in general are more accurate than divergence-cleaning techniques, and, when coupled to a moving mesh can exploit the advantages of automatic spatial/temporal adaptivity and reduced advection errors, allowing for improved astrophysical MHD simulations.

  12. High-order central ENO finite-volume scheme for hyperbolic conservation laws on three-dimensional cubed-sphere grids

    NASA Astrophysics Data System (ADS)

    Ivan, L.; De Sterck, H.; Susanto, A.; Groth, C. P. T.

    2015-02-01

    A fourth-order accurate finite-volume scheme for hyperbolic conservation laws on three-dimensional (3D) cubed-sphere grids is described. The approach is based on a central essentially non-oscillatory (CENO) finite-volume method that was recently introduced for two-dimensional compressible flows and is extended to 3D geometries with structured hexahedral grids. Cubed-sphere grids feature hexahedral cells with nonplanar cell surfaces, which are handled with high-order accuracy using trilinear geometry representations in the proposed approach. Varying stencil sizes and slope discontinuities in grid lines occur at the boundaries and corners of the six sectors of the cubed-sphere grid where the grid topology is unstructured, and these difficulties are handled naturally with high-order accuracy by the multidimensional least-squares based 3D CENO reconstruction with overdetermined stencils. A rotation-based mechanism is introduced to automatically select appropriate smaller stencils at degenerate block boundaries, where fewer ghost cells are available and the grid topology changes, requiring stencils to be modified. Combining these building blocks results in a finite-volume discretization for conservation laws on 3D cubed-sphere grids that is uniformly high-order accurate in all three grid directions. While solution-adaptivity is natural in the multi-block setting of our code, high-order accurate adaptive refinement on cubed-sphere grids is not pursued in this paper. The 3D CENO scheme is an accurate and robust solution method for hyperbolic conservation laws on general hexahedral grids that is attractive because it is inherently multidimensional by employing a K-exact overdetermined reconstruction scheme, and it avoids the complexity of considering multiple non-central stencil configurations that characterizes traditional ENO schemes. Extensive numerical tests demonstrate fourth-order convergence for stationary and time-dependent Euler and magnetohydrodynamic flows on

  13. Time-stable boundary conditions for finite-difference schemes solving hyperbolic systems: Methodology and application to high-order compact schemes

    NASA Technical Reports Server (NTRS)

    Carpenter, Mark H.; Gottlieb, David; Abarbanel, Saul

    1993-01-01

    We present a systematic method for constructing boundary conditions (numerical and physical) of the required accuracy, for compact (Pade-like) high-order finite-difference schemes for hyperbolic systems. First, a roper summation-by-parts formula is found for the approximate derivative. A 'simultaneous approximation term' (SAT) is then introduced to treat the boundary conditions. This procedure leads to time-stable schemes even in the system case. An explicit construction of the fourth-order compact case is given. Numerical studies are presented to verify the efficacy of the approach.

  14. High-Order Residual-Distribution Schemes for Discontinuous Problems on Irregular Triangular Grids

    NASA Technical Reports Server (NTRS)

    Mazaheri, Alireza; Nishikawa, Hiroaki

    2016-01-01

    In this paper, we develop second- and third-order non-oscillatory shock-capturing hyperbolic residual distribution schemes for irregular triangular grids, extending our second- and third-order schemes to discontinuous problems. We present extended first-order N- and Rusanov-scheme formulations for hyperbolic advection-diffusion system, and demonstrate that the hyperbolic diffusion term does not affect the solution of inviscid problems for vanishingly small viscous coefficient. We then propose second- and third-order blended hyperbolic residual-distribution schemes with the extended first-order Rusanov-scheme. We show that these proposed schemes are extremely accurate in predicting non-oscillatory solutions for discontinuous problems. We also propose a characteristics-based nonlinear wave sensor for accurately detecting shocks, compression, and expansion regions. Using this proposed sensor, we demonstrate that the developed hyperbolic blended schemes do not produce entropy-violating solutions (unphysical stocks). We then verify the design order of accuracy of these blended schemes on irregular triangular grids.

  15. Numerical solution of 3D Navier-Stokes equations with upwind implicit schemes

    NASA Technical Reports Server (NTRS)

    Marx, Yves P.

    1990-01-01

    An upwind MUSCL type implicit scheme for the three-dimensional Navier-Stokes equations is presented. Comparison between different approximate Riemann solvers (Roe and Osher) are performed and the influence of the reconstructions schemes on the accuracy of the solution as well as on the convergence of the method is studied. A new limiter is introduced in order to remove the problems usually associated with non-linear upwind schemes. The implementation of a diagonal upwind implicit operator for the three-dimensional Navier-Stokes equations is also discussed. Finally the turbulence modeling is assessed. Good prediction of separated flows are demonstrated if a non-equilibrium turbulence model is used.

  16. Numerical Hydrodynamics in General Relativity.

    PubMed

    Font, José A

    2000-01-01

    The current status of numerical solutions for the equations of ideal general relativistic hydrodynamics is reviewed. Different formulations of the equations are presented, with special mention of conservative and hyperbolic formulations well-adapted to advanced numerical methods. A representative sample of available numerical schemes is discussed and particular emphasis is paid to solution procedures based on schemes exploiting the characteristic structure of the equations through linearized Riemann solvers. A comprehensive summary of relevant astrophysical simulations in strong gravitational fields, including gravitational collapse, accretion onto black holes and evolution of neutron stars, is also presented. Supplementary material is available for this article at 10.12942/lrr-2000-2.

  17. A numerical study of confined turbulent jets

    NASA Technical Reports Server (NTRS)

    Zhu, J.; Shih, T.-H.

    1993-01-01

    A numerical investigation is reported of turbulent incompressible jets confined in two ducts, one cylindrical and the other conical with a 5 degree divergence. In each case, three Craya-Curtet numbers are considered which correspond, respectively, to flow situations with no moderate and strong recirculation. Turbulence closure is achieved by using the k-epsilon model and a recently proposed realizable Reynolds stress algebraic equation model that relates the Reynolds stresses explicitly to the quadratic terms of the mean velocity gradients and ensures the positiveness of each component of the turbulent kinetic energy. Calculations are carried out with a finite-volume procedure using boundary-fitted curvilinear coordinates. A second-order accurate, bounded convection scheme and sufficiently fine grids are used to prevent the solutions from being contaminated by numerical diffusion. The calculated results are compared extensively with the available experimental data. It is shown that the numerical methods presented are capable of capturing the essential flow features observed in the experiments and that the realizable Reynolds stress algebraic equation model performs much better than the k-epsilon model for this class of flows of great practical importance.

  18. Numerical simulation of the interaction between a flowfield and chemical reaction on premixed pulsed jet combustion

    NASA Astrophysics Data System (ADS)

    Hishida, Manabu; Hayashi, A. Koichi

    1992-12-01

    Pulsed Jet Combustion (PJC) is numerically simulated using time-dependent, axisymmetric, full Navier-Stokes equations with the mass, momentum, energy, and species conservation equations for a hydrogen-air mixture. A hydrogen-air reaction mechanism is modeled by nine species and nineteen elementary forward and backward reactions to evaluate the effect of the chemical reactions accurately. A point implicit method with the Harten and Yee's non-MUSCL (Monotone Upstream-centerd Schemes for Conservation Laws) modified-flux type TVD (Total Variation Diminishing) scheme is applied to deal with the stiff partial differential equations. Furthermore, a zonal method making use of the Fortified Solution Algorithm (FSA) is applied to simulate the phenomena in the complicated shape of the sub-chamber. The numerical result shows that flames propagating in the sub-chamber interact with pressure waves and are deformed to be wrinkled like a 'tulip' flame and a jet passed through the orifice changes its mass flux quasi-periodically.

  19. A Quantitative Investigation of Entrainment and Detrainment in Numerically Simulated Convective Clouds. Pt. 1; Model Development

    NASA Technical Reports Server (NTRS)

    Cohen, Charles

    1998-01-01

    A method is developed which uses numerical tracers to make accurate diagnoses of entraimnent and detrainment rates and of the properties of the entrained and detrained air in numerically simulated clouds. The numerical advection scheme is modified to make it nondispersive, as required by the use of the tracers. Tests of the new method are made, and an appropriate definition of clouds is selected. Distributions of mixing fractions in the model consistently show maximums at the end points, for nearly undilute environmental air or nearly undilute cloud air, with a uniform distribution between. The cumulonimbus clouds simulated here entrain air that had been substantially changed by the clouds, and detrained air that is not necessarily representative of the cloud air at the same level.

  20. A Highly Accurate Technique for the Treatment of Flow Equations at the Polar Axis in Cylindrical Coordinates using Series Expansions. Appendix A

    NASA Technical Reports Server (NTRS)

    Constantinescu, George S.; Lele, S. K.

    2001-01-01

    Numerical methods for solving the flow equations in cylindrical or spherical coordinates should be able to capture the behavior of the exact solution near the regions where the particular form of the governing equations is singular. In this work we focus on the treatment of these numerical singularities for finite-differences methods by reinterpreting the regularity conditions developed in the context of pseudo-spectral methods. A generally applicable numerical method for treating the singularities present at the polar axis, when nonaxisymmetric flows are solved in cylindrical, coordinates using highly accurate finite differences schemes (e.g., Pade schemes) on non-staggered grids, is presented. Governing equations for the flow at the polar axis are derived using series expansions near r=0. The only information needed to calculate the coefficients in these equations are the values of the flow variables and their radial derivatives at the previous iteration (or time) level. These derivatives, which are multi-valued at the polar axis, are calculated without dropping the accuracy of the numerical method using a mapping of the flow domain from (0,R)*(0,2pi) to (-R,R)*(0,pi), where R is the radius of the computational domain. This allows the radial derivatives to be evaluated using high-order differencing schemes (e.g., compact schemes) at points located on the polar axis. The proposed technique is illustrated by results from simulations of laminar-forced jets and turbulent compressible jets using large eddy simulation (LES) methods. In term of the general robustness of the numerical method and smoothness of the solution close to the polar axis, the present results compare very favorably to similar calculations in which the equations are solved in Cartesian coordinates at the polar axis, or in which the singularity is removed by employing a staggered mesh in the radial direction without a mesh point at r=0, following the method proposed recently by Mohseni and Colonius

  1. Toward Hamiltonian Adaptive QM/MM: Accurate Solvent Structures Using Many-Body Potentials.

    PubMed

    Boereboom, Jelle M; Potestio, Raffaello; Donadio, Davide; Bulo, Rosa E

    2016-08-09

    Adaptive quantum mechanical (QM)/molecular mechanical (MM) methods enable efficient molecular simulations of chemistry in solution. Reactive subregions are modeled with an accurate QM potential energy expression while the rest of the system is described in a more approximate manner (MM). As solvent molecules diffuse in and out of the reactive region, they are gradually included into (and excluded from) the QM expression. It would be desirable to model such a system with a single adaptive Hamiltonian, but thus far this has resulted in distorted structures at the boundary between the two regions. Solving this long outstanding problem will allow microcanonical adaptive QM/MM simulations that can be used to obtain vibrational spectra and dynamical properties. The difficulty lies in the complex QM potential energy expression, with a many-body expansion that contains higher order terms. Here, we outline a Hamiltonian adaptive multiscale scheme within the framework of many-body potentials. The adaptive expressions are entirely general, and complementary to all standard (nonadaptive) QM/MM embedding schemes available. We demonstrate the merit of our approach on a molecular system defined by two different MM potentials (MM/MM'). For the long-range interactions a numerical scheme is used (particle mesh Ewald), which yields energy expressions that are many-body in nature. Our Hamiltonian approach is the first to provide both energy conservation and the correct solvent structure everywhere in this system.

  2. 7 CFR 1412.64 - Inaccurate representation, misrepresentation, and scheme or device.

    Code of Federal Regulations, 2011 CFR

    2011-01-01

    ... scheme or device. 1412.64 Section 1412.64 Agriculture Regulations of the Department of Agriculture..., misrepresentation, and scheme or device. (a) Producers must report and certify program matters accurately. Errors in... a misrepresentation or scheme or device, such person will be ineligible to receive DCP or ACRE...

  3. 7 CFR 1412.64 - Inaccurate representation, misrepresentation, and scheme or device.

    Code of Federal Regulations, 2014 CFR

    2014-01-01

    ... scheme or device. 1412.64 Section 1412.64 Agriculture Regulations of the Department of Agriculture..., misrepresentation, and scheme or device. (a) Producers must report and certify program matters accurately. Errors in... a misrepresentation or scheme or device, such person will be ineligible to receive DCP or ACRE...

  4. 7 CFR 1412.64 - Inaccurate representation, misrepresentation, and scheme or device.

    Code of Federal Regulations, 2012 CFR

    2012-01-01

    ... scheme or device. 1412.64 Section 1412.64 Agriculture Regulations of the Department of Agriculture..., misrepresentation, and scheme or device. (a) Producers must report and certify program matters accurately. Errors in... a misrepresentation or scheme or device, such person will be ineligible to receive DCP or ACRE...

  5. 7 CFR 1412.64 - Inaccurate representation, misrepresentation, and scheme or device.

    Code of Federal Regulations, 2013 CFR

    2013-01-01

    ... scheme or device. 1412.64 Section 1412.64 Agriculture Regulations of the Department of Agriculture..., misrepresentation, and scheme or device. (a) Producers must report and certify program matters accurately. Errors in... a misrepresentation or scheme or device, such person will be ineligible to receive DCP or ACRE...

  6. 7 CFR 1412.64 - Inaccurate representation, misrepresentation, and scheme or device.

    Code of Federal Regulations, 2010 CFR

    2010-01-01

    ... scheme or device. 1412.64 Section 1412.64 Agriculture Regulations of the Department of Agriculture..., misrepresentation, and scheme or device. (a) Producers must report and certify program matters accurately. Errors in... a misrepresentation or scheme or device, such person will be ineligible to receive DCP or ACRE...

  7. A numerical method for simulating the dynamics of 3D axisymmetric vesicles suspended in viscous flows

    NASA Astrophysics Data System (ADS)

    Veerapaneni, Shravan K.; Gueyffier, Denis; Biros, George; Zorin, Denis

    2009-10-01

    We extend [Shravan K. Veerapaneni, Denis Gueyffier, Denis Zorin, George Biros, A boundary integral method for simulating the dynamics of inextensible vesicles suspended in a viscous fluid in 2D, Journal of Computational Physics 228(7) (2009) 2334-2353] to the case of three-dimensional axisymmetric vesicles of spherical or toroidal topology immersed in viscous flows. Although the main components of the algorithm are similar in spirit to the 2D case—spectral approximation in space, semi-implicit time-stepping scheme—the main differences are that the bending and viscous force require new analysis, the linearization for the semi-implicit schemes must be rederived, a fully implicit scheme must be used for the toroidal topology to eliminate a CFL-type restriction and a novel numerical scheme for the evaluation of the 3D Stokes single layer potential on an axisymmetric surface is necessary to speed up the calculations. By introducing these novel components, we obtain a time-scheme that experimentally is unconditionally stable, has low cost per time step, and is third-order accurate in time. We present numerical results to analyze the cost and convergence rates of the scheme. To verify the solver, we compare it to a constrained variational approach to compute equilibrium shapes that does not involve interactions with a viscous fluid. To illustrate the applicability of method, we consider a few vesicle-flow interaction problems: the sedimentation of a vesicle, interactions of one and three vesicles with a background Poiseuille flow.

  8. A new hybrid numerical scheme for simulating fault ruptures with near-fault bulk inhomogeneities

    NASA Astrophysics Data System (ADS)

    Hajarolasvadi, S.; Elbanna, A. E.

    2017-12-01

    The Finite Difference (FD) and Boundary Integral (BI) Method have been extensively used to model spontaneously propagating shear cracks, which can serve as a useful idealization of natural earthquakes. While FD suffers from artificial dispersion and numerical dissipation and has a large computational cost as it requires the discretization of the whole volume of interest, it can be applied to a wider range of problems including ones with bulk nonlinearities and heterogeneities. On the other hand, in the BI method, the numerical consideration is confined to the crack path only, with the elastodynamic response of the bulk expressed in terms of integral relations between displacement discontinuities and tractions along the crack. Therefore, this method - its spectral boundary integral (SBI) formulation in particular - is much faster and more computationally efficient than other bulk methods such as FD. However, its application is restricted to linear elastic bulk and planar faults. This work proposes a novel hybrid numerical scheme that combines FD and the SBI to enable treating fault zone nonlinearities and heterogeneities with unprecedented resolution and in a more computationally efficient way. The main idea of the method is to enclose the inhomgeneities in a virtual strip that is introduced for computational purposes only. This strip is then discretized using a volume-based numerical method, chosen here to be the finite difference method while the virtual boundaries of the strip are handled using the SBI formulation that represents the two elastic half spaces outside the strip. Modeling the elastodynamic response in these two halfspaces needs to be carried out by an Independent Spectral Formulation before joining them to the strip with the appropriate boundary conditions. Dirichlet and Neumann boundary conditions are imposed on the strip and the two half-spaces, respectively, at each time step to propagate the solution forward. We demonstrate the validity of the

  9. A dispersion minimizing scheme for the 3-D Helmholtz equation based on ray theory

    NASA Astrophysics Data System (ADS)

    Stolk, Christiaan C.

    2016-06-01

    We develop a new dispersion minimizing compact finite difference scheme for the Helmholtz equation in 2 and 3 dimensions. The scheme is based on a newly developed ray theory for difference equations. A discrete Helmholtz operator and a discrete operator to be applied to the source and the wavefields are constructed. Their coefficients are piecewise polynomial functions of hk, chosen such that phase and amplitude errors are minimal. The phase errors of the scheme are very small, approximately as small as those of the 2-D quasi-stabilized FEM method and substantially smaller than those of alternatives in 3-D, assuming the same number of gridpoints per wavelength is used. In numerical experiments, accurate solutions are obtained in constant and smoothly varying media using meshes with only five to six points per wavelength and wave propagation over hundreds of wavelengths. When used as a coarse level discretization in a multigrid method the scheme can even be used with down to three points per wavelength. Tests on 3-D examples with up to 108 degrees of freedom show that with a recently developed hybrid solver, the use of coarser meshes can lead to corresponding savings in computation time, resulting in good simulation times compared to the literature.

  10. Hybrid model based unified scheme for endoscopic Cerenkov and radio-luminescence tomography: Simulation demonstration

    NASA Astrophysics Data System (ADS)

    Wang, Lin; Cao, Xin; Ren, Qingyun; Chen, Xueli; He, Xiaowei

    2018-05-01

    Cerenkov luminescence imaging (CLI) is an imaging method that uses an optical imaging scheme to probe a radioactive tracer. Application of CLI with clinically approved radioactive tracers has opened an opportunity for translating optical imaging from preclinical to clinical applications. Such translation was further improved by developing an endoscopic CLI system. However, two-dimensional endoscopic imaging cannot identify accurate depth and obtain quantitative information. Here, we present an imaging scheme to retrieve the depth and quantitative information from endoscopic Cerenkov luminescence tomography, which can also be applied for endoscopic radio-luminescence tomography. In the scheme, we first constructed a physical model for image collection, and then a mathematical model for characterizing the luminescent light propagation from tracer to the endoscopic detector. The mathematical model is a hybrid light transport model combined with the 3rd order simplified spherical harmonics approximation, diffusion, and radiosity equations to warrant accuracy and speed. The mathematical model integrates finite element discretization, regularization, and primal-dual interior-point optimization to retrieve the depth and the quantitative information of the tracer. A heterogeneous-geometry-based numerical simulation was used to explore the feasibility of the unified scheme, which demonstrated that it can provide a satisfactory balance between imaging accuracy and computational burden.

  11. Mixed finite-difference scheme for analysis of simply supported thick plates.

    NASA Technical Reports Server (NTRS)

    Noor, A. K.

    1973-01-01

    A mixed finite-difference scheme is presented for the stress and free vibration analysis of simply supported nonhomogeneous and layered orthotropic thick plates. The analytical formulation is based on the linear, three-dimensional theory of orthotropic elasticity and a Fourier approach is used to reduce the governing equations to six first-order ordinary differential equations in the thickness coordinate. The governing equations possess a symmetric coefficient matrix and are free of derivatives of the elastic characteristics of the plate. In the finite difference discretization two interlacing grids are used for the different fundamental unknowns in such a way as to reduce both the local discretization error and the bandwidth of the resulting finite-difference field equations. Numerical studies are presented for the effects of reducing the interior and boundary discretization errors and of mesh refinement on the accuracy and convergence of solutions. It is shown that the proposed scheme, in addition to a number of other advantages, leads to highly accurate results, even when a small number of finite difference intervals is used.

  12. Third-order 2N-storage Runge-Kutta schemes with error control

    NASA Technical Reports Server (NTRS)

    Carpenter, Mark H.; Kennedy, Christopher A.

    1994-01-01

    A family of four-stage third-order explicit Runge-Kutta schemes is derived that requires only two storage locations and has desirable stability characteristics. Error control is achieved by embedding a second-order scheme within the four-stage procedure. Certain schemes are identified that are as efficient and accurate as conventional embedded schemes of comparable order and require fewer storage locations.

  13. Spectral collocation method with a flexible angular discretization scheme for radiative transfer in multi-layer graded index medium

    NASA Astrophysics Data System (ADS)

    Wei, Linyang; Qi, Hong; Sun, Jianping; Ren, Yatao; Ruan, Liming

    2017-05-01

    The spectral collocation method (SCM) is employed to solve the radiative transfer in multi-layer semitransparent medium with graded index. A new flexible angular discretization scheme is employed to discretize the solid angle domain freely to overcome the limit of the number of discrete radiative direction when adopting traditional SN discrete ordinate scheme. Three radial basis function interpolation approaches, named as multi-quadric (MQ), inverse multi-quadric (IMQ) and inverse quadratic (IQ) interpolation, are employed to couple the radiative intensity at the interface between two adjacent layers and numerical experiments show that MQ interpolation has the highest accuracy and best stability. Variable radiative transfer problems in double-layer semitransparent media with different thermophysical properties are investigated and the influence of these thermophysical properties on the radiative transfer procedure in double-layer semitransparent media is also analyzed. All the simulated results show that the present SCM with the new angular discretization scheme can predict the radiative transfer in multi-layer semitransparent medium with graded index efficiently and accurately.

  14. Upwind schemes and bifurcating solutions in real gas computations

    NASA Technical Reports Server (NTRS)

    Suresh, Ambady; Liou, Meng-Sing

    1992-01-01

    The area of high speed flow is seeing a renewed interest due to advanced propulsion concepts such as the National Aerospace Plane (NASP), Space Shuttle, and future civil transport concepts. Upwind schemes to solve such flows have become increasingly popular in the last decade due to their excellent shock capturing properties. In the first part of this paper the authors present the extension of the Osher scheme to equilibrium and non-equilibrium gases. For simplicity, the source terms are treated explicitly. Computations based on the above scheme are presented to demonstrate the feasibility, accuracy and efficiency of the proposed scheme. One of the test problems is a Chapman-Jouguet detonation problem for which numerical solutions have been known to bifurcate into spurious weak detonation solutions on coarse grids. Results indicate that the numerical solution obtained depends both on the upwinding scheme used and the limiter employed to obtain second order accuracy. For example, the Osher scheme gives the correct CJ solution when the super-bee limiter is used, but gives the spurious solution when the Van Leer limiter is used. With the Roe scheme the spurious solution is obtained for all limiters.

  15. A multistage time-stepping scheme for the Navier-Stokes equations

    NASA Technical Reports Server (NTRS)

    Swanson, R. C.; Turkel, E.

    1985-01-01

    A class of explicit multistage time-stepping schemes is used to construct an algorithm for solving the compressible Navier-Stokes equations. Flexibility in treating arbitrary geometries is obtained with a finite-volume formulation. Numerical efficiency is achieved by employing techniques for accelerating convergence to steady state. Computer processing is enhanced through vectorization of the algorithm. The scheme is evaluated by solving laminar and turbulent flows over a flat plate and an NACA 0012 airfoil. Numerical results are compared with theoretical solutions or other numerical solutions and/or experimental data.

  16. Multigrid schemes for viscous hypersonic flows

    NASA Technical Reports Server (NTRS)

    Swanson, R. C.; Radespiel, R.

    1993-01-01

    Several multigrid schemes are considered for the numerical computation of viscous hypersonic flows. For each scheme, the basic solution algorithm employs upwind spatial discretization with explicit multistage time stepping. Two-level versions of the various multigrid algorithms are applied to the two-dimensional advection equation, and Fourier analysis is used to determine their damping properties. The capabilities of the multigrid methods are assessed by solving two different hypersonic flow problems. Some new multigrid schemes, based on semicoarsening strategies, are shown to be quite effective in relieving the stiffness caused by the high-aspect-ratio cells required to resolve high Reynolds number flows. These schemes exhibit good convergence rates for Reynolds numbers up to 200 x 10(exp 6).

  17. Self-consistent field theory and numerical scheme for calculating the phase diagram of wormlike diblock copolymers

    NASA Astrophysics Data System (ADS)

    Jiang, Ying; Chen, Jeff Z. Y.

    2013-10-01

    This paper concerns establishing a theoretical basis and numerical scheme for studying the phase behavior of AB diblock copolymers made of wormlike chains. The general idea of a self-consistent field theory is the combination of the mean-field approach together with a statistical weight that describes the configurational properties of a polymer chain. In recent years, this approach has been extensively used for structural prediction of block copolymers, based on the Gaussian-model description of a polymer chain. The wormlike-chain model has played an important role in the description of polymer systems, covering the semiflexible-to-rod crossover of the polymer properties and the highly stretching regime, which the Gaussian-chain model has difficulties to describe. Although the idea of developing a self-consistent field theory for wormlike chains could be traced back to early development in polymer physics, the solution of such a theory has been limited due to technical difficulties. In particular, a challenge has been to develop a numerical algorithm enabling the calculation of the phase diagram containing three-dimensional structures for wormlike AB diblock copolymers. This paper describes a computational algorithm that combines a number of numerical tricks, which can be used for such a calculation. A phase diagram covering major parameter areas was constructed for the wormlike-chain system and reported by us, where the ratio between the total length and the persistence length of a constituent polymer is suggested as another tuning parameter for the microphase-separated structures; all detailed technical issues are carefully addressed in the current paper.

  18. Numerical solution of the stochastic parabolic equation with the dependent operator coefficient

    DOE Office of Scientific and Technical Information (OSTI.GOV)

    Ashyralyev, Allaberen; Department of Mathematics, ITTU, Ashgabat; Okur, Ulker

    2015-09-18

    In the present paper, a single step implicit difference scheme for the numerical solution of the stochastic parabolic equation with the dependent operator coefficient is presented. Theorem on convergence estimates for the solution of this difference scheme is established. In applications, this abstract result permits us to obtain the convergence estimates for the solution of difference schemes for the numerical solution of initial boundary value problems for parabolic equations. The theoretical statements for the solution of this difference scheme are supported by the results of numerical experiments.

  19. High-Order Central WENO Schemes for 1D Hamilton-Jacobi Equations

    NASA Technical Reports Server (NTRS)

    Bryson, Steve; Levy, Doron; Biegel, Bryan A. (Technical Monitor)

    2002-01-01

    In this paper we derive fully-discrete Central WENO (CWENO) schemes for approximating solutions of one dimensional Hamilton-Jacobi (HJ) equations, which combine our previous works. We introduce third and fifth-order accurate schemes, which are the first central schemes for the HJ equations of order higher than two. The core ingredient is the derivation of our schemes is a high-order CWENO reconstructions in space.

  20. Numerical investigation of sixth order Boussinesq equation

    NASA Astrophysics Data System (ADS)

    Kolkovska, N.; Vucheva, V.

    2017-10-01

    We propose a family of conservative finite difference schemes for the Boussinesq equation with sixth order dispersion terms. The schemes are of second order of approximation. The method is conditionally stable with a mild restriction τ = O(h) on the step sizes. Numerical tests are performed for quadratic and cubic nonlinearities. The numerical experiments show second order of convergence of the discrete solution to the exact one.

  1. Optimal rotated staggered-grid finite-difference schemes for elastic wave modeling in TTI media

    NASA Astrophysics Data System (ADS)

    Yang, Lei; Yan, Hongyong; Liu, Hong

    2015-11-01

    The rotated staggered-grid finite-difference (RSFD) is an effective approach for numerical modeling to study the wavefield characteristics in tilted transversely isotropic (TTI) media. But it surfaces from serious numerical dispersion, which directly affects the modeling accuracy. In this paper, we propose two different optimal RSFD schemes based on the sampling approximation (SA) method and the least-squares (LS) method respectively to overcome this problem. We first briefly introduce the RSFD theory, based on which we respectively derive the SA-based RSFD scheme and the LS-based RSFD scheme. Then different forms of analysis are used to compare the SA-based RSFD scheme and the LS-based RSFD scheme with the conventional RSFD scheme, which is based on the Taylor-series expansion (TE) method. The contrast in numerical accuracy analysis verifies the greater accuracy of the two proposed optimal schemes, and indicates that these schemes can effectively widen the wavenumber range with great accuracy compared with the TE-based RSFD scheme. Further comparisons between these two optimal schemes show that at small wavenumbers, the SA-based RSFD scheme performs better, while at large wavenumbers, the LS-based RSFD scheme leads to a smaller error. Finally, the modeling results demonstrate that for the same operator length, the SA-based RSFD scheme and the LS-based RSFD scheme can achieve greater accuracy than the TE-based RSFD scheme, while for the same accuracy, the optimal schemes can adopt shorter difference operators to save computing time.

  2. TOPICA: an accurate and efficient numerical tool for analysis and design of ICRF antennas

    NASA Astrophysics Data System (ADS)

    Lancellotti, V.; Milanesio, D.; Maggiora, R.; Vecchi, G.; Kyrytsya, V.

    2006-07-01

    The demand for a predictive tool to help in designing ion-cyclotron radio frequency (ICRF) antenna systems for today's fusion experiments has driven the development of codes such as ICANT, RANT3D, and the early development of TOPICA (TOrino Polytechnic Ion Cyclotron Antenna) code. This paper describes the substantive evolution of TOPICA formulation and implementation that presently allow it to handle the actual geometry of ICRF antennas (with curved, solid straps, a general-shape housing, Faraday screen, etc) as well as an accurate plasma description, accounting for density and temperature profiles and finite Larmor radius effects. The antenna is assumed to be housed in a recess-like enclosure. Both goals have been attained by formally separating the problem into two parts: the vacuum region around the antenna and the plasma region inside the toroidal chamber. Field continuity and boundary conditions allow formulating of a set of two coupled integral equations for the unknown equivalent (current) sources; then the equations are reduced to a linear system by a method of moments solution scheme employing 2D finite elements defined over a 3D non-planar surface triangular-cell mesh. In the vacuum region calculations are done in the spatial (configuration) domain, whereas in the plasma region a spectral (wavenumber) representation of fields and currents is adopted, thus permitting a description of the plasma by a surface impedance matrix. Owing to this approach, any plasma model can be used in principle, and at present the FELICE code has been employed. The natural outcomes of TOPICA are the induced currents on the conductors (antenna, housing, etc) and the electric field in front of the plasma, whence the antenna circuit parameters (impedance/scattering matrices), the radiated power and the fields (at locations other than the chamber aperture) are then obtained. An accurate model of the feeding coaxial lines is also included. The theoretical model and its TOPICA

  3. Multichannel feedforward control schemes with coupling compensation for active sound profiling

    NASA Astrophysics Data System (ADS)

    Mosquera-Sánchez, Jaime A.; Desmet, Wim; de Oliveira, Leopoldo P. R.

    2017-05-01

    Active sound profiling includes a number of control techniques that enables the equalization, rather than the mere reduction, of acoustic noise. Challenges may rise when trying to achieve distinct targeted sound profiles simultaneously at multiple locations, e.g., within a vehicle cabin. This paper introduces distributed multichannel control schemes for independently tailoring structural borne sound reaching a number of locations within a cavity. The proposed techniques address the cross interactions amongst feedforward active sound profiling units, which compensate for interferences of the primary sound at each location of interest by exchanging run-time data amongst the control units, while attaining the desired control targets. Computational complexity, convergence, and stability of the proposed multichannel schemes are examined in light of the physical system at which they are implemented. The tuning performance of the proposed algorithms is benchmarked with the centralized and pure-decentralized control schemes through computer simulations on a simplified numerical model, which has also been subjected to plant magnitude variations. Provided that the representation of the plant is accurate enough, the proposed multichannel control schemes have been shown as the only ones that properly deliver targeted active sound profiling tasks at each error sensor location. Experimental results in a 1:3-scaled vehicle mock-up further demonstrate that the proposed schemes are able to attain reductions of more than 60 dB upon periodic disturbances at a number of positions, while resolving cross-channel interferences. Moreover, when the sensor/actuator placement is found as defective at a given frequency, the inclusion of a regularization parameter in the cost function is seen to not hinder the proper operation of the proposed compensation schemes, at the time that it assures their stability, at the expense of losing control performance.

  4. Development of a fully implicit particle-in-cell scheme for gyrokinetic electromagnetic turbulence simulation in XGC1

    NASA Astrophysics Data System (ADS)

    Ku, Seung-Hoe; Hager, R.; Chang, C. S.; Chacon, L.; Chen, G.; EPSI Team

    2016-10-01

    The cancelation problem has been a long-standing issue for long wavelengths modes in electromagnetic gyrokinetic PIC simulations in toroidal geometry. As an attempt of resolving this issue, we implemented a fully implicit time integration scheme in the full-f, gyrokinetic PIC code XGC1. The new scheme - based on the implicit Vlasov-Darwin PIC algorithm by G. Chen and L. Chacon - can potentially resolve cancelation problem. The time advance for the field and the particle equations is space-time-centered, with particle sub-cycling. The resulting system of equations is solved by a Picard iteration solver with fixed-point accelerator. The algorithm is implemented in the parallel velocity formalism instead of the canonical parallel momentum formalism. XGC1 specializes in simulating the tokamak edge plasma with magnetic separatrix geometry. A fully implicit scheme could be a way to accurate and efficient gyrokinetic simulations. We will test if this numerical scheme overcomes the cancelation problem, and reproduces the dispersion relation of Alfven waves and tearing modes in cylindrical geometry. Funded by US DOE FES and ASCR, and computing resources provided by OLCF through ALCC.

  5. An extrapolation scheme for solid-state NMR chemical shift calculations

    NASA Astrophysics Data System (ADS)

    Nakajima, Takahito

    2017-06-01

    Conventional quantum chemical and solid-state physical approaches include several problems to accurately calculate solid-state nuclear magnetic resonance (NMR) properties. We propose a reliable computational scheme for solid-state NMR chemical shifts using an extrapolation scheme that retains the advantages of these approaches but reduces their disadvantages. Our scheme can satisfactorily yield solid-state NMR magnetic shielding constants. The estimated values have only a small dependence on the low-level density functional theory calculation with the extrapolation scheme. Thus, our approach is efficient because the rough calculation can be performed in the extrapolation scheme.

  6. A new shock-capturing numerical scheme for ideal hydrodynamics

    NASA Astrophysics Data System (ADS)

    Fecková, Z.; Tomášik, B.

    2015-05-01

    We present a new algorithm for solving ideal relativistic hydrodynamics based on Godunov method with an exact solution of Riemann problem for an arbitrary equation of state. Standard numerical tests are executed, such as the sound wave propagation and the shock tube problem. Low numerical viscosity and high precision are attained with proper discretization.

  7. Ferrofluids: Modeling, numerical analysis, and scientific computation

    NASA Astrophysics Data System (ADS)

    Tomas, Ignacio

    This dissertation presents some developments in the Numerical Analysis of Partial Differential Equations (PDEs) describing the behavior of ferrofluids. The most widely accepted PDE model for ferrofluids is the Micropolar model proposed by R.E. Rosensweig. The Micropolar Navier-Stokes Equations (MNSE) is a subsystem of PDEs within the Rosensweig model. Being a simplified version of the much bigger system of PDEs proposed by Rosensweig, the MNSE are a natural starting point of this thesis. The MNSE couple linear velocity u, angular velocity w, and pressure p. We propose and analyze a first-order semi-implicit fully-discrete scheme for the MNSE, which decouples the computation of the linear and angular velocities, is unconditionally stable and delivers optimal convergence rates under assumptions analogous to those used for the Navier-Stokes equations. Moving onto the much more complex Rosensweig's model, we provide a definition (approximation) for the effective magnetizing field h, and explain the assumptions behind this definition. Unlike previous definitions available in the literature, this new definition is able to accommodate the effect of external magnetic fields. Using this definition we setup the system of PDEs coupling linear velocity u, pressure p, angular velocity w, magnetization m, and magnetic potential ϕ We show that this system is energy-stable and devise a numerical scheme that mimics the same stability property. We prove that solutions of the numerical scheme always exist and, under certain simplifying assumptions, that the discrete solutions converge. A notable outcome of the analysis of the numerical scheme for the Rosensweig's model is the choice of finite element spaces that allow the construction of an energy-stable scheme. Finally, with the lessons learned from Rosensweig's model, we develop a diffuse-interface model describing the behavior of two-phase ferrofluid flows and present an energy-stable numerical scheme for this model. For a

  8. Numerical study of dam-break induced tsunami-like bore with a hump of different slopes

    NASA Astrophysics Data System (ADS)

    Cheng, Du; Zhao, Xi-zeng; Zhang, Da-ke; Chen, Yong

    2017-12-01

    Numerical simulation of dam-break wave, as an imitation of tsunami hydraulic bore, with a hump of different slopes is performed in this paper using an in-house code, named a Constrained Interpolation Profile (CIP)-based model. The model is built on a Cartesian grid system with the Navier Stokes equations using a CIP method for the flow solver, and employs an immersed boundary method (IBM) for the treatment of solid body boundary. A more accurate interface capturing scheme, the Tangent of hyperbola for interface capturing/Slope weighting (THINC/SW) scheme, is adopted as the interface capturing method. Then, the CIP-based model is applied to simulate the dam break flow problem in a bumpy channel. Considerable attention is paid to the spilling type reflected bore, the following spilling type wave breaking, free surface profiles and water level variations over time. Computations are compared with available experimental data and other numerical results quantitatively and qualitatively. Further investigation is conducted to analyze the influence of variable slopes on the flow features of the tsunami-like bore.

  9. Numerical scoring for the Classic BILAG index.

    PubMed

    Cresswell, Lynne; Yee, Chee-Seng; Farewell, Vernon; Rahman, Anisur; Teh, Lee-Suan; Griffiths, Bridget; Bruce, Ian N; Ahmad, Yasmeen; Prabu, Athiveeraramapandian; Akil, Mohammed; McHugh, Neil; Toescu, Veronica; D'Cruz, David; Khamashta, Munther A; Maddison, Peter; Isenberg, David A; Gordon, Caroline

    2009-12-01

    To develop an additive numerical scoring scheme for the Classic BILAG index. SLE patients were recruited into this multi-centre cross-sectional study. At every assessment, data were collected on disease activity and therapy. Logistic regression was used to model an increase in therapy, as an indicator of active disease, by the Classic BILAG score in eight systems. As both indicate inactivity, scores of D and E were set to 0 and used as the baseline in the fitted model. The coefficients from the fitted model were used to determine the numerical values for Grades A, B and C. Different scoring schemes were then compared using receiver operating characteristic (ROC) curves. Validation analysis was performed using assessments from a single centre. There were 1510 assessments from 369 SLE patients. The currently used coding scheme (A = 9, B = 3, C = 1 and D/E = 0) did not fit the data well. The regression model suggested three possible numerical scoring schemes: (i) A = 11, B = 6, C = 1 and D/E = 0; (ii) A = 12, B = 6, C = 1 and D/E = 0; and (iii) A = 11, B = 7, C = 1 and D/E = 0. These schemes produced comparable ROC curves. Based on this, A = 12, B = 6, C = 1 and D/E = 0 seemed a reasonable and practical choice. The validation analysis suggested that although the A = 12, B = 6, C = 1 and D/E = 0 coding is still reasonable, a scheme with slightly less weighting for B, such as A = 12, B = 5, C = 1 and D/E = 0, may be more appropriate. A reasonable additive numerical scoring scheme based on treatment decision for the Classic BILAG index is A = 12, B = 5, C = 1, D = 0 and E = 0.

  10. Numerical scoring for the Classic BILAG index

    PubMed Central

    Cresswell, Lynne; Yee, Chee-Seng; Farewell, Vernon; Rahman, Anisur; Teh, Lee-Suan; Griffiths, Bridget; Bruce, Ian N.; Ahmad, Yasmeen; Prabu, Athiveeraramapandian; Akil, Mohammed; McHugh, Neil; Toescu, Veronica; D’Cruz, David; Khamashta, Munther A.; Maddison, Peter; Isenberg, David A.

    2009-01-01

    Objective. To develop an additive numerical scoring scheme for the Classic BILAG index. Methods. SLE patients were recruited into this multi-centre cross-sectional study. At every assessment, data were collected on disease activity and therapy. Logistic regression was used to model an increase in therapy, as an indicator of active disease, by the Classic BILAG score in eight systems. As both indicate inactivity, scores of D and E were set to 0 and used as the baseline in the fitted model. The coefficients from the fitted model were used to determine the numerical values for Grades A, B and C. Different scoring schemes were then compared using receiver operating characteristic (ROC) curves. Validation analysis was performed using assessments from a single centre. Results. There were 1510 assessments from 369 SLE patients. The currently used coding scheme (A = 9, B = 3, C = 1 and D/E = 0) did not fit the data well. The regression model suggested three possible numerical scoring schemes: (i) A = 11, B = 6, C = 1 and D/E = 0; (ii) A = 12, B = 6, C = 1 and D/E = 0; and (iii) A = 11, B = 7, C = 1 and D/E = 0. These schemes produced comparable ROC curves. Based on this, A = 12, B = 6, C = 1 and D/E = 0 seemed a reasonable and practical choice. The validation analysis suggested that although the A = 12, B = 6, C = 1 and D/E = 0 coding is still reasonable, a scheme with slightly less weighting for B, such as A = 12, B = 5, C = 1 and D/E = 0, may be more appropriate. Conclusions. A reasonable additive numerical scoring scheme based on treatment decision for the Classic BILAG index is A = 12, B = 5, C = 1, D = 0 and E = 0. PMID:19779027

  11. Order of accuracy of QUICK and related convection-diffusion schemes

    NASA Technical Reports Server (NTRS)

    Leonard, B. P.

    1993-01-01

    This report attempts to correct some misunderstandings that have appeared in the literature concerning the order of accuracy of the QUICK scheme for steady-state convective modeling. Other related convection-diffusion schemes are also considered. The original one-dimensional QUICK scheme written in terms of nodal-point values of the convected variable (with a 1/8-factor multiplying the 'curvature' term) is indeed a third-order representation of the finite volume formulation of the convection operator average across the control volume, written naturally in flux-difference form. An alternative single-point upwind difference scheme (SPUDS) using node values (with a 1/6-factor) is a third-order representation of the finite difference single-point formulation; this can be written in a pseudo-flux difference form. These are both third-order convection schemes; however, the QUICK finite volume convection operator is 33 percent more accurate than the single-point implementation of SPUDS. Another finite volume scheme, writing convective fluxes in terms of cell-average values, requires a 1/6-factor for third-order accuracy. For completeness, one can also write a single-point formulation of the convective derivative in terms of cell averages, and then express this in pseudo-flux difference form; for third-order accuracy, this requires a curvature factor of 5/24. Diffusion operators are also considered in both single-point and finite volume formulations. Finite volume formulations are found to be significantly more accurate. For example, classical second-order central differencing for the second derivative is exactly twice as accurate in a finite volume formulation as it is in single-point.

  12. The nonlinear modified equation approach to analyzing finite difference schemes

    NASA Technical Reports Server (NTRS)

    Klopfer, G. H.; Mcrae, D. S.

    1981-01-01

    The nonlinear modified equation approach is taken in this paper to analyze the generalized Lax-Wendroff explicit scheme approximation to the unsteady one- and two-dimensional equations of gas dynamics. Three important applications of the method are demonstrated. The nonlinear modified equation analysis is used to (1) generate higher order accurate schemes, (2) obtain more accurate estimates of the discretization error for nonlinear systems of partial differential equations, and (3) generate an adaptive mesh procedure for the unsteady gas dynamic equations. Results are obtained for all three areas. For the adaptive mesh procedure, mesh point requirements for equal resolution of discontinuities were reduced by a factor of five for a 1-D shock tube problem solved by the explicit MacCormack scheme.

  13. Symplectic partitioned Runge-Kutta scheme for Maxwell's equations

    NASA Astrophysics Data System (ADS)

    Huang, Zhi-Xiang; Wu, Xian-Liang

    Using the symplectic partitioned Runge-Kutta (PRK) method, we construct a new scheme for approximating the solution to infinite dimensional nonseparable Hamiltonian systems of Maxwell's equations for the first time. The scheme is obtained by discretizing the Maxwell's equations in the time direction based on symplectic PRK method, and then evaluating the equation in the spatial direction with a suitable finite difference approximation. Several numerical examples are presented to verify the efficiency of the scheme.

  14. LES of Temporally Evolving Mixing Layers by an Eighth-Order Filter Scheme

    NASA Technical Reports Server (NTRS)

    Hadjadj, A; Yee, H. C.; Sjogreen, B.

    2011-01-01

    An eighth-order filter method for a wide range of compressible flow speeds (H.C. Yee and B. Sjogreen, Proceedings of ICOSAHOM09, June 22-26, 2009, Trondheim, Norway) are employed for large eddy simulations (LES) of temporally evolving mixing layers (TML) for different convective Mach numbers (Mc) and Reynolds numbers. The high order filter method is designed for accurate and efficient simulations of shock-free compressible turbulence, turbulence with shocklets and turbulence with strong shocks with minimum tuning of scheme parameters. The value of Mc considered is for the TML range from the quasi-incompressible regime to the highly compressible supersonic regime. The three main characteristics of compressible TML (the self similarity property, compressibility effects and the presence of large-scale structure with shocklets for high Mc) are considered for the LES study. The LES results using the same scheme parameters for all studied cases agree well with experimental results of Barone et al. (2006), and published direct numerical simulations (DNS) work of Rogers & Moser (1994) and Pantano & Sarkar (2002).

  15. Numerical Simulations of Acoustically Driven, Burning Droplets

    NASA Technical Reports Server (NTRS)

    Kim, H.-C.; Karagozian, A. R.; Smith, O. I.; Urban, Dave (Technical Monitor)

    1999-01-01

    This computational study focuses on understanding and quantifying the effects of external acoustical perturbations on droplet combustion. A one-dimensional, axisymmetric representation of the essential diffusion and reaction processes occurring in the vicinity of the droplet stagnation point is used here in order to isolate the effects of the imposed acoustic disturbance. The simulation is performed using a third order accurate, essentially non-oscillatory (ENO) numerical scheme with a full methanol-air reaction mechanism. Consistent with recent microgravity and normal gravity combustion experiments, focus is placed on conditions where the droplet is situated at a velocity antinode in order for the droplet to experience the greatest effects of fluid mechanical straining of flame structures. The effects of imposed sound pressure level and frequency are explored here, and conditions leading to maximum burning rates are identified.

  16. Involution and Difference Schemes for the Navier-Stokes Equations

    NASA Astrophysics Data System (ADS)

    Gerdt, Vladimir P.; Blinkov, Yuri A.

    In the present paper we consider the Navier-Stokes equations for the two-dimensional viscous incompressible fluid flows and apply to these equations our earlier designed general algorithmic approach to generation of finite-difference schemes. In doing so, we complete first the Navier-Stokes equations to involution by computing their Janet basis and discretize this basis by its conversion into the integral conservation law form. Then we again complete the obtained difference system to involution with eliminating the partial derivatives and extracting the minimal Gröbner basis from the Janet basis. The elements in the obtained difference Gröbner basis that do not contain partial derivatives of the dependent variables compose a conservative difference scheme. By exploiting arbitrariness in the numerical integration approximation we derive two finite-difference schemes that are similar to the classical scheme by Harlow and Welch. Each of the two schemes is characterized by a 5×5 stencil on an orthogonal and uniform grid. We also demonstrate how an inconsistent difference scheme with a 3×3 stencil is generated by an inappropriate numerical approximation of the underlying integrals.

  17. Anisotropic diffusion in mesh-free numerical magnetohydrodynamics

    NASA Astrophysics Data System (ADS)

    Hopkins, Philip F.

    2017-04-01

    We extend recently developed mesh-free Lagrangian methods for numerical magnetohydrodynamics (MHD) to arbitrary anisotropic diffusion equations, including: passive scalar diffusion, Spitzer-Braginskii conduction and viscosity, cosmic ray diffusion/streaming, anisotropic radiation transport, non-ideal MHD (Ohmic resistivity, ambipolar diffusion, the Hall effect) and turbulent 'eddy diffusion'. We study these as implemented in the code GIZMO for both new meshless finite-volume Godunov schemes (MFM/MFV). We show that the MFM/MFV methods are accurate and stable even with noisy fields and irregular particle arrangements, and recover the correct behaviour even in arbitrarily anisotropic cases. They are competitive with state-of-the-art AMR/moving-mesh methods, and can correctly treat anisotropic diffusion-driven instabilities (e.g. the MTI and HBI, Hall MRI). We also develop a new scheme for stabilizing anisotropic tensor-valued fluxes with high-order gradient estimators and non-linear flux limiters, which is trivially generalized to AMR/moving-mesh codes. We also present applications of some of these improvements for SPH, in the form of a new integral-Godunov SPH formulation that adopts a moving-least squares gradient estimator and introduces a flux-limited Riemann problem between particles.

  18. A robust and accurate numerical method for transcritical turbulent flows at supercritical pressure with an arbitrary equation of state

    NASA Astrophysics Data System (ADS)

    Kawai, Soshi; Terashima, Hiroshi; Negishi, Hideyo

    2015-11-01

    This paper addresses issues in high-fidelity numerical simulations of transcritical turbulent flows at supercritical pressure. The proposed strategy builds on a tabulated look-up table method based on REFPROP database for an accurate estimation of non-linear behaviors of thermodynamic and fluid transport properties at the transcritical conditions. Based on the look-up table method we propose a numerical method that satisfies high-order spatial accuracy, spurious-oscillation-free property, and capability of capturing the abrupt variation in thermodynamic properties across the transcritical contact surface. The method introduces artificial mass diffusivity to the continuity and momentum equations in a physically-consistent manner in order to capture the steep transcritical thermodynamic variations robustly while maintaining spurious-oscillation-free property in the velocity field. The pressure evolution equation is derived from the full compressible Navier-Stokes equations and solved instead of solving the total energy equation to achieve the spurious pressure oscillation free property with an arbitrary equation of state including the present look-up table method. Flow problems with and without physical diffusion are employed for the numerical tests to validate the robustness, accuracy, and consistency of the proposed approach.

  19. A robust and accurate numerical method for transcritical turbulent flows at supercritical pressure with an arbitrary equation of state

    DOE Office of Scientific and Technical Information (OSTI.GOV)

    Kawai, Soshi, E-mail: kawai@cfd.mech.tohoku.ac.jp; Terashima, Hiroshi; Negishi, Hideyo

    2015-11-01

    This paper addresses issues in high-fidelity numerical simulations of transcritical turbulent flows at supercritical pressure. The proposed strategy builds on a tabulated look-up table method based on REFPROP database for an accurate estimation of non-linear behaviors of thermodynamic and fluid transport properties at the transcritical conditions. Based on the look-up table method we propose a numerical method that satisfies high-order spatial accuracy, spurious-oscillation-free property, and capability of capturing the abrupt variation in thermodynamic properties across the transcritical contact surface. The method introduces artificial mass diffusivity to the continuity and momentum equations in a physically-consistent manner in order to capture themore » steep transcritical thermodynamic variations robustly while maintaining spurious-oscillation-free property in the velocity field. The pressure evolution equation is derived from the full compressible Navier–Stokes equations and solved instead of solving the total energy equation to achieve the spurious pressure oscillation free property with an arbitrary equation of state including the present look-up table method. Flow problems with and without physical diffusion are employed for the numerical tests to validate the robustness, accuracy, and consistency of the proposed approach.« less

  20. Numerical modeling of suspended sediment tansfers at the catchment scale with TELEMAC

    NASA Astrophysics Data System (ADS)

    Taccone, Florent; Antoine, Germain; Delestre, Olivier; Goutal, Nicole

    2017-04-01

    In the mountainous regions, the filling of reservoirs is an important issue in terms of efficiency and environmental acceptability for producing hydro-electricity. Thus, the modelling of the sediment transfers on highly erodible watershed is a key challenge from both economic and scientific points of view. The sediment transfers at the watershed scale involve different local flow regimes due to the complex topography of the field and the time and space variability of the meteorological conditions, as well as several physical processes, because of the heterogeneity of the soil composition and cover. A physically-based modelling approach, associated with a fine discretization of the domain, provides an explicit representation of the hydraulic and sedimentary variables, and gives the opportunity to river managers to simulate the global effects of local solutions for decreasing erosion. On the other hand, this approach is time consuming, and needs both detailed data set for validation and robust numerical schemes for simulating various hydraulic and sediment transport conditions. The erosion processes being heavily reliant on the flow characteristics, this paper focus on a robust and accurate numerical resolution of the Shallow Water equations using TELEMAC 2D (www.opentelemac.org). One of the main difficulties is to have a numerical scheme able to represent correctly the hydraulic transfers, preserving the positivity of the water depths, dealing with the wet/dry interface and being well-balanced. Few schemes verifying these properties exist, and their accuracy still needs to be evaluated in the case of rain induced runoff on steep slopes. First, a straight channel test case with a variable slope (Kirstetter et al., 2015) is used to qualify the properties of several Finite Volume numerical schemes. For this test case, a steady rain applied on a dry domain has been performed experimentally in laboratory, and this configuration gives an analytical solution of the Shallow

  1. Spectral-based propagation schemes for time-dependent quantum systems with application to carbon nanotubes

    NASA Astrophysics Data System (ADS)

    Chen, Zuojing; Polizzi, Eric

    2010-11-01

    Effective modeling and numerical spectral-based propagation schemes are proposed for addressing the challenges in time-dependent quantum simulations of systems ranging from atoms, molecules, and nanostructures to emerging nanoelectronic devices. While time-dependent Hamiltonian problems can be formally solved by propagating the solutions along tiny simulation time steps, a direct numerical treatment is often considered too computationally demanding. In this paper, however, we propose to go beyond these limitations by introducing high-performance numerical propagation schemes to compute the solution of the time-ordered evolution operator. In addition to the direct Hamiltonian diagonalizations that can be efficiently performed using the new eigenvalue solver FEAST, we have designed a Gaussian propagation scheme and a basis-transformed propagation scheme (BTPS) which allow to reduce considerably the simulation times needed by time intervals. It is outlined that BTPS offers the best computational efficiency allowing new perspectives in time-dependent simulations. Finally, these numerical schemes are applied to study the ac response of a (5,5) carbon nanotube within a three-dimensional real-space mesh framework.

  2. Two-level schemes for the advection equation

    NASA Astrophysics Data System (ADS)

    Vabishchevich, Petr N.

    2018-06-01

    The advection equation is the basis for mathematical models of continuum mechanics. In the approximate solution of nonstationary problems it is necessary to inherit main properties of the conservatism and monotonicity of the solution. In this paper, the advection equation is written in the symmetric form, where the advection operator is the half-sum of advection operators in conservative (divergent) and non-conservative (characteristic) forms. The advection operator is skew-symmetric. Standard finite element approximations in space are used. The standard explicit two-level scheme for the advection equation is absolutely unstable. New conditionally stable regularized schemes are constructed, on the basis of the general theory of stability (well-posedness) of operator-difference schemes, the stability conditions of the explicit Lax-Wendroff scheme are established. Unconditionally stable and conservative schemes are implicit schemes of the second (Crank-Nicolson scheme) and fourth order. The conditionally stable implicit Lax-Wendroff scheme is constructed. The accuracy of the investigated explicit and implicit two-level schemes for an approximate solution of the advection equation is illustrated by the numerical results of a model two-dimensional problem.

  3. Modified symplectic schemes with nearly-analytic discrete operators for acoustic wave simulations

    NASA Astrophysics Data System (ADS)

    Liu, Shaolin; Yang, Dinghui; Lang, Chao; Wang, Wenshuai; Pan, Zhide

    2017-04-01

    Using a structure-preserving algorithm significantly increases the computational efficiency of solving wave equations. However, only a few explicit symplectic schemes are available in the literature, and the capabilities of these symplectic schemes have not been sufficiently exploited. Here, we propose a modified strategy to construct explicit symplectic schemes for time advance. The acoustic wave equation is transformed into a Hamiltonian system. The classical symplectic partitioned Runge-Kutta (PRK) method is used for the temporal discretization. Additional spatial differential terms are added to the PRK schemes to form the modified symplectic methods and then two modified time-advancing symplectic methods with all of positive symplectic coefficients are then constructed. The spatial differential operators are approximated by nearly-analytic discrete (NAD) operators, and we call the fully discretized scheme modified symplectic nearly analytic discrete (MSNAD) method. Theoretical analyses show that the MSNAD methods exhibit less numerical dispersion and higher stability limits than conventional methods. Three numerical experiments are conducted to verify the advantages of the MSNAD methods, such as their numerical accuracy, computational cost, stability, and long-term calculation capability.

  4. Multidimensional directional flux weighted upwind scheme for multiphase flow modeling in heterogeneous porous media

    NASA Astrophysics Data System (ADS)

    Jin, G.

    2012-12-01

    Multiphase flow modeling is an important numerical tool for a better understanding of transport processes in the fields including, but not limited to, petroleum reservoir engineering, remedy of ground water contamination, and risk evaluation of greenhouse gases such as CO2 injected into deep saline reservoirs. However, accurate numerical modeling for multiphase flow remains many challenges that arise from the inherent tight coupling and strong non-linear nature of the governing equations and the highly heterogeneous media. The existence of counter current flow which is caused by the effect of adverse relative mobility contrast and gravitational and capillary forces will introduce additional numerical instability. Recently multipoint flux approximation (MPFA) has become a subject of extensive research and has been demonstrated with great success in reducing considerable grid orientation effects compared to the conventional single point upstream (SPU) weighting scheme, especially in higher dimensions. However, the present available MPFA schemes are mathematically targeted to certain types of grids in two dimensions, a more general form of MPFA scheme is needed for both 2-D and 3-D problems. In this work a new upstream weighting scheme based on multipoint directional incoming fluxes is proposed which incorporates full permeability tensor to account for the heterogeneity of the porous media. First, the multiphase governing equations are decoupled into an elliptic pressure equation and a hyperbolic or parabolic saturation depends on whether the gravitational and capillary pressures are presented or not. Next, a dual secondary grid (called finite volume grid) is formulated from a primary grid (called finite element grid) to create interaction regions for each grid cell over the entire simulation domain. Such a discretization must ensure the conservation of mass and maintain the continuity of the Darcy velocity across the boundaries between neighboring interaction regions

  5. Experiments with a three-dimensional statistical objective analysis scheme using FGGE data

    NASA Technical Reports Server (NTRS)

    Baker, Wayman E.; Bloom, Stephen C.; Woollen, John S.; Nestler, Mark S.; Brin, Eugenia

    1987-01-01

    A three-dimensional (3D), multivariate, statistical objective analysis scheme (referred to as optimum interpolation or OI) has been developed for use in numerical weather prediction studies with the FGGE data. Some novel aspects of the present scheme include: (1) a multivariate surface analysis over the oceans, which employs an Ekman balance instead of the usual geostrophic relationship, to model the pressure-wind error cross correlations, and (2) the capability to use an error correlation function which is geographically dependent. A series of 4-day data assimilation experiments are conducted to examine the importance of some of the key features of the OI in terms of their effects on forecast skill, as well as to compare the forecast skill using the OI with that utilizing a successive correction method (SCM) of analysis developed earlier. For the three cases examined, the forecast skill is found to be rather insensitive to varying the error correlation function geographically. However, significant differences are noted between forecasts from a two-dimensional (2D) version of the OI and those from the 3D OI, with the 3D OI forecasts exhibiting better forecast skill. The 3D OI forecasts are also more accurate than those from the SCM initial conditions. The 3D OI with the multivariate oceanic surface analysis was found to produce forecasts which were slightly more accurate, on the average, than a univariate version.

  6. Finance schemes for funding private orthodontic treatment.

    PubMed

    Perks, S

    1997-02-01

    Over the last ten years there has been a steady increase in the volume of private dental treatment and numerous finance schemes have been developed to help both patients and dentists. Private orthodontic treatment is increasing and the purpose of this article is to summarise the main features of the schemes currently available to fund private orthodontic treatment and to provide a source of reference.

  7. Dynamic Restarting Schemes for Eigenvalue Problems

    DOE Office of Scientific and Technical Information (OSTI.GOV)

    Wu, Kesheng; Simon, Horst D.

    1999-03-10

    In studies of restarted Davidson method, a dynamic thick-restart scheme was found to be excellent in improving the overall effectiveness of the eigen value method. This paper extends the study of the dynamic thick-restart scheme to the Lanczos method for symmetric eigen value problems and systematically explore a range of heuristics and strategies. We conduct a series of numerical tests to determine their relative strength and weakness on a class of electronic structure calculation problems.

  8. Convenient total variation diminishing conditions for nonlinear difference schemes

    NASA Technical Reports Server (NTRS)

    Tadmor, Eitan

    1986-01-01

    Convenient conditions for nonlinear difference schemes to be total-variation diminishing (TVD) are reviewed. It is shown that such schemes share the TVD property, provided their numerical fluxes meet a certain positivity condition at extrema values but can be arbitrary otherwise. The conditions are invariant under different incremental representations of the nonlinear schemes, and thus provide a simplified generalization of the TVD conditions due to Harten and others.

  9. Spatial and temporal accuracy of asynchrony-tolerant finite difference schemes for partial differential equations at extreme scales

    NASA Astrophysics Data System (ADS)

    Kumari, Komal; Donzis, Diego

    2017-11-01

    Highly resolved computational simulations on massively parallel machines are critical in understanding the physics of a vast number of complex phenomena in nature governed by partial differential equations. Simulations at extreme levels of parallelism present many challenges with communication between processing elements (PEs) being a major bottleneck. In order to fully exploit the computational power of exascale machines one needs to devise numerical schemes that relax global synchronizations across PEs. This asynchronous computations, however, have a degrading effect on the accuracy of standard numerical schemes.We have developed asynchrony-tolerant (AT) schemes that maintain order of accuracy despite relaxed communications. We show, analytically and numerically, that these schemes retain their numerical properties with multi-step higher order temporal Runge-Kutta schemes. We also show that for a range of optimized parameters,the computation time and error for AT schemes is less than their synchronous counterpart. Stability of the AT schemes which depends upon history and random nature of delays, are also discussed. Support from NSF is gratefully acknowledged.

  10. Stratified flows with variable density: mathematical modelling and numerical challenges.

    NASA Astrophysics Data System (ADS)

    Murillo, Javier; Navas-Montilla, Adrian

    2017-04-01

    Stratified flows appear in a wide variety of fundamental problems in hydrological and geophysical sciences. They may involve from hyperconcentrated floods carrying sediment causing collapse, landslides and debris flows, to suspended material in turbidity currents where turbulence is a key process. Also, in stratified flows variable horizontal density is present. Depending on the case, density varies according to the volumetric concentration of different components or species that can represent transported or suspended materials or soluble substances. Multilayer approaches based on the shallow water equations provide suitable models but are not free from difficulties when moving to the numerical resolution of the governing equations. Considering the variety of temporal and spatial scales, transfer of mass and energy among layers may strongly differ from one case to another. As a consequence, in order to provide accurate solutions, very high order methods of proved quality are demanded. Under these complex scenarios it is necessary to observe that the numerical solution provides the expected order of accuracy but also converges to the physically based solution, which is not an easy task. To this purpose, this work will focus in the use of Energy balanced augmented solvers, in particular, the Augmented Roe Flux ADER scheme. References: J. Murillo , P. García-Navarro, Wave Riemann description of friction terms in unsteady shallow flows: Application to water and mud/debris floods. J. Comput. Phys. 231 (2012) 1963-2001. J. Murillo B. Latorre, P. García-Navarro. A Riemann solver for unsteady computation of 2D shallow flows with variable density. J. Comput. Phys.231 (2012) 4775-4807. A. Navas-Montilla, J. Murillo, Energy balanced numerical schemes with very high order. The Augmented Roe Flux ADER scheme. Application to the shallow water equations, J. Comput. Phys. 290 (2015) 188-218. A. Navas-Montilla, J. Murillo, Asymptotically and exactly energy balanced augmented flux

  11. Numerical implementation of non-local polycrystal plasticity using fast Fourier transforms

    DOE Office of Scientific and Technical Information (OSTI.GOV)

    Lebensohn, Ricardo A.; Needleman, Alan

    Here, we present the numerical implementation of a non-local polycrystal plasticity theory using the FFT-based formulation of Suquet and co-workers. Gurtin (2002) non-local formulation, with geometry changes neglected, has been incorporated in the EVP-FFT algorithm of Lebensohn et al. (2012). Numerical procedures for the accurate estimation of higher order derivatives of micromechanical fields, required for feedback into single crystal constitutive relations, are identified and applied. A simple case of a periodic laminate made of two fcc crystals with different plastic properties is first used to assess the soundness and numerical stability of the proposed algorithm and to study the influencemore » of different model parameters on the predictions of the non-local model. Different behaviors at grain boundaries are explored, and the one consistent with the micro-clamped condition gives the most pronounced size effect. The formulation is applied next to 3-D fcc polycrystals, illustrating the possibilities offered by the proposed numerical scheme to analyze the mechanical response of polycrystalline aggregates in three dimensions accounting for size dependence arising from plastic strain gradients with reasonable computing times.« less

  12. Numerical implementation of non-local polycrystal plasticity using fast Fourier transforms

    DOE PAGES

    Lebensohn, Ricardo A.; Needleman, Alan

    2016-03-28

    Here, we present the numerical implementation of a non-local polycrystal plasticity theory using the FFT-based formulation of Suquet and co-workers. Gurtin (2002) non-local formulation, with geometry changes neglected, has been incorporated in the EVP-FFT algorithm of Lebensohn et al. (2012). Numerical procedures for the accurate estimation of higher order derivatives of micromechanical fields, required for feedback into single crystal constitutive relations, are identified and applied. A simple case of a periodic laminate made of two fcc crystals with different plastic properties is first used to assess the soundness and numerical stability of the proposed algorithm and to study the influencemore » of different model parameters on the predictions of the non-local model. Different behaviors at grain boundaries are explored, and the one consistent with the micro-clamped condition gives the most pronounced size effect. The formulation is applied next to 3-D fcc polycrystals, illustrating the possibilities offered by the proposed numerical scheme to analyze the mechanical response of polycrystalline aggregates in three dimensions accounting for size dependence arising from plastic strain gradients with reasonable computing times.« less

  13. Comparitive Study of High-Order Positivity-Preserving WENO Schemes

    NASA Technical Reports Server (NTRS)

    Kotov, D. V.; Yee, H. C.; Sjogreen, B.

    2014-01-01

    In gas dynamics and magnetohydrodynamics flows, physically, the density ? and the pressure p should both be positive. In a standard conservative numerical scheme, however, the computed internal energy is The ideas of Zhang & Shu (2012) and Hu et al. (2012) precisely address the aforementioned issue. Zhang & Shu constructed a new conservative positivity-preserving procedure to preserve positive density and pressure for high-order Weighted Essentially Non-Oscillatory (WENO) schemes by the Lax-Friedrichs flux (WENO/LLF). In general, WENO/LLF is obtained by subtracting the kinetic energy from the total energy, resulting in a computed p that may be negative. Examples are problems in which the dominant energy is kinetic. Negative ? may often emerge in computing blast waves. In such situations the computed eigenvalues of the Jacobian will become imaginary. Consequently, the initial value problem for the linearized system will be ill posed. This explains why failure of preserving positivity of density or pressure may cause blow-ups of the numerical algorithm. The adhoc methods in numerical strategy which modify the computed negative density and/or the computed negative pressure to be positive are neither a conservative cure nor a stable solution. Conservative positivity-preserving schemes are more appropriate for such flow problems. too dissipative for flows such as turbulence with strong shocks computed in direct numerical simulations (DNS) and large eddy simulations (LES). The new conservative positivity-preserving procedure proposed in Hu et al. (2012) can be used with any high-order shock-capturing scheme, including high-order WENO schemes using the Roe's flux (WENO/Roe). The goal of this study is to compare the results obtained by non-positivity-preserving methods with the recently developed positivity-preserving schemes for representative test cases. In particular the more di cult 3D Noh and Sedov problems are considered. These test cases are chosen because of the

  14. Efficient Low Dissipative High Order Schemes for Multiscale MHD Flows, I: Basic Theory

    NASA Technical Reports Server (NTRS)

    Sjoegreen, Bjoern; Yee, H. C.

    2003-01-01

    The objective of this paper is to extend our recently developed highly parallelizable nonlinear stable high order schemes for complex multiscale hydrodynamic applications to the viscous MHD equations. These schemes employed multiresolution wavelets as adaptive numerical dissipation controls t o limit the amount of and to aid the selection and/or blending of the appropriate types of dissipation to be used. The new scheme is formulated for both the conservative and non-conservative form of the MHD equations in curvilinear grids. The four advantages of the present approach over existing MHD schemes reported in the open literature are as follows. First, the scheme is constructed for long-time integrations of shock/turbulence/combustion MHD flows. Available schemes are too diffusive for long-time integrations and/or turbulence/combustion problems. Second, unlike exist- ing schemes for the conservative MHD equations which suffer from ill-conditioned eigen- decompositions, the present scheme makes use of a well-conditioned eigen-decomposition obtained from a minor modification of the eigenvectors of the non-conservative MHD equations t o solve the conservative form of the MHD equations. Third, this approach of using the non-conservative eigensystem when solving the conservative equations also works well in the context of standard shock-capturing schemes for the MHD equations. Fourth, a new approach to minimize the numerical error of the divergence-free magnetic condition for high order schemes is introduced. Numerical experiments with typical MHD model problems revealed the applicability of the newly developed schemes for the MHD equations.

  15. Computing Evans functions numerically via boundary-value problems

    NASA Astrophysics Data System (ADS)

    Barker, Blake; Nguyen, Rose; Sandstede, Björn; Ventura, Nathaniel; Wahl, Colin

    2018-03-01

    The Evans function has been used extensively to study spectral stability of travelling-wave solutions in spatially extended partial differential equations. To compute Evans functions numerically, several shooting methods have been developed. In this paper, an alternative scheme for the numerical computation of Evans functions is presented that relies on an appropriate boundary-value problem formulation. Convergence of the algorithm is proved, and several examples, including the computation of eigenvalues for a multi-dimensional problem, are given. The main advantage of the scheme proposed here compared with earlier methods is that the scheme is linear and scalable to large problems.

  16. An upwind space-time conservation element and solution element scheme for solving dusty gas flow model

    NASA Astrophysics Data System (ADS)

    Rehman, Asad; Ali, Ishtiaq; Qamar, Shamsul

    An upwind space-time conservation element and solution element (CE/SE) scheme is extended to numerically approximate the dusty gas flow model. Unlike central CE/SE schemes, the current method uses the upwind procedure to derive the numerical fluxes through the inner boundary of conservation elements. These upwind fluxes are utilized to calculate the gradients of flow variables. For comparison and validation, the central upwind scheme is also applied to solve the same dusty gas flow model. The suggested upwind CE/SE scheme resolves the contact discontinuities more effectively and preserves the positivity of flow variables in low density flows. Several case studies are considered and the results of upwind CE/SE are compared with the solutions of central upwind scheme. The numerical results show better performance of the upwind CE/SE method as compared to the central upwind scheme.

  17. An accurate real-time model of maglev planar motor based on compound Simpson numerical integration

    NASA Astrophysics Data System (ADS)

    Kou, Baoquan; Xing, Feng; Zhang, Lu; Zhou, Yiheng; Liu, Jiaqi

    2017-05-01

    To realize the high-speed and precise control of the maglev planar motor, a more accurate real-time electromagnetic model, which considers the influence of the coil corners, is proposed in this paper. Three coordinate systems for the stator, mover and corner coil are established. The coil is divided into two segments, the straight coil segment and the corner coil segment, in order to obtain a complete electromagnetic model. When only take the first harmonic of the flux density distribution of a Halbach magnet array into account, the integration method can be carried out towards the two segments according to Lorenz force law. The force and torque analysis formula of the straight coil segment can be derived directly from Newton-Leibniz formula, however, this is not applicable to the corner coil segment. Therefore, Compound Simpson numerical integration method is proposed in this paper to solve the corner segment. With the validation of simulation and experiment, the proposed model has high accuracy and can realize practical application easily.

  18. Entropy Splitting and Numerical Dissipation

    NASA Technical Reports Server (NTRS)

    Yee, H. C.; Vinokur, M.; Djomehri, M. J.

    1999-01-01

    A rigorous stability estimate for arbitrary order of accuracy of spatial central difference schemes for initial-boundary value problems of nonlinear symmetrizable systems of hyperbolic conservation laws was established recently by Olsson and Oliger (1994) and Olsson (1995) and was applied to the two-dimensional compressible Euler equations for a perfect gas by Gerritsen and Olsson (1996) and Gerritsen (1996). The basic building block in developing the stability estimate is a generalized energy approach based on a special splitting of the flux derivative via a convex entropy function and certain homogeneous properties. Due to some of the unique properties of the compressible Euler equations for a perfect gas, the splitting resulted in the sum of a conservative portion and a non-conservative portion of the flux derivative. hereafter referred to as the "Entropy Splitting." There are several potential desirable attributes and side benefits of the entropy splitting for the compressible Euler equations that were not fully explored in Gerritsen and Olsson. The paper has several objectives. The first is to investigate the choice of the arbitrary parameter that determines the amount of splitting and its dependence on the type of physics of current interest to computational fluid dynamics. The second is to investigate in what manner the splitting affects the nonlinear stability of the central schemes for long time integrations of unsteady flows such as in nonlinear aeroacoustics and turbulence dynamics. If numerical dissipation indeed is needed to stabilize the central scheme, can the splitting help minimize the numerical dissipation compared to its un-split cousin? Extensive numerical study on the vortex preservation capability of the splitting in conjunction with central schemes for long time integrations will be presented. The third is to study the effect of the non-conservative proportion of splitting in obtaining the correct shock location for high speed complex shock

  19. A simple extension of Roe's scheme for real gases

    DOE Office of Scientific and Technical Information (OSTI.GOV)

    Arabi, Sina, E-mail: sina.arabi@polymtl.ca; Trépanier, Jean-Yves; Camarero, Ricardo

    The purpose of this paper is to develop a highly accurate numerical algorithm to model real gas flows in local thermodynamic equilibrium (LTE). The Euler equations are solved using a finite volume method based on Roe's flux difference splitting scheme including real gas effects. A novel algorithm is proposed to calculate the Jacobian matrix which satisfies the flux difference splitting exactly in the average state for a general equation of state. This algorithm increases the robustness and accuracy of the method, especially around the contact discontinuities and shock waves where the gas properties jump appreciably. The results are compared withmore » an exact solution of the Riemann problem for the shock tube which considers the real gas effects. In addition, the method is applied to a blunt cone to illustrate the capability of the proposed extension in solving two dimensional flows.« less

  20. Residual Distribution Schemes for Conservation Laws Via Adaptive Quadrature

    NASA Technical Reports Server (NTRS)

    Barth, Timothy; Abgrall, Remi; Biegel, Bryan (Technical Monitor)

    2000-01-01

    This paper considers a family of nonconservative numerical discretizations for conservation laws which retains the correct weak solution behavior in the limit of mesh refinement whenever sufficient order numerical quadrature is used. Our analysis of 2-D discretizations in nonconservative form follows the 1-D analysis of Hou and Le Floch. For a specific family of nonconservative discretizations, it is shown under mild assumptions that the error arising from non-conservation is strictly smaller than the discretization error in the scheme. In the limit of mesh refinement under the same assumptions, solutions are shown to satisfy an entropy inequality. Using results from this analysis, a variant of the "N" (Narrow) residual distribution scheme of van der Weide and Deconinck is developed for first-order systems of conservation laws. The modified form of the N-scheme supplants the usual exact single-state mean-value linearization of flux divergence, typically used for the Euler equations of gasdynamics, by an equivalent integral form on simplex interiors. This integral form is then numerically approximated using an adaptive quadrature procedure. This renders the scheme nonconservative in the sense described earlier so that correct weak solutions are still obtained in the limit of mesh refinement. Consequently, we then show that the modified form of the N-scheme can be easily applied to general (non-simplicial) element shapes and general systems of first-order conservation laws equipped with an entropy inequality where exact mean-value linearization of the flux divergence is not readily obtained, e.g. magnetohydrodynamics, the Euler equations with certain forms of chemistry, etc. Numerical examples of subsonic, transonic and supersonic flows containing discontinuities together with multi-level mesh refinement are provided to verify the analysis.

  1. Study on launch scheme of space-net capturing system.

    PubMed

    Gao, Qingyu; Zhang, Qingbin; Feng, Zhiwei; Tang, Qiangang

    2017-01-01

    With the continuous progress in active debris-removal technology, scientists are increasingly concerned about the concept of space-net capturing system. The space-net capturing system is a long-range-launch flexible capture system, which has great potential to capture non-cooperative targets such as inactive satellites and upper stages. In this work, the launch scheme is studied by experiment and simulation, including two-step ejection and multi-point-traction analyses. The numerical model of the tether/net is based on finite element method and is verified by full-scale ground experiment. The results of the ground experiment and numerical simulation show that the two-step ejection and six-point traction scheme of the space-net system is superior to the traditional one-step ejection and four-point traction launch scheme.

  2. Study on launch scheme of space-net capturing system

    PubMed Central

    Zhang, Qingbin; Feng, Zhiwei; Tang, Qiangang

    2017-01-01

    With the continuous progress in active debris-removal technology, scientists are increasingly concerned about the concept of space-net capturing system. The space-net capturing system is a long-range-launch flexible capture system, which has great potential to capture non-cooperative targets such as inactive satellites and upper stages. In this work, the launch scheme is studied by experiment and simulation, including two-step ejection and multi-point-traction analyses. The numerical model of the tether/net is based on finite element method and is verified by full-scale ground experiment. The results of the ground experiment and numerical simulation show that the two-step ejection and six-point traction scheme of the space-net system is superior to the traditional one-step ejection and four-point traction launch scheme. PMID:28877187

  3. Power corrections in the N -jettiness subtraction scheme

    DOE Office of Scientific and Technical Information (OSTI.GOV)

    Boughezal, Radja; Liu, Xiaohui; Petriello, Frank

    We discuss the leading-logarithmic power corrections in the N-jettiness subtraction scheme for higher-order perturbative QCD calculations. We compute the next-to-leading order power corrections for an arbitrary N-jet process, and we explicitly calculate the power correction through next-to-next-to-leading order for color-singlet production for bothmore » $$q\\bar{q}$$ and gg initiated processes. Our results are compact and simple to implement numerically. Including the leading power correction in the N-jettiness subtraction scheme substantially improves its numerical efficiency. Finally, we discuss what features of our techniques extend to processes containing final-state jets.« less

  4. Power corrections in the N -jettiness subtraction scheme

    DOE PAGES

    Boughezal, Radja; Liu, Xiaohui; Petriello, Frank

    2017-03-30

    We discuss the leading-logarithmic power corrections in the N-jettiness subtraction scheme for higher-order perturbative QCD calculations. We compute the next-to-leading order power corrections for an arbitrary N-jet process, and we explicitly calculate the power correction through next-to-next-to-leading order for color-singlet production for bothmore » $$q\\bar{q}$$ and gg initiated processes. Our results are compact and simple to implement numerically. Including the leading power correction in the N-jettiness subtraction scheme substantially improves its numerical efficiency. Finally, we discuss what features of our techniques extend to processes containing final-state jets.« less

  5. The Super Tuesday Outbreak: Forecast Sensitivities to Single-Moment Microphysics Schemes

    NASA Technical Reports Server (NTRS)

    Molthan, Andrew L.; Case, Jonathan L.; Dembek, Scott R.; Jedlovec, Gary J.; Lapenta, William M.

    2008-01-01

    Forecast precipitation and radar characteristics are used by operational centers to guide the issuance of advisory products. As operational numerical weather prediction is performed at increasingly finer spatial resolution, convective precipitation traditionally represented by sub-grid scale parameterization schemes is now being determined explicitly through single- or multi-moment bulk water microphysics routines. Gains in forecasting skill are expected through improved simulation of clouds and their microphysical processes. High resolution model grids and advanced parameterizations are now available through steady increases in computer resources. As with any parameterization, their reliability must be measured through performance metrics, with errors noted and targeted for improvement. Furthermore, the use of these schemes within an operational framework requires an understanding of limitations and an estimate of biases so that forecasters and model development teams can be aware of potential errors. The National Severe Storms Laboratory (NSSL) Spring Experiments have produced daily, high resolution forecasts used to evaluate forecast skill among an ensemble with varied physical parameterizations and data assimilation techniques. In this research, high resolution forecasts of the 5-6 February 2008 Super Tuesday Outbreak are replicated using the NSSL configuration in order to evaluate two components of simulated convection on a large domain: sensitivities of quantitative precipitation forecasts to assumptions within a single-moment bulk water microphysics scheme, and to determine if these schemes accurately depict the reflectivity characteristics of well-simulated, organized, cold frontal convection. As radar returns are sensitive to the amount of hydrometeor mass and the distribution of mass among variably sized targets, radar comparisons may guide potential improvements to a single-moment scheme. In addition, object-based verification metrics are evaluated for

  6. NUMERICAL NOISE PM SIMULATION IN CMAQ

    EPA Science Inventory

    We have found that numerical noise in the latest release of CMAQ using the yamo advection scheme when compiled on Linux cluster with pgf90 (5.0 or 6.0). We recommend to use -C option to eliminate the numerical noise.

  7. A New Family of Compact High Order Coupled Time-Space Unconditionally Stable Vertical Advection Schemes

    NASA Astrophysics Data System (ADS)

    Lemarié, F.; Debreu, L.

    2016-02-01

    Recent papers by Shchepetkin (2015) and Lemarié et al. (2015) have emphasized that the time-step of an oceanic model with an Eulerian vertical coordinate and an explicit time-stepping scheme is very often restricted by vertical advection in a few hot spots (i.e. most of the grid points are integrated with small Courant numbers, compared to the Courant-Friedrichs-Lewy (CFL) condition, except just few spots where numerical instability of the explicit scheme occurs first). The consequence is that the numerics for vertical advection must have good stability properties while being robust to changes in Courant number in terms of accuracy. An other constraint for oceanic models is the strict control of numerical mixing imposed by the highly adiabatic nature of the oceanic interior (i.e. mixing must be very small in the vertical direction below the boundary layer). We examine in this talk the possibility of mitigating vertical Courant-Friedrichs-Lewy (CFL) restriction, while avoiding numerical inaccuracies associated with standard implicit advection schemes (i.e. large sensitivity of the solution on Courant number, large phase delay, and possibly excess of numerical damping with unphysical orientation). Most regional oceanic models have been successfully using fourth order compact schemes for vertical advection. In this talk we present a new general framework to derive generic expressions for (one-step) coupled time and space high order compact schemes (see Daru & Tenaud (2004) for a thorough description of coupled time and space schemes). Among other properties, we show that those schemes are unconditionally stable and have very good accuracy properties even for large Courant numbers while having a very reasonable computational cost. To our knowledge no unconditionally stable scheme with such high order accuracy in time and space have been presented so far in the literature. Furthermore, we show how those schemes can be made monotonic without compromising their stability

  8. Dispersion-relation-preserving finite difference schemes for computational acoustics

    NASA Technical Reports Server (NTRS)

    Tam, Christopher K. W.; Webb, Jay C.

    1993-01-01

    Time-marching dispersion-relation-preserving (DRP) schemes can be constructed by optimizing the finite difference approximations of the space and time derivatives in wave number and frequency space. A set of radiation and outflow boundary conditions compatible with the DRP schemes is constructed, and a sequence of numerical simulations is conducted to test the effectiveness of the DRP schemes and the radiation and outflow boundary conditions. Close agreement with the exact solutions is obtained.

  9. A Comparison of Some Difference Schemes for a Parabolic Problem of Zero-Coupon Bond Pricing

    NASA Astrophysics Data System (ADS)

    Chernogorova, Tatiana; Vulkov, Lubin

    2009-11-01

    This paper describes a comparison of some numerical methods for solving a convection-diffusion equation subjected by dynamical boundary conditions which arises in the zero-coupon bond pricing. The one-dimensional convection-diffusion equation is solved by using difference schemes with weights including standard difference schemes as the monotone Samarskii's scheme, FTCS and Crank-Nicolson methods. The schemes are free of spurious oscillations and satisfy the positivity and maximum principle as demanded for the financial and diffusive solution. Numerical results are compared with analytical solutions.

  10. Implementation of a gust front head collapse scheme in the WRF numerical model

    NASA Astrophysics Data System (ADS)

    Lompar, Miloš; Ćurić, Mladjen; Romanic, Djordje

    2018-05-01

    Gust fronts are thunderstorm-related phenomena usually associated with severe winds which are of great importance in theoretical meteorology, weather forecasting, cloud dynamics and precipitation, and wind engineering. An important feature of gust fronts demonstrated through both theoretical and observational studies is the periodic collapse and rebuild of the gust front head. This cyclic behavior of gust fronts results in periodic forcing of vertical velocity ahead of the parent thunderstorm, which consequently influences the storm dynamics and microphysics. This paper introduces the first gust front pulsation parameterization scheme in the WRF-ARW model (Weather Research and Forecasting-Advanced Research WRF). The influence of this new scheme on model performances is tested through investigation of the characteristics of an idealized supercell cumulonimbus cloud, as well as studying a real case of thunderstorms above the United Arab Emirates. In the ideal case, WRF with the gust front scheme produced more precipitation and showed different time evolution of mixing ratios of cloud water and rain, whereas the mixing ratios of ice and graupel are almost unchanged when compared to the default WRF run without the parameterization of gust front pulsation. The included parameterization did not disturb the general characteristics of thunderstorm cloud, such as the location of updraft and downdrafts, and the overall shape of the cloud. New cloud cells in front of the parent thunderstorm are also evident in both ideal and real cases due to the included forcing of vertical velocity caused by the periodic collapse of the gust front head. Despite some differences between the two WRF simulations and satellite observations, the inclusion of the gust front parameterization scheme produced more cumuliform clouds and seem to match better with real observations. Both WRF simulations gave poor results when it comes to matching the maximum composite radar reflectivity from radar

  11. Semi-Numerical Studies of the Three-Meter Spherical Couette Experiment Utilizing Data Assimilation

    NASA Astrophysics Data System (ADS)

    Burnett, Sarah; Rojas, Ruben; Perevalov, Artur; Lathrop, Daniel; Ide, Kayo; Schaeffer, Nathanael

    2017-11-01

    The model of the Earth's magnetic field has been investigated in recent years through experiments and numerical models. At the University of Maryland, experimental studies are implemented in a three-meter spherical Couette device filled with liquid sodium. The inner and outer spheres of this apparatus mimic the planet's inner core and core-mantle boundary, respectively. These experiments incorporate high velocity flows with Reynolds numbers 108 . In spherical Couette geometry, the numerical scheme applied to this work features finite difference methods in the radial direction and pseudospectral spherical harmonic transforms elsewhere. Adding to the numerical model, data assimilation integrates the experimental outer-layer magnetic field measurements. This semi-numerical model can then be compared to the experimental results as well as forecasting magnetic field changes. Data assimilation makes it possible to get estimates of internal motions of the three-meter experiment that would otherwise be intrusive or impossible to obtain in experiments or too computationally expensive with a purely numerical code. If we can provide accurate models of the three-meter device, it is possible to attempt to model the geomagnetic field. We gratefully acknowledge the support of NSF Grant No. EAR1417148 & DGE1322106.

  12. Spurious sea ice formation caused by oscillatory ocean tracer advection schemes

    NASA Astrophysics Data System (ADS)

    Naughten, Kaitlin A.; Galton-Fenzi, Benjamin K.; Meissner, Katrin J.; England, Matthew H.; Brassington, Gary B.; Colberg, Frank; Hattermann, Tore; Debernard, Jens B.

    2017-08-01

    Tracer advection schemes used by ocean models are susceptible to artificial oscillations: a form of numerical error whereby the advected field alternates between overshooting and undershooting the exact solution, producing false extrema. Here we show that these oscillations have undesirable interactions with a coupled sea ice model. When oscillations cause the near-surface ocean temperature to fall below the freezing point, sea ice forms for no reason other than numerical error. This spurious sea ice formation has significant and wide-ranging impacts on Southern Ocean simulations, including the disappearance of coastal polynyas, stratification of the water column, erosion of Winter Water, and upwelling of warm Circumpolar Deep Water. This significantly limits the model's suitability for coupled ocean-ice and climate studies. Using the terrain-following-coordinate ocean model ROMS (Regional Ocean Modelling System) coupled to the sea ice model CICE (Community Ice CodE) on a circumpolar Antarctic domain, we compare the performance of three different tracer advection schemes, as well as two levels of parameterised diffusion and the addition of flux limiters to prevent numerical oscillations. The upwind third-order advection scheme performs better than the centered fourth-order and Akima fourth-order advection schemes, with far fewer incidents of spurious sea ice formation. The latter two schemes are less problematic with higher parameterised diffusion, although some supercooling artifacts persist. Spurious supercooling was eliminated by adding flux limiters to the upwind third-order scheme. We present this comparison as evidence of the problematic nature of oscillatory advection schemes in sea ice formation regions, and urge other ocean/sea-ice modellers to exercise caution when using such schemes.

  13. The a(4) Scheme-A High Order Neutrally Stable CESE Solver

    NASA Technical Reports Server (NTRS)

    Chang, Sin-Chung

    2009-01-01

    The CESE development is driven by a belief that a solver should (i) enforce conservation laws in both space and time, and (ii) be built from a nondissipative (i.e., neutrally stable) core scheme so that the numerical dissipation can be controlled effectively. To provide a solid foundation for a systematic CESE development of high order schemes, in this paper we describe a new high order (4-5th order) and neutrally stable CESE solver of a 1D advection equation with a constant advection speed a. The space-time stencil of this two-level explicit scheme is formed by one point at the upper time level and two points at the lower time level. Because it is associated with four independent mesh variables (the numerical analogues of the dependent variable and its first, second, and third-order spatial derivatives) and four equations per mesh point, the new scheme is referred to as the a(4) scheme. As in the case of other similar CESE neutrally stable solvers, the a(4) scheme enforces conservation laws in space-time locally and globally, and it has the basic, forward marching, and backward marching forms. Except for a singular case, these forms are equivalent and satisfy a space-time inversion (STI) invariant property which is shared by the advection equation. Based on the concept of STI invariance, a set of algebraic relations is developed and used to prove the a(4) scheme must be neutrally stable when it is stable. Numerically, it has been established that the scheme is stable if the value of the Courant number is less than 1/3

  14. A family of compact high order coupled time-space unconditionally stable vertical advection schemes

    NASA Astrophysics Data System (ADS)

    Lemarié, Florian; Debreu, Laurent

    2016-04-01

    Recent papers by Shchepetkin (2015) and Lemarié et al. (2015) have emphasized that the time-step of an oceanic model with an Eulerian vertical coordinate and an explicit time-stepping scheme is very often restricted by vertical advection in a few hot spots (i.e. most of the grid points are integrated with small Courant numbers, compared to the Courant-Friedrichs-Lewy (CFL) condition, except just few spots where numerical instability of the explicit scheme occurs first). The consequence is that the numerics for vertical advection must have good stability properties while being robust to changes in Courant number in terms of accuracy. An other constraint for oceanic models is the strict control of numerical mixing imposed by the highly adiabatic nature of the oceanic interior (i.e. mixing must be very small in the vertical direction below the boundary layer). We examine in this talk the possibility of mitigating vertical Courant-Friedrichs-Lewy (CFL) restriction, while avoiding numerical inaccuracies associated with standard implicit advection schemes (i.e. large sensitivity of the solution on Courant number, large phase delay, and possibly excess of numerical damping with unphysical orientation). Most regional oceanic models have been successfully using fourth order compact schemes for vertical advection. In this talk we present a new general framework to derive generic expressions for (one-step) coupled time and space high order compact schemes (see Daru & Tenaud (2004) for a thorough description of coupled time and space schemes). Among other properties, we show that those schemes are unconditionally stable and have very good accuracy properties even for large Courant numbers while having a very reasonable computational cost.

  15. A fast numerical method for ideal fluid flow in domains with multiple stirrers

    NASA Astrophysics Data System (ADS)

    Nasser, Mohamed M. S.; Green, Christopher C.

    2018-03-01

    A collection of arbitrarily-shaped solid objects, each moving at a constant speed, can be used to mix or stir ideal fluid, and can give rise to interesting flow patterns. Assuming these systems of fluid stirrers are two-dimensional, the mathematical problem of resolving the flow field—given a particular distribution of any finite number of stirrers of specified shape and speed—can be formulated as a Riemann-Hilbert (R-H) problem. We show that this R-H problem can be solved numerically using a fast and accurate algorithm for any finite number of stirrers based around a boundary integral equation with the generalized Neumann kernel. Various systems of fluid stirrers are considered, and our numerical scheme is shown to handle highly multiply connected domains (i.e. systems of many fluid stirrers) with minimal computational expense.

  16. Experience in using a numerical scheme with artificial viscosity at solving the Riemann problem for a multi-fluid model of multiphase flow

    NASA Astrophysics Data System (ADS)

    Bulovich, S. V.; Smirnov, E. M.

    2018-05-01

    The paper covers application of the artificial viscosity technique to numerical simulation of unsteady one-dimensional multiphase compressible flows on the base of the multi-fluid approach. The system of the governing equations is written under assumption of the pressure equilibrium between the "fluids" (phases). No interfacial exchange is taken into account. A model for evaluation of the artificial viscosity coefficient that (i) assumes identity of this coefficient for all interpenetrating phases and (ii) uses the multiphase-mixture Wood equation for evaluation of a scale speed of sound has been suggested. Performance of the artificial viscosity technique has been evaluated via numerical solution of a model problem of pressure discontinuity breakdown in a three-fluid medium. It has been shown that a relatively simple numerical scheme, explicit and first-order, combined with the suggested artificial viscosity model, predicts a physically correct behavior of the moving shock and expansion waves, and a subsequent refinement of the computational grid results in a monotonic approaching to an asymptotic time-dependent solution, without non-physical oscillations.

  17. Numerical Treatment of Stokes Solvent Flow and Solute-Solvent Interfacial Dynamics for Nonpolar Molecules.

    PubMed

    Sun, Hui; Zhou, Shenggao; Moore, David K; Cheng, Li-Tien; Li, Bo

    2016-05-01

    We design and implement numerical methods for the incompressible Stokes solvent flow and solute-solvent interface motion for nonpolar molecules in aqueous solvent. The balance of viscous force, surface tension, and van der Waals type dispersive force leads to a traction boundary condition on the solute-solvent interface. To allow the change of solute volume, we design special numerical boundary conditions on the boundary of a computational domain through a consistency condition. We use a finite difference ghost fluid scheme to discretize the Stokes equation with such boundary conditions. The method is tested to have a second-order accuracy. We combine this ghost fluid method with the level-set method to simulate the motion of the solute-solvent interface that is governed by the solvent fluid velocity. Numerical examples show that our method can predict accurately the blow up time for a test example of curvature flow and reproduce the polymodal (e.g., dry and wet) states of hydration of some simple model molecular systems.

  18. Numerical Treatment of Stokes Solvent Flow and Solute-Solvent Interfacial Dynamics for Nonpolar Molecules

    PubMed Central

    Sun, Hui; Zhou, Shenggao; Moore, David K.; Cheng, Li-Tien; Li, Bo

    2015-01-01

    We design and implement numerical methods for the incompressible Stokes solvent flow and solute-solvent interface motion for nonpolar molecules in aqueous solvent. The balance of viscous force, surface tension, and van der Waals type dispersive force leads to a traction boundary condition on the solute-solvent interface. To allow the change of solute volume, we design special numerical boundary conditions on the boundary of a computational domain through a consistency condition. We use a finite difference ghost fluid scheme to discretize the Stokes equation with such boundary conditions. The method is tested to have a second-order accuracy. We combine this ghost fluid method with the level-set method to simulate the motion of the solute-solvent interface that is governed by the solvent fluid velocity. Numerical examples show that our method can predict accurately the blow up time for a test example of curvature flow and reproduce the polymodal (e.g., dry and wet) states of hydration of some simple model molecular systems. PMID:27365866

  19. A new multi-symplectic scheme for the generalized Kadomtsev-Petviashvili equation

    NASA Astrophysics Data System (ADS)

    Li, Haochen; Sun, Jianqiang

    2012-09-01

    We propose a new scheme for the generalized Kadomtsev-Petviashvili (KP) equation. The multi-symplectic conservation property of the new scheme is proved. Back error analysis shows that the new multi-symplectic scheme has second order accuracy in space and time. Numerical application on studying the KPI equation and the KPII equation are presented in detail.

  20. Simple Numerical Modelling for Gasdynamic Design of Wave Rotors

    NASA Astrophysics Data System (ADS)

    Okamoto, Koji; Nagashima, Toshio

    The precise estimation of pressure waves generated in the passages is a crucial factor in wave rotor design. However, it is difficult to estimate the pressure wave analytically, e.g. by the method of characteristics, because the mechanism of pressure-wave generation and propagation in the passages is extremely complicated as compared to that in a shock tube. In this study, a simple numerical modelling scheme was developed to facilitate the design procedure. This scheme considers the three dominant factors in the loss mechanism —gradual passage opening, wall friction and leakage— for simulating the pressure waves precisely. The numerical scheme itself is based on the one-dimensional Euler equations with appropriate source terms to reduce the calculation time. The modelling of these factors was verified by comparing the results with those of a two-dimensional numerical simulation, which were previously validated by the experimental data in our previous study. Regarding wave rotor miniaturization, the leakage flow effect, which involves the interaction between adjacent cells, was investigated extensively. A port configuration principle was also examined and analyzed in detail to verify the applicability of the present numerical modelling scheme to the wave rotor design.

  1. Central Schemes for Multi-Dimensional Hamilton-Jacobi Equations

    NASA Technical Reports Server (NTRS)

    Bryson, Steve; Levy, Doron; Biegel, Bryan (Technical Monitor)

    2002-01-01

    We present new, efficient central schemes for multi-dimensional Hamilton-Jacobi equations. These non-oscillatory, non-staggered schemes are first- and second-order accurate and are designed to scale well with an increasing dimension. Efficiency is obtained by carefully choosing the location of the evolution points and by using a one-dimensional projection step. First-and second-order accuracy is verified for a variety of multi-dimensional, convex and non-convex problems.

  2. A well-balanced scheme for Ten-Moment Gaussian closure equations with source term

    NASA Astrophysics Data System (ADS)

    Meena, Asha Kumari; Kumar, Harish

    2018-02-01

    In this article, we consider the Ten-Moment equations with source term, which occurs in many applications related to plasma flows. We present a well-balanced second-order finite volume scheme. The scheme is well-balanced for general equation of state, provided we can write the hydrostatic solution as a function of the space variables. This is achieved by combining hydrostatic reconstruction with contact preserving, consistent numerical flux, and appropriate source discretization. Several numerical experiments are presented to demonstrate the well-balanced property and resulting accuracy of the proposed scheme.

  3. Constrained H1-regularization schemes for diffeomorphic image registration

    PubMed Central

    Mang, Andreas; Biros, George

    2017-01-01

    We propose regularization schemes for deformable registration and efficient algorithms for their numerical approximation. We treat image registration as a variational optimal control problem. The deformation map is parametrized by its velocity. Tikhonov regularization ensures well-posedness. Our scheme augments standard smoothness regularization operators based on H1- and H2-seminorms with a constraint on the divergence of the velocity field, which resembles variational formulations for Stokes incompressible flows. In our formulation, we invert for a stationary velocity field and a mass source map. This allows us to explicitly control the compressibility of the deformation map and by that the determinant of the deformation gradient. We also introduce a new regularization scheme that allows us to control shear. We use a globalized, preconditioned, matrix-free, reduced space (Gauss–)Newton–Krylov scheme for numerical optimization. We exploit variable elimination techniques to reduce the number of unknowns of our system; we only iterate on the reduced space of the velocity field. Our current implementation is limited to the two-dimensional case. The numerical experiments demonstrate that we can control the determinant of the deformation gradient without compromising registration quality. This additional control allows us to avoid oversmoothing of the deformation map. We also demonstrate that we can promote or penalize shear whilst controlling the determinant of the deformation gradient. PMID:29075361

  4. Comparative Study on High-Order Positivity-preserving WENO Schemes

    NASA Technical Reports Server (NTRS)

    Kotov, D. V.; Yee, H. C.; Sjogreen, B.

    2013-01-01

    In gas dynamics and magnetohydrodynamics flows, physically, the density and the pressure p should both be positive. In a standard conservative numerical scheme, however, the computed internal energy is obtained by subtracting the kinetic energy from the total energy, resulting in a computed p that may be negative. Examples are problems in which the dominant energy is kinetic. Negative may often emerge in computing blast waves. In such situations the computed eigenvalues of the Jacobian will become imaginary. Consequently, the initial value problem for the linearized system will be ill posed. This explains why failure of preserving positivity of density or pressure may cause blow-ups of the numerical algorithm. The adhoc methods in numerical strategy which modify the computed negative density and/or the computed negative pressure to be positive are neither a conservative cure nor a stable solution. Conservative positivity-preserving schemes are more appropriate for such flow problems. The ideas of Zhang & Shu (2012) and Hu et al. (2012) precisely address the aforementioned issue. Zhang & Shu constructed a new conservative positivity-preserving procedure to preserve positive density and pressure for high-order WENO schemes by the Lax-Friedrichs flux (WENO/LLF). In general, WENO/LLF is too dissipative for flows such as turbulence with strong shocks computed in direct numerical simulations (DNS) and large eddy simulations (LES). The new conservative positivity-preserving procedure proposed in Hu et al. (2012) can be used with any high-order shock-capturing scheme, including high-order WENO schemes using the Roe's flux (WENO/Roe). The goal of this study is to compare the results obtained by non-positivity-preserving methods with the recently developed positivity-preserving schemes for representative test cases. In particular the more difficult 3D Noh and Sedov problems are considered. These test cases are chosen because of the negative pressure/density most often

  5. The Impacts of Numerical Schemes on Asymmetric Hurricane Intensification

    NASA Astrophysics Data System (ADS)

    Guimond, S.; Reisner, J. M.; Marras, S.; Giraldo, F.

    2015-12-01

    The fundamental pathways for tropical cyclone (TC) intensification are explored by considering axisymmetric and asymmetric impulsive thermal perturbations to balanced, TC-like vortices using the dynamic cores of three different numerical models. Attempts at reproducing the results of previous work, which used the community atmospheric model WRF (Nolan and Grasso 2003; NG03), revealed a discrepancy with the impacts of purely asymmetric thermal forcing. The current study finds that thermal asymmetries can have an important, largely positive role on the vortex intensification whereas NG03 and other studies find that asymmetric impacts are negligible. Analysis of the spectral energetics of each numerical model indicates that the vortex response to asymmetric thermal perturbations is significantly damped in WRF relative to the other numerical models. Spectral kinetic energy budgets show that this anomalous damping is due to the increased removal of kinetic energy from the convergence of the vertical pressure flux, which is related to the flux of inertia-gravity wave energy. The increased kinetic energy in the other two models is shown to originate around the scales of the heating and propagate upscale with time. For very large thermal amplitudes (~ 50 K and above), the anomalous removal of kinetic energy due to inertia-gravity wave activity is much smaller resulting in little differences between models. The results of this paper indicate that the numerical treatment of small-scale processes that project strongly onto inertia-gravity wave energy are responsible for these differences, with potentially important impacts for the understanding and prediction of TC intensification.

  6. ULTRA-SHARP nonoscillatory convection schemes for high-speed steady multidimensional flow

    NASA Technical Reports Server (NTRS)

    Leonard, B. P.; Mokhtari, Simin

    1990-01-01

    For convection-dominated flows, classical second-order methods are notoriously oscillatory and often unstable. For this reason, many computational fluid dynamicists have adopted various forms of (inherently stable) first-order upwinding over the past few decades. Although it is now well known that first-order convection schemes suffer from serious inaccuracies attributable to artificial viscosity or numerical diffusion under high convection conditions, these methods continue to enjoy widespread popularity for numerical heat transfer calculations, apparently due to a perceived lack of viable high accuracy alternatives. But alternatives are available. For example, nonoscillatory methods used in gasdynamics, including currently popular TVD schemes, can be easily adapted to multidimensional incompressible flow and convective transport. This, in itself, would be a major advance for numerical convective heat transfer, for example. But, as is shown, second-order TVD schemes form only a small, overly restrictive, subclass of a much more universal, and extremely simple, nonoscillatory flux-limiting strategy which can be applied to convection schemes of arbitrarily high order accuracy, while requiring only a simple tridiagonal ADI line-solver, as used in the majority of general purpose iterative codes for incompressible flow and numerical heat transfer. The new universal limiter and associated solution procedures form the so-called ULTRA-SHARP alternative for high resolution nonoscillatory multidimensional steady state high speed convective modelling.

  7. Convergence Acceleration of Runge-Kutta Schemes for Solving the Navier-Stokes Equations

    NASA Technical Reports Server (NTRS)

    Swanson, Roy C., Jr.; Turkel, Eli; Rossow, C.-C.

    2007-01-01

    The convergence of a Runge-Kutta (RK) scheme with multigrid is accelerated by preconditioning with a fully implicit operator. With the extended stability of the Runge-Kutta scheme, CFL numbers as high as 1000 can be used. The implicit preconditioner addresses the stiffness in the discrete equations associated with stretched meshes. This RK/implicit scheme is used as a smoother for multigrid. Fourier analysis is applied to determine damping properties. Numerical dissipation operators based on the Roe scheme, a matrix dissipation, and the CUSP scheme are considered in evaluating the RK/implicit scheme. In addition, the effect of the number of RK stages is examined. Both the numerical and computational efficiency of the scheme with the different dissipation operators are discussed. The RK/implicit scheme is used to solve the two-dimensional (2-D) and three-dimensional (3-D) compressible, Reynolds-averaged Navier-Stokes equations. Turbulent flows over an airfoil and wing at subsonic and transonic conditions are computed. The effects of the cell aspect ratio on convergence are investigated for Reynolds numbers between 5:7 x 10(exp 6) and 100 x 10(exp 6). It is demonstrated that the implicit preconditioner can reduce the computational time of a well-tuned standard RK scheme by a factor between four and ten.

  8. A 3D Optimal Interpolation Assimilation Scheme of HF Radar Current Data into a Numerical Ocean Model

    NASA Astrophysics Data System (ADS)

    Ragnoli, Emanuele; Zhuk, Sergiy; Donncha, Fearghal O.; Suits, Frank; Hartnett, Michael

    2013-04-01

    In this work a technique for the 3D assimilation of ocean surface current measurements into a numerical ocean model based on data from High Frequency Radar (HFR) systems is presented. The technique is the combination of supplementary forcing on the surface and of and Ekman layer projection of the correction in the depth. Optimal interpolation through BLUE (Best Linear Unbiased Estimator) of the model predicted velocity and HFR observations is computed in order to derive a supplementary forcing applied at the surface boundary. In the depth the assimilation is propagated using an additional Ekman pumping (vertical velocity) based on the correction achieved by BLUE. In this work a HFR data assimilation system for hydrodynamic modelling of Galway Bay in Ireland is developed; it demonstrates the viability of adopting data assimilation techniques to improve the performance of numerical models in regions characterized by significant wind-driven flows. A network of CODAR Seasonde high frequency radars (HFR) deployed within Galway Bay, on the West Coast of Ireland, provides flow measurements adopted for this study. This system provides real-time synoptic measurements of both ocean surface currents and ocean surface waves in regions of the bay where radials from two or more radars intersect. Radar systems have a number of unique advantages in ocean modelling data assimilation schemes, namely, the ability to provide two-dimensional mapping of surface currents at resolutions that capture the complex structure related to coastal topography and the intrinsic instability scales of coastal circulation at a relatively low-cost. The radar system used in this study operates at a frequency of 25MHz which provides a sampling range of 25km at a spatial resolution of 300m.A detailed dataset of HFR observed velocities is collected at 60 minute intervals for a period chosen for comparison due to frequent occurrences of highly-energetic, storm-force events. In conjunction with this, a

  9. Monte Carlo closure for moment-based transport schemes in general relativistic radiation hydrodynamic simulations

    NASA Astrophysics Data System (ADS)

    Foucart, Francois

    2018-04-01

    General relativistic radiation hydrodynamic simulations are necessary to accurately model a number of astrophysical systems involving black holes and neutron stars. Photon transport plays a crucial role in radiatively dominated accretion discs, while neutrino transport is critical to core-collapse supernovae and to the modelling of electromagnetic transients and nucleosynthesis in neutron star mergers. However, evolving the full Boltzmann equations of radiative transport is extremely expensive. Here, we describe the implementation in the general relativistic SPEC code of a cheaper radiation hydrodynamic method that theoretically converges to a solution of Boltzmann's equation in the limit of infinite numerical resources. The algorithm is based on a grey two-moment scheme, in which we evolve the energy density and momentum density of the radiation. Two-moment schemes require a closure that fills in missing information about the energy spectrum and higher order moments of the radiation. Instead of the approximate analytical closure currently used in core-collapse and merger simulations, we complement the two-moment scheme with a low-accuracy Monte Carlo evolution. The Monte Carlo results can provide any or all of the missing information in the evolution of the moments, as desired by the user. As a first test of our methods, we study a set of idealized problems demonstrating that our algorithm performs significantly better than existing analytical closures. We also discuss the current limitations of our method, in particular open questions regarding the stability of the fully coupled scheme.

  10. Real time numerical shake prediction incorporating attenuation structure: a case for the 2016 Kumamoto Earthquake

    NASA Astrophysics Data System (ADS)

    Ogiso, M.; Hoshiba, M.; Shito, A.; Matsumoto, S.

    2016-12-01

    Needless to say, heterogeneous attenuation structure is important for ground motion prediction, including earthquake early warning, that is, real time ground motion prediction. Hoshiba and Ogiso (2015, AGU Fall meeting) showed that the heterogeneous attenuation and scattering structure will lead to earlier and more accurate ground motion prediction in the numerical shake prediction scheme proposed by Hoshiba and Aoki (2015, BSSA). Hoshiba and Ogiso (2015) used assumed heterogeneous structure, and we discuss the effect of them in the case of 2016 Kumamoto Earthquake, using heterogeneous structure estimated by actual observation data. We conducted Multiple Lapse Time Window Analysis (Hoshiba, 1993, JGR) to the seismic stations located on western part of Japan to estimate heterogeneous attenuation and scattering structure. The characteristics are similar to the previous work of Carcole and Sato (2010, GJI), e.g. strong intrinsic and scattering attenuation around the volcanoes located on the central part of Kyushu, and relatively weak heterogeneities in the other area. Real time ground motion prediction simulation for the 2016 Kumamoto Earthquake was conducted using the numerical shake prediction scheme with 474 strong ground motion stations. Comparing the snapshot of predicted and observed wavefield showed a tendency for underprediction around the volcanic area in spite of the heterogeneous structure. These facts indicate the necessity of improving the heterogeneous structure for the numerical shake prediction scheme.In this study, we used the waveforms of Hi-net, K-NET, KiK-net stations operated by the NIED for estimating structure and conducting ground motion prediction simulation. Part of this study was supported by the Earthquake Research Institute, the University of Tokyo cooperative research program and JSPS KAKENHI Grant Number 25282114.

  11. Accurate solution of the Helmholtz equation by Lanczos orthogonalization for media with loss or gain.

    PubMed

    Ratowsky, R P; Fleck, J A; Feit, M D

    1992-01-01

    The numerical scheme for solving the Helmholtz equation, based on the Lanczos orthogonalization scheme, is generalized so that it can be applied to media with space-dependent absorption or gain profiles.

  12. Idealized Simulations of a Squall Line from the MC3E Field Campaign Applying Three Bin Microphysics Schemes: Dynamic and Thermodynamic Structure

    DOE Office of Scientific and Technical Information (OSTI.GOV)

    Xue, Lulin; Fan, Jiwen; Lebo, Zachary J.

    The squall line event on May 20, 2011, during the Midlatitude Continental Convective Clouds (MC3E) field campaign has been simulated by three bin (spectral) microphysics schemes coupled into the Weather Research and Forecasting (WRF) model. Semi-idealized three-dimensional simulations driven by temperature and moisture profiles acquired by a radiosonde released in the pre-convection environment at 1200 UTC in Morris, Oklahoma show that each scheme produced a squall line with features broadly consistent with the observed storm characteristics. However, substantial differences in the details of the simulated dynamic and thermodynamic structure are evident. These differences are attributed to different algorithms and numericalmore » representations of microphysical processes, assumptions of the hydrometeor processes and properties, especially ice particle mass, density, and terminal velocity relationships with size, and the resulting interactions between the microphysics, cold pool, and dynamics. This study shows that different bin microphysics schemes, designed to be conceptually more realistic and thus arguably more accurate than bulk microphysics schemes, still simulate a wide spread of microphysical, thermodynamic, and dynamic characteristics of a squall line, qualitatively similar to the spread of squall line characteristics using various bulk schemes. Future work may focus on improving the representation of ice particle properties in bin schemes to reduce this uncertainty and using the similar assumptions for all schemes to isolate the impact of physics from numerics.« less

  13. Numerical Simulation of the 2004 Indian Ocean Tsunami: Accurate Flooding and drying in Banda Aceh

    NASA Astrophysics Data System (ADS)

    Cui, Haiyang; Pietrzak, Julie; Stelling, Guus; Androsov, Alexey; Harig, Sven

    2010-05-01

    The Indian Ocean Tsunami on December 26, 2004 caused one of the largest tsunamis in recent times and led to widespread devastation and loss of life. One of the worst hit regions was Banda Aceh, which is the capital of the Aceh province, located in the northern part of Sumatra, 150km from the source of the earthquake. A German-Indonesian Tsunami Early Warning System (GITEWS) (www.gitews.de) is currently under active development. The work presented here is carried out within the GITEWS framework. One of the aims of this project is the development of accurate models with which to simulate the propagation, flooding and drying, and run-up of a tsunami. In this context, TsunAWI has been developed by the Alfred Wegener Institute; it is an explicit, () finite element model. However, the accurate numerical simulation of flooding and drying requires the conservation of mass and momentum. This is not possible in the current version of TsunAWi. The P1NC - P1element guarantees mass conservation in a global sense, yet as we show here it is important to guarantee mass conservation at the local level, that is within each individual cell. Here an unstructured grid, finite volume ocean model is presented. It is derived from the P1NC - P1 element, and is shown to be mass and momentum conserving. Then a number of simulations are presented, including dam break problems flooding over both a wet and a dry bed. Excellent agreement is found. Then we present simulations for Banda Aceh, and compare the results to on-site survey data, as well as to results from the original TsunAWI code.

  14. Proper use of colour schemes for image data visualization

    NASA Astrophysics Data System (ADS)

    Vozenilek, Vit; Vondrakova, Alena

    2018-04-01

    With the development of information and communication technologies, new technologies are leading to an exponential increase in the volume and types of data available. At this time of the information society, data is one of the most important arguments for policy making, crisis management, research and education, and many other fields. An essential task for experts is to share high-quality data providing the right information at the right time. Designing of data presentation can largely influence the user perception and the cognitive aspects of data interpretation. Significant amounts of data can be visualised in some way. One image can thus replace a considerable number of numeric tables and texts. The paper focuses on the accurate visualisation of data from the point of view of used colour schemes. Bad choose of colours can easily confuse the user and lead to the data misinterpretation. On the contrary, correctly created visualisations can make information transfer much simpler and more efficient.

  15. Boson expansion theory in the seniority scheme

    DOE Office of Scientific and Technical Information (OSTI.GOV)

    Tamura, T.; Li, C.; Pedrocchi, V.G.

    1985-12-01

    A boson expansion formalism in the seniority scheme is presented and its relation with number-conserving quasiparticle calculations is elucidated. Accuracy and convergence are demonstrated numerically. A comparative discussion with other related approaches is given.

  16. Efficient C1-continuous phase-potential upwind (C1-PPU) schemes for coupled multiphase flow and transport with gravity

    NASA Astrophysics Data System (ADS)

    Jiang, Jiamin; Younis, Rami M.

    2017-10-01

    In the presence of counter-current flow, nonlinear convergence problems may arise in implicit time-stepping when the popular phase-potential upwinding (PPU) scheme is used. The PPU numerical flux is non-differentiable across the co-current/counter-current flow regimes. This may lead to cycles or divergence in the Newton iterations. Recently proposed methods address improved smoothness of the numerical flux. The objective of this work is to devise and analyze an alternative numerical flux scheme called C1-PPU that, in addition to improving smoothness with respect to saturations and phase potentials, also improves the level of scalar nonlinearity and accuracy. C1-PPU involves a novel use of the flux limiter concept from the context of high-resolution methods, and allows a smooth variation between the co-current/counter-current flow regimes. The scheme is general and applies to fully coupled flow and transport formulations with an arbitrary number of phases. We analyze the consistency property of the C1-PPU scheme, and derive saturation and pressure estimates, which are used to prove the solution existence. Several numerical examples for two- and three-phase flows in heterogeneous and multi-dimensional reservoirs are presented. The proposed scheme is compared to the conventional PPU and the recently proposed Hybrid Upwinding schemes. We investigate three properties of these numerical fluxes: smoothness, nonlinearity, and accuracy. The results indicate that in addition to smoothness, nonlinearity may also be critical for convergence behavior and thus needs to be considered in the design of an efficient numerical flux scheme. Moreover, the numerical examples show that the C1-PPU scheme exhibits superior convergence properties for large time steps compared to the other alternatives.

  17. A Novel WA-BPM Based on the Generalized Multistep Scheme in the Propagation Direction in the Waveguide

    NASA Astrophysics Data System (ADS)

    Ji, Yang; Chen, Hong; Tang, Hongwu

    2017-06-01

    A highly accurate wide-angle scheme, based on the generalized mutistep scheme in the propagation direction, is developed for the finite difference beam propagation method (FD-BPM). Comparing with the previously presented method, the simulation shows that our method results in a more accurate solution, and the step size can be much larger

  18. Second- and third-order upwind difference schemes for hyperbolic conservation laws

    NASA Technical Reports Server (NTRS)

    Yang, J. Y.

    1984-01-01

    Second- and third-order two time-level five-point explicit upwind-difference schemes are described for the numerical solution of hyperbolic systems of conservation laws and applied to the Euler equations of inviscid gas dynamics. Nonliner smoothing techniques are used to make the schemes total variation diminishing. In the method both hyperbolicity and conservation properties of the hyperbolic conservation laws are combined in a very natural way by introducing a normalized Jacobian matrix of the hyperbolic system. Entropy satisfying shock transition operators which are consistent with the upwind differencing are locally introduced when transonic shock transition is detected. Schemes thus constructed are suitable for shockcapturing calculations. The stability and the global order of accuracy of the proposed schemes are examined. Numerical experiments for the inviscid Burgers equation and the compressible Euler equations in one and two space dimensions involving various situations of aerodynamic interest are included and compared.

  19. Contribution of the Recent AUSM Schemes to the Overflow Code: Implementation and Validation

    NASA Technical Reports Server (NTRS)

    Liou, Meng-Sing; Buning, Pieter G.

    2000-01-01

    We shall present results of a recent collaborative effort between the authors attempting to implement the numerical flux scheme, AUSM+ and its new developments, into a widely used NASA code, OVERFLOW. This paper is intended to give a thorough and systematic documentation about the solutions of default test cases using the AUSNI+ scheme. Hence we will address various aspects of numerical solutions, such as accuracy, convergence rate, and effects of turbulence models, over a variety of geometries, speed regimes. We will briefly describe the numerical schemes employed in the calculations, including the capability of solving for low-speed flows and multiphase flows by employing the concept of numerical speed of sound. As a bonus, this low Mach number formulations also enhances convergence to steady solutions for flows even at transonic speed. Calculations for complex 3D turbulent flows were performed with several turbulence models and the results display excellent agreements with measured data.

  20. Encryption of QR code and grayscale image in interference-based scheme with high quality retrieval and silhouette problem removal

    NASA Astrophysics Data System (ADS)

    Qin, Yi; Wang, Hongjuan; Wang, Zhipeng; Gong, Qiong; Wang, Danchen

    2016-09-01

    In optical interference-based encryption (IBE) scheme, the currently available methods have to employ the iterative algorithms in order to encrypt two images and retrieve cross-talk free decrypted images. In this paper, we shall show that this goal can be achieved via an analytical process if one of the two images is QR code. For decryption, the QR code is decrypted in the conventional architecture and the decryption has a noisy appearance. Nevertheless, the robustness of QR code against noise enables the accurate acquisition of its content from the noisy retrieval, as a result of which the primary QR code can be exactly regenerated. Thereafter, a novel optical architecture is proposed to recover the grayscale image by aid of the QR code. In addition, the proposal has totally eliminated the silhouette problem existing in the previous IBE schemes, and its effectiveness and feasibility have been demonstrated by numerical simulations.

  1. Advances in numerical and applied mathematics

    NASA Technical Reports Server (NTRS)

    South, J. C., Jr. (Editor); Hussaini, M. Y. (Editor)

    1986-01-01

    This collection of papers covers some recent developments in numerical analysis and computational fluid dynamics. Some of these studies are of a fundamental nature. They address basic issues such as intermediate boundary conditions for approximate factorization schemes, existence and uniqueness of steady states for time dependent problems, and pitfalls of implicit time stepping. The other studies deal with modern numerical methods such as total variation diminishing schemes, higher order variants of vortex and particle methods, spectral multidomain techniques, and front tracking techniques. There is also a paper on adaptive grids. The fluid dynamics papers treat the classical problems of imcompressible flows in helically coiled pipes, vortex breakdown, and transonic flows.

  2. Comparison of Several Dissipation Algorithms for Central Difference Schemes

    NASA Technical Reports Server (NTRS)

    Swanson, R. C.; Radespiel, R.; Turkel, E.

    1997-01-01

    Several algorithms for introducing artificial dissipation into a central difference approximation to the Euler and Navier Stokes equations are considered. The focus of the paper is on the convective upwind and split pressure (CUSP) scheme, which is designed to support single interior point discrete shock waves. This scheme is analyzed and compared in detail with scalar and matrix dissipation (MATD) schemes. Resolution capability is determined by solving subsonic, transonic, and hypersonic flow problems. A finite-volume discretization and a multistage time-stepping scheme with multigrid are used to compute solutions to the flow equations. Numerical results are also compared with either theoretical solutions or experimental data. For transonic airfoil flows the best accuracy on coarse meshes for aerodynamic coefficients is obtained with a simple MATD scheme.

  3. Fast auto-focus scheme based on optical defocus fitting model

    NASA Astrophysics Data System (ADS)

    Wang, Yeru; Feng, Huajun; Xu, Zhihai; Li, Qi; Chen, Yueting; Cen, Min

    2018-04-01

    An optical defocus fitting model-based (ODFM) auto-focus scheme is proposed. Considering the basic optical defocus principle, the optical defocus fitting model is derived to approximate the potential-focus position. By this accurate modelling, the proposed auto-focus scheme can make the stepping motor approach the focal plane more accurately and rapidly. Two fitting positions are first determined for an arbitrary initial stepping motor position. Three images (initial image and two fitting images) at these positions are then collected to estimate the potential-focus position based on the proposed ODFM method. Around the estimated potential-focus position, two reference images are recorded. The auto-focus procedure is then completed by processing these two reference images and the potential-focus image to confirm the in-focus position using a contrast based method. Experimental results prove that the proposed scheme can complete auto-focus within only 5 to 7 steps with good performance even under low-light condition.

  4. A new scheme for velocity analysis and imaging of diffractions

    NASA Astrophysics Data System (ADS)

    Lin, Peng; Peng, Suping; Zhao, Jingtao; Cui, Xiaoqin; Du, Wenfeng

    2018-06-01

    Seismic diffractions are the responses of small-scale inhomogeneities or discontinuous geological features, which play a vital role in the exploitation and development of oil and gas reservoirs. However, diffractions are generally ignored and considered as interference noise in conventional data processing. In this paper, a new scheme for velocity analysis and imaging of seismic diffractions is proposed. Two steps compose of this scheme in our application. First, the plane-wave destruction method is used to separate diffractions from specular reflections in the prestack domain. Second, in order to accurately estimate migration velocity of the diffractions, the time-domain dip-angle gathers are derived from a Kirchhoff-based angle prestack time migration using separated diffractions. Diffraction events appear flat in the dip-angle gathers when imaged above the diffraction point with selected accurate migration velocity for diffractions. The selected migration velocity helps to produce the desired prestack imaging of diffractions. Synthetic and field examples are applied to test the validity of the new scheme. The diffraction imaging results indicate that the proposed scheme for velocity analysis and imaging of diffractions can provide more detailed information about small-scale geologic features for seismic interpretation.

  5. Numerical solution of non-linear dual-phase-lag bioheat transfer equation within skin tissues.

    PubMed

    Kumar, Dinesh; Kumar, P; Rai, K N

    2017-11-01

    This paper deals with numerical modeling and simulation of heat transfer in skin tissues using non-linear dual-phase-lag (DPL) bioheat transfer model under periodic heat flux boundary condition. The blood perfusion is assumed temperature-dependent which results in non-linear DPL bioheat transfer model in order to predict more accurate results. A numerical method of line which is based on finite difference and Runge-Kutta (4,5) schemes, is used to solve the present non-linear problem. Under specific case, the exact solution has been obtained and compared with the present numerical scheme, and we found that those are in good agreement. A comparison based on model selection criterion (AIC) has been made among non-linear DPL models when the variation of blood perfusion rate with temperature is of constant, linear and exponential type with the experimental data and it has been found that non-linear DPL model with exponential variation of blood perfusion rate is closest to the experimental data. In addition, it is found that due to absence of phase-lag phenomena in Pennes bioheat transfer model, it achieves steady state more quickly and always predict higher temperature than thermal and DPL non-linear models. The effect of coefficient of blood perfusion rate, dimensionless heating frequency and Kirchoff number on dimensionless temperature distribution has also been analyzed. The whole analysis is presented in dimensionless form. Copyright © 2017 Elsevier Inc. All rights reserved.

  6. The Linear Bicharacteristic Scheme for Computational Electromagnetics

    NASA Technical Reports Server (NTRS)

    Beggs, John H.; Chan, Siew-Loong

    2000-01-01

    The upwind leapfrog or Linear Bicharacteristic Scheme (LBS) has previously been implemented and demonstrated on electromagnetic wave propagation problems. This paper extends the Linear Bicharacteristic Scheme for computational electromagnetics to treat lossy dielectric and magnetic materials and perfect electrical conductors. This is accomplished by proper implementation of the LBS for homogeneous lossy dielectric and magnetic media, and treatment of perfect electrical conductors (PECs) are shown to follow directly in the limit of high conductivity. Heterogeneous media are treated through implementation of surface boundary conditions and no special extrapolations or interpolations at dielectric material boundaries are required. Results are presented for one-dimensional model problems on both uniform and nonuniform grids, and the FDTD algorithm is chosen as a convenient reference algorithm for comparison. The results demonstrate that the explicit LBS is a dissipation-free, second-order accurate algorithm which uses a smaller stencil than the FDTD algorithm, yet it has approximately one-third the phase velocity error. The LBS is also more accurate on nonuniform grids.

  7. Assessment of a high-resolution central scheme for the solution of the relativistic hydrodynamics equations

    NASA Astrophysics Data System (ADS)

    Lucas-Serrano, A.; Font, J. A.; Ibáñez, J. M.; Martí, J. M.

    2004-12-01

    We assess the suitability of a recent high-resolution central scheme developed by \\cite{kurganov} for the solution of the relativistic hydrodynamic equations. The novelty of this approach relies on the absence of Riemann solvers in the solution procedure. The computations we present are performed in one and two spatial dimensions in Minkowski spacetime. Standard numerical experiments such as shock tubes and the relativistic flat-faced step test are performed. As an astrophysical application the article includes two-dimensional simulations of the propagation of relativistic jets using both Cartesian and cylindrical coordinates. The simulations reported clearly show the capabilities of the numerical scheme of yielding satisfactory results, with an accuracy comparable to that obtained by the so-called high-resolution shock-capturing schemes based upon Riemann solvers (Godunov-type schemes), even well inside the ultrarelativistic regime. Such a central scheme can be straightforwardly applied to hyperbolic systems of conservation laws for which the characteristic structure is not explicitly known, or in cases where a numerical computation of the exact solution of the Riemann problem is prohibitively expensive. Finally, we present comparisons with results obtained using various Godunov-type schemes as well as with those obtained using other high-resolution central schemes which have recently been reported in the literature.

  8. On epicardial potential reconstruction using regularization schemes with the L1-norm data term.

    PubMed

    Shou, Guofa; Xia, Ling; Liu, Feng; Jiang, Mingfeng; Crozier, Stuart

    2011-01-07

    The electrocardiographic (ECG) inverse problem is ill-posed and usually solved by regularization schemes. These regularization methods, such as the Tikhonov method, are often based on the L2-norm data and constraint terms. However, L2-norm-based methods inherently provide smoothed inverse solutions that are sensitive to measurement errors, and also lack the capability of localizing and distinguishing multiple proximal cardiac electrical sources. This paper presents alternative regularization schemes employing the L1-norm data term for the reconstruction of epicardial potentials (EPs) from measured body surface potentials (BSPs). During numerical implementation, the iteratively reweighted norm algorithm was applied to solve the L1-norm-related schemes, and measurement noises were considered in the BSP data. The proposed L1-norm data term-based regularization schemes (with L1 and L2 penalty terms of the normal derivative constraint (labelled as L1TV and L1L2)) were compared with the L2-norm data terms (Tikhonov with zero-order and normal derivative constraints, labelled as ZOT and FOT, and the total variation method labelled as L2TV). The studies demonstrated that, with averaged measurement noise, the inverse solutions provided by the L1L2 and FOT algorithms have less relative error values. However, when larger noise occurred in some electrodes (for example, signal lost during measurement), the L1TV and L1L2 methods can obtain more accurate EPs in a robust manner. Therefore the L1-norm data term-based solutions are generally less perturbed by measurement noises, suggesting that the new regularization scheme is promising for providing practical ECG inverse solutions.

  9. Computational electrodynamics in material media with constraint-preservation, multidimensional Riemann solvers and sub-cell resolution - Part II, higher order FVTD schemes

    NASA Astrophysics Data System (ADS)

    Balsara, Dinshaw S.; Garain, Sudip; Taflove, Allen; Montecinos, Gino

    2018-02-01

    schemes. The computer algebra system scripts for generating ADER time update schemes for any general PDE with stiff source terms are also given in the electronic supplements to this paper. Second, third and fourth order accurate schemes for numerically solving Maxwell's equations in material media are presented in this paper. Several stringent tests are also presented to show that the method works and meets its design goals even when material permittivity and permeability vary by an order of magnitude over just a few zones. Furthermore, since the method is unconditionally stable and sub-cell-resolving in the presence of stiff source terms (i.e. for problems involving giant variations in conductivity over just a few zones), it can accurately handle such problems without any reduction in timestep. We also show that increasing the order of accuracy offers distinct advantages for resolving sub-cell variations in material properties. Most importantly, we show that when the accuracy requirements are stringent the higher order schemes offer the shortest time to solution. This makes a compelling case for the use of higher order, sub-cell resolving schemes in CED.

  10. Progress with multigrid schemes for hypersonic flow problems

    NASA Technical Reports Server (NTRS)

    Radespiel, R.; Swanson, R. C.

    1991-01-01

    Several multigrid schemes are considered for the numerical computation of viscous hypersonic flows. For each scheme, the basic solution algorithm uses upwind spatial discretization with explicit multistage time stepping. Two level versions of the various multigrid algorithms are applied to the two dimensional advection equation, and Fourier analysis is used to determine their damping properties. The capabilities of the multigrid methods are assessed by solving three different hypersonic flow problems. Some new multigrid schemes based on semicoarsening strategies are shown to be quite effective in relieving the stiffness caused by the high aspect ratio cells required to resolve high Reynolds number flows. These schemes exhibit good convergence rates for Reynolds numbers up to 200 x 10(exp 6) and Mach numbers up to 25.

  11. Efficient Numerical Methods for Nonlinear-Facilitated Transport and Exchange in a Blood-Tissue Exchange Unit

    PubMed Central

    Poulain, Christophe A.; Finlayson, Bruce A.; Bassingthwaighte, James B.

    2010-01-01

    The analysis of experimental data obtained by the multiple-indicator method requires complex mathematical models for which capillary blood-tissue exchange (BTEX) units are the building blocks. This study presents a new, nonlinear, two-region, axially distributed, single capillary, BTEX model. A facilitated transporter model is used to describe mass transfer between plasma and intracellular spaces. To provide fast and accurate solutions, numerical techniques suited to nonlinear convection-dominated problems are implemented. These techniques are the random choice method, an explicit Euler-Lagrange scheme, and the MacCormack method with and without flux correction. The accuracy of the numerical techniques is demonstrated, and their efficiencies are compared. The random choice, Euler-Lagrange and plain MacCormack method are the best numerical techniques for BTEX modeling. However, the random choice and Euler-Lagrange methods are preferred over the MacCormack method because they allow for the derivation of a heuristic criterion that makes the numerical methods stable without degrading their efficiency. Numerical solutions are also used to illustrate some nonlinear behaviors of the model and to show how the new BTEX model can be used to estimate parameters from experimental data. PMID:9146808

  12. Numerical solution of modified differential equations based on symmetry preservation.

    PubMed

    Ozbenli, Ersin; Vedula, Prakash

    2017-12-01

    In this paper, we propose a method to construct invariant finite-difference schemes for solution of partial differential equations (PDEs) via consideration of modified forms of the underlying PDEs. The invariant schemes, which preserve Lie symmetries, are obtained based on the method of equivariant moving frames. While it is often difficult to construct invariant numerical schemes for PDEs due to complicated symmetry groups associated with cumbersome discrete variable transformations, we note that symmetries associated with more convenient transformations can often be obtained by appropriately modifying the original PDEs. In some cases, modifications to the original PDEs are also found to be useful in order to avoid trivial solutions that might arise from particular selections of moving frames. In our proposed method, modified forms of PDEs can be obtained either by addition of perturbation terms to the original PDEs or through defect correction procedures. These additional terms, whose primary purpose is to enable symmetries with more convenient transformations, are then removed from the system by considering moving frames for which these specific terms go to zero. Further, we explore selection of appropriate moving frames that result in improvement in accuracy of invariant numerical schemes based on modified PDEs. The proposed method is tested using the linear advection equation (in one- and two-dimensions) and the inviscid Burgers' equation. Results obtained for these tests cases indicate that numerical schemes derived from the proposed method perform significantly better than existing schemes not only by virtue of improvement in numerical accuracy but also due to preservation of qualitative properties or symmetries of the underlying differential equations.

  13. An efficient and stable hybrid extended Lagrangian/self-consistent field scheme for solving classical mutual induction

    DOE Office of Scientific and Technical Information (OSTI.GOV)

    Albaugh, Alex; Demerdash, Omar; Head-Gordon, Teresa, E-mail: thg@berkeley.edu

    2015-11-07

    We have adapted a hybrid extended Lagrangian self-consistent field (EL/SCF) approach, developed for time reversible Born Oppenheimer molecular dynamics for quantum electronic degrees of freedom, to the problem of classical polarization. In this context, the initial guess for the mutual induction calculation is treated by auxiliary induced dipole variables evolved via a time-reversible velocity Verlet scheme. However, we find numerical instability, which is manifested as an accumulation in the auxiliary velocity variables, that in turn results in an unacceptable increase in the number of SCF cycles to meet even loose convergence tolerances for the real induced dipoles over the coursemore » of a 1 ns trajectory of the AMOEBA14 water model. By diagnosing the numerical instability as a problem of resonances that corrupt the dynamics, we introduce a simple thermostating scheme, illustrated using Berendsen weak coupling and Nose-Hoover chain thermostats, applied to the auxiliary dipole velocities. We find that the inertial EL/SCF (iEL/SCF) method provides superior energy conservation with less stringent convergence thresholds and a correspondingly small number of SCF cycles, to reproduce all properties of the polarization model in the NVT and NVE ensembles accurately. Our iEL/SCF approach is a clear improvement over standard SCF approaches to classical mutual induction calculations and would be worth investigating for application to ab initio molecular dynamics as well.« less

  14. Linearly first- and second-order, unconditionally energy stable schemes for the phase field crystal model

    DOE Office of Scientific and Technical Information (OSTI.GOV)

    Yang, Xiaofeng, E-mail: xfyang@math.sc.edu; Han, Daozhi, E-mail: djhan@iu.edu

    2017-02-01

    In this paper, we develop a series of linear, unconditionally energy stable numerical schemes for solving the classical phase field crystal model. The temporal discretizations are based on the first order Euler method, the second order backward differentiation formulas (BDF2) and the second order Crank–Nicolson method, respectively. The schemes lead to linear elliptic equations to be solved at each time step, and the induced linear systems are symmetric positive definite. We prove that all three schemes are unconditionally energy stable rigorously. Various classical numerical experiments in 2D and 3D are performed to validate the accuracy and efficiency of the proposedmore » schemes.« less

  15. Tensor numerical methods in quantum chemistry: from Hartree-Fock to excitation energies.

    PubMed

    Khoromskaia, Venera; Khoromskij, Boris N

    2015-12-21

    We resume the recent successes of the grid-based tensor numerical methods and discuss their prospects in real-space electronic structure calculations. These methods, based on the low-rank representation of the multidimensional functions and integral operators, first appeared as an accurate tensor calculus for the 3D Hartree potential using 1D complexity operations, and have evolved to entirely grid-based tensor-structured 3D Hartree-Fock eigenvalue solver. It benefits from tensor calculation of the core Hamiltonian and two-electron integrals (TEI) in O(n log n) complexity using the rank-structured approximation of basis functions, electron densities and convolution integral operators all represented on 3D n × n × n Cartesian grids. The algorithm for calculating TEI tensor in a form of the Cholesky decomposition is based on multiple factorizations using algebraic 1D "density fitting" scheme, which yield an almost irreducible number of product basis functions involved in the 3D convolution integrals, depending on a threshold ε > 0. The basis functions are not restricted to separable Gaussians, since the analytical integration is substituted by high-precision tensor-structured numerical quadratures. The tensor approaches to post-Hartree-Fock calculations for the MP2 energy correction and for the Bethe-Salpeter excitation energies, based on using low-rank factorizations and the reduced basis method, were recently introduced. Another direction is towards the tensor-based Hartree-Fock numerical scheme for finite lattices, where one of the numerical challenges is the summation of electrostatic potentials of a large number of nuclei. The 3D grid-based tensor method for calculation of a potential sum on a L × L × L lattice manifests the linear in L computational work, O(L), instead of the usual O(L(3) log L) scaling by the Ewald-type approaches.

  16. Numerical Simulation of Two Phase Flows

    NASA Technical Reports Server (NTRS)

    Liou, Meng-Sing

    2001-01-01

    Two phase flows can be found in broad situations in nature, biology, and industry devices and can involve diverse and complex mechanisms. While the physical models may be specific for certain situations, the mathematical formulation and numerical treatment for solving the governing equations can be general. Hence, we will require information concerning each individual phase as needed in a single phase. but also the interactions between them. These interaction terms, however, pose additional numerical challenges because they are beyond the basis that we use to construct modern numerical schemes, namely the hyperbolicity of equations. Moreover, due to disparate differences in time scales, fluid compressibility and nonlinearity become acute, further complicating the numerical procedures. In this paper, we will show the ideas and procedure how the AUSM-family schemes are extended for solving two phase flows problems. Specifically, both phases are assumed in thermodynamic equilibrium, namely, the time scales involved in phase interactions are extremely short in comparison with those in fluid speeds and pressure fluctuations. Details of the numerical formulation and issues involved are discussed and the effectiveness of the method are demonstrated for several industrial examples.

  17. Asynchronous discrete event schemes for PDEs

    NASA Astrophysics Data System (ADS)

    Stone, D.; Geiger, S.; Lord, G. J.

    2017-08-01

    A new class of asynchronous discrete-event simulation schemes for advection-diffusion-reaction equations is introduced, based on the principle of allowing quanta of mass to pass through faces of a (regular, structured) Cartesian finite volume grid. The timescales of these events are linked to the flux on the face. The resulting schemes are self-adaptive, and local in both time and space. Experiments are performed on realistic physical systems related to porous media flow applications, including a large 3D advection diffusion equation and advection diffusion reaction systems. The results are compared to highly accurate reference solutions where the temporal evolution is computed with exponential integrator schemes using the same finite volume discretisation. This allows a reliable estimation of the solution error. Our results indicate a first order convergence of the error as a control parameter is decreased, and we outline a framework for analysis.

  18. High-Order Central WENO Schemes for Multi-Dimensional Hamilton-Jacobi Equations

    NASA Technical Reports Server (NTRS)

    Bryson, Steve; Levy, Doron; Biegel, Bryan (Technical Monitor)

    2002-01-01

    We present new third- and fifth-order Godunov-type central schemes for approximating solutions of the Hamilton-Jacobi (HJ) equation in an arbitrary number of space dimensions. These are the first central schemes for approximating solutions of the HJ equations with an order of accuracy that is greater than two. In two space dimensions we present two versions for the third-order scheme: one scheme that is based on a genuinely two-dimensional Central WENO reconstruction, and another scheme that is based on a simpler dimension-by-dimension reconstruction. The simpler dimension-by-dimension variant is then extended to a multi-dimensional fifth-order scheme. Our numerical examples in one, two and three space dimensions verify the expected order of accuracy of the schemes.

  19. Numerical Analysis of the Dynamics of Nonlinear Solids and Structures

    DTIC Science & Technology

    2008-08-01

    to arrive to a new numerical scheme that exhibits rigorously the dissipative character of the so-called canonical free en - ergy characteristic of...UCLA), February 14 2006. 5. "Numerical Integration of the Nonlinear Dynamics of Elastoplastic Solids," keynote lecture , 3rd European Conference on...Computational Mechanics (ECCM 3), Lisbon, Portugal, June 5-9 2006. 6. "Energy-Momentum Schemes for Finite Strain Plasticity," keynote lecture , 7th

  20. Projection scheme for a reflected stochastic heat equation with additive noise

    NASA Astrophysics Data System (ADS)

    Higa, Arturo Kohatsu; Pettersson, Roger

    2005-02-01

    We consider a projection scheme as a numerical solution of a reflected stochastic heat equation driven by a space-time white noise. Convergence is obtained via a discrete contraction principle and known convergence results for numerical solutions of parabolic variational inequalities.

  1. Equivalence between the Energy Stable Flux Reconstruction and Filtered Discontinuous Galerkin Schemes

    NASA Astrophysics Data System (ADS)

    Zwanenburg, Philip; Nadarajah, Siva

    2016-02-01

    The aim of this paper is to demonstrate the equivalence between filtered Discontinuous Galerkin (DG) schemes and the Energy Stable Flux Reconstruction (ESFR) schemes, expanding on previous demonstrations in 1D [1] and for straight-sided elements in 3D [2]. We first derive the DG and ESFR schemes in strong form and compare the respective flux penalization terms while highlighting the implications of the fundamental assumptions for stability in the ESFR formulations, notably that all ESFR scheme correction fields can be interpreted as modally filtered DG correction fields. We present the result in the general context of all higher dimensional curvilinear element formulations. Through a demonstration that there exists a weak form of the ESFR schemes which is both discretely and analytically equivalent to the strong form, we then extend the results obtained for the strong formulations to demonstrate that ESFR schemes can be interpreted as a DG scheme in weak form where discontinuous edge flux is substituted for numerical edge flux correction. Theoretical derivations are then verified with numerical results obtained from a 2D Euler testcase with curved boundaries. Given the current choice of high-order DG-type schemes and the question as to which might be best to use for a specific application, the main significance of this work is the bridge that it provides between them. Clearly outlining the similarities between the schemes results in the important conclusion that it is always less efficient to use ESFR schemes, as opposed to the weak DG scheme, when solving problems implicitly.

  2. Forcing scheme analysis for the axisymmetric lattice Boltzmann method under incompressible limit.

    PubMed

    Zhang, Liangqi; Yang, Shiliang; Zeng, Zhong; Chen, Jie; Yin, Linmao; Chew, Jia Wei

    2017-04-01

    Because the standard lattice Boltzmann (LB) method is proposed for Cartesian Navier-Stokes (NS) equations, additional source terms are necessary in the axisymmetric LB method for representing the axisymmetric effects. Therefore, the accuracy and applicability of the axisymmetric LB models depend on the forcing schemes adopted for discretization of the source terms. In this study, three forcing schemes, namely, the trapezium rule based scheme, the direct forcing scheme, and the semi-implicit centered scheme, are analyzed theoretically by investigating their derived macroscopic equations in the diffusive scale. Particularly, the finite difference interpretation of the standard LB method is extended to the LB equations with source terms, and then the accuracy of different forcing schemes is evaluated for the axisymmetric LB method. Theoretical analysis indicates that the discrete lattice effects arising from the direct forcing scheme are part of the truncation error terms and thus would not affect the overall accuracy of the standard LB method with general force term (i.e., only the source terms in the momentum equation are considered), but lead to incorrect macroscopic equations for the axisymmetric LB models. On the other hand, the trapezium rule based scheme and the semi-implicit centered scheme both have the advantage of avoiding the discrete lattice effects and recovering the correct macroscopic equations. Numerical tests applied for validating the theoretical analysis show that both the numerical stability and the accuracy of the axisymmetric LB simulations are affected by the direct forcing scheme, which indicate that forcing schemes free of the discrete lattice effects are necessary for the axisymmetric LB method.

  3. a Numerical Model for Flue Gas Desulfurization System.

    NASA Astrophysics Data System (ADS)

    Kim, Sung Joon

    The purpose of this work is to develop a reliable numerical model for spray dryer desulfurization systems. The shape of the spray dryer requires that a body fitted orthogonal coordinate system be used for the numerical model. The governing equations are developed in the general orthogonal coordinates and discretized to yield a system of algebraic equations. A turbulence model is also included in the numerical program. A new second order numerical scheme is developed and included in the numerical model. The trajectory approach is used to simulate the flow of the dispersed phase. Two-way coupling phenomena is modeled by this scheme. The absorption of sulfur dioxide into lime slurry droplets is simulated by a model based on gas -phase mass transfer. The program is applied to a typical spray dryer desulfurization system. The results show the capability of the program to predict the sensitivity of system performance to changes in operational parameters.

  4. Toward the Reliability of Fault Representation Methods in Finite Difference Schemes for Simulation of Shear Rupture Propagation

    NASA Astrophysics Data System (ADS)

    Dalguer, L. A.; Day, S. M.

    2006-12-01

    Accuracy in finite difference (FD) solutions to spontaneous rupture problems is controlled principally by the scheme used to represent the fault discontinuity, and not by the grid geometry used to represent the continuum. We have numerically tested three fault representation methods, the Thick Fault (TF) proposed by Madariaga et al (1998), the Stress Glut (SG) described by Andrews (1999), and the Staggered-Grid Split-Node (SGSN) methods proposed by Dalguer and Day (2006), each implemented in a the fourth-order velocity-stress staggered-grid (VSSG) FD scheme. The TF and the SG methods approximate the discontinuity through inelastic increments to stress components ("inelastic-zone" schemes) at a set of stress grid points taken to lie on the fault plane. With this type of scheme, the fault surface is indistinguishable from an inelastic zone with a thickness given by a spatial step dx for the SG, and 2dx for the TF model. The SGSN method uses the traction-at-split-node (TSN) approach adapted to the VSSG FD. This method represents the fault discontinuity by explicitly incorporating discontinuity terms at velocity nodes in the grid, with interactions between the "split nodes" occurring exclusively through the tractions (frictional resistance) acting between them. These tractions in turn are controlled by the jump conditions and a friction law. Our 3D tests problem solutions show that the inelastic-zone TF and SG methods show much poorer performance than does the SGSN formulation. The SG inelastic-zone method achieved solutions that are qualitatively meaningful and quantitatively reliable to within a few percent. The TF inelastic-zone method did not achieve qualitatively agreement with the reference solutions to the 3D test problem, and proved to be sufficiently computationally inefficient that it was not feasible to explore convergence quantitatively. The SGSN method gives very accurate solutions, and is also very efficient. Reliable solution of the rupture time is

  5. LCC-Demons: a robust and accurate symmetric diffeomorphic registration algorithm.

    PubMed

    Lorenzi, M; Ayache, N; Frisoni, G B; Pennec, X

    2013-11-01

    Non-linear registration is a key instrument for computational anatomy to study the morphology of organs and tissues. However, in order to be an effective instrument for the clinical practice, registration algorithms must be computationally efficient, accurate and most importantly robust to the multiple biases affecting medical images. In this work we propose a fast and robust registration framework based on the log-Demons diffeomorphic registration algorithm. The transformation is parameterized by stationary velocity fields (SVFs), and the similarity metric implements a symmetric local correlation coefficient (LCC). Moreover, we show how the SVF setting provides a stable and consistent numerical scheme for the computation of the Jacobian determinant and the flux of the deformation across the boundaries of a given region. Thus, it provides a robust evaluation of spatial changes. We tested the LCC-Demons in the inter-subject registration setting, by comparing with state-of-the-art registration algorithms on public available datasets, and in the intra-subject longitudinal registration problem, for the statistically powered measurements of the longitudinal atrophy in Alzheimer's disease. Experimental results show that LCC-Demons is a generic, flexible, efficient and robust algorithm for the accurate non-linear registration of images, which can find several applications in the field of medical imaging. Without any additional optimization, it solves equally well intra & inter-subject registration problems, and compares favorably to state-of-the-art methods. Copyright © 2013 Elsevier Inc. All rights reserved.

  6. Fourth order Douglas implicit scheme for solving three dimension reaction diffusion equation with non-linear source term

    NASA Astrophysics Data System (ADS)

    Hasnain, Shahid; Saqib, Muhammad; Mashat, Daoud Suleiman

    2017-07-01

    This research paper represents a numerical approximation to non-linear three dimension reaction diffusion equation with non-linear source term from population genetics. Since various initial and boundary value problems exist in three dimension reaction diffusion phenomena, which are studied numerically by different numerical methods, here we use finite difference schemes (Alternating Direction Implicit and Fourth Order Douglas Implicit) to approximate the solution. Accuracy is studied in term of L2, L∞ and relative error norms by random selected grids along time levels for comparison with analytical results. The test example demonstrates the accuracy, efficiency and versatility of the proposed schemes. Numerical results showed that Fourth Order Douglas Implicit scheme is very efficient and reliable for solving 3-D non-linear reaction diffusion equation.

  7. An optimal implicit staggered-grid finite-difference scheme based on the modified Taylor-series expansion with minimax approximation method for elastic modeling

    NASA Astrophysics Data System (ADS)

    Yang, Lei; Yan, Hongyong; Liu, Hong

    2017-03-01

    Implicit staggered-grid finite-difference (ISFD) scheme is competitive for its great accuracy and stability, whereas its coefficients are conventionally determined by the Taylor-series expansion (TE) method, leading to a loss in numerical precision. In this paper, we modify the TE method using the minimax approximation (MA), and propose a new optimal ISFD scheme based on the modified TE (MTE) with MA method. The new ISFD scheme takes the advantage of the TE method that guarantees great accuracy at small wavenumbers, and keeps the property of the MA method that keeps the numerical errors within a limited bound at the same time. Thus, it leads to great accuracy for numerical solution of the wave equations. We derive the optimal ISFD coefficients by applying the new method to the construction of the objective function, and using a Remez algorithm to minimize its maximum. Numerical analysis is made in comparison with the conventional TE-based ISFD scheme, indicating that the MTE-based ISFD scheme with appropriate parameters can widen the wavenumber range with high accuracy, and achieve greater precision than the conventional ISFD scheme. The numerical modeling results also demonstrate that the MTE-based ISFD scheme performs well in elastic wave simulation, and is more efficient than the conventional ISFD scheme for elastic modeling.

  8. A rotationally biased upwind difference scheme for the Euler equations

    NASA Technical Reports Server (NTRS)

    Davis, S. F.

    1983-01-01

    The upwind difference schemes of Godunov, Osher, Roe and van Leer are able to resolve one dimensional steady shocks for the Euler equations within one or two mesh intervals. Unfortunately, this resolution is lost in two dimensions when the shock crosses the computing grid at an oblique angle. To correct this problem, a numerical scheme was developed which automatically locates the angle at which a shock might be expected to cross the computing grid and then constructs separate finite difference formulas for the flux components normal and tangential to this direction. Numerical results which illustrate the ability of this method to resolve steady oblique shocks are presented.

  9. Alternating Direction Implicit (ADI) schemes for a PDE-based image osmosis model

    NASA Astrophysics Data System (ADS)

    Calatroni, L.; Estatico, C.; Garibaldi, N.; Parisotto, S.

    2017-10-01

    We consider Alternating Direction Implicit (ADI) splitting schemes to compute efficiently the numerical solution of the PDE osmosis model considered by Weickert et al. in [10] for several imaging applications. The discretised scheme is shown to preserve analogous properties to the continuous model. The dimensional splitting strategy traduces numerically into the solution of simple tridiagonal systems for which standard matrix factorisation techniques can be used to improve upon the performance of classical implicit methods, even for large time steps. Applications to the shadow removal problem are presented.

  10. High-order ENO schemes applied to two- and three-dimensional compressible flow

    NASA Technical Reports Server (NTRS)

    Shu, Chi-Wang; Erlebacher, Gordon; Zang, Thomas A.; Whitaker, David; Osher, Stanley

    1991-01-01

    High order essentially non-oscillatory (ENO) finite difference schemes are applied to the 2-D and 3-D compressible Euler and Navier-Stokes equations. Practical issues, such as vectorization, efficiency of coding, cost comparison with other numerical methods, and accuracy degeneracy effects, are discussed. Numerical examples are provided which are representative of computational problems of current interest in transition and turbulence physics. These require both nonoscillatory shock capturing and high resolution for detailed structures in the smooth regions and demonstrate the advantage of ENO schemes.

  11. Laplace-Fourier-domain dispersion analysis of an average derivative optimal scheme for scalar-wave equation

    NASA Astrophysics Data System (ADS)

    Chen, Jing-Bo

    2014-06-01

    By using low-frequency components of the damped wavefield, Laplace-Fourier-domain full waveform inversion (FWI) can recover a long-wavelength velocity model from the original undamped seismic data lacking low-frequency information. Laplace-Fourier-domain modelling is an important foundation of Laplace-Fourier-domain FWI. Based on the numerical phase velocity and the numerical attenuation propagation velocity, a method for performing Laplace-Fourier-domain numerical dispersion analysis is developed in this paper. This method is applied to an average-derivative optimal scheme. The results show that within the relative error of 1 per cent, the Laplace-Fourier-domain average-derivative optimal scheme requires seven gridpoints per smallest wavelength and smallest pseudo-wavelength for both equal and unequal directional sampling intervals. In contrast, the classical five-point scheme requires 23 gridpoints per smallest wavelength and smallest pseudo-wavelength to achieve the same accuracy. Numerical experiments demonstrate the theoretical analysis.

  12. A quantification method for numerical dissipation in quasi-DNS and under-resolved DNS, and effects of numerical dissipation in quasi-DNS and under-resolved DNS of turbulent channel flows

    NASA Astrophysics Data System (ADS)

    Komen, E. M. J.; Camilo, L. H.; Shams, A.; Geurts, B. J.; Koren, B.

    2017-09-01

    LES for industrial applications with complex geometries is mostly characterised by: a) a finite volume CFD method using a non-staggered arrangement of the flow variables and second order accurate spatial and temporal discretisation schemes, b) an implicit top-hat filter, where the filter length is equal to the local computational cell size, and c) eddy-viscosity type LES models. LES based on these three main characteristics is indicated as industrial LES in this paper. It becomes increasingly clear that the numerical dissipation in CFD codes typically used in industrial applications with complex geometries may inhibit the predictive capabilities of explicit LES. Therefore, there is a need to quantify the numerical dissipation rate in such CFD codes. In this paper, we quantify the numerical dissipation rate in physical space based on an analysis of the transport equation for the mean turbulent kinetic energy. Using this method, we quantify the numerical dissipation rate in a quasi-Direct Numerical Simulation (DNS) and in under-resolved DNS of, as a basic demonstration case, fully-developed turbulent channel flow. With quasi-DNS, we indicate a DNS performed using a second order accurate finite volume method typically used in industrial applications. Furthermore, we determine and explain the trends in the performance of industrial LES for fully-developed turbulent channel flow for four different Reynolds numbers for three different LES mesh resolutions. The presented explanation of the mechanisms behind the observed trends is based on an analysis of the turbulent kinetic energy budgets. The presented quantitative analyses demonstrate that the numerical errors in the industrial LES computations of the considered turbulent channel flows result in a net numerical dissipation rate which is larger than the subgrid-scale dissipation rate. No new computational methods are presented in this paper. Instead, the main new elements in this paper are our detailed quantification

  13. A Gas-Kinetic Scheme for Reactive Flows

    NASA Technical Reports Server (NTRS)

    Lian,Youg-Sheng; Xu, Kun

    1998-01-01

    In this paper, the gas-kinetic BGK scheme for the compressible flow equations is extended to chemical reactive flow. The mass fraction of the unburnt gas is implemented into the gas kinetic equation by assigning a new internal degree of freedom to the particle distribution function. The new variable can be also used to describe fluid trajectory for the nonreactive flows. Due to the gas-kinetic BGK model, the current scheme basically solves the Navier-Stokes chemical reactive flow equations. Numerical tests validate the accuracy and robustness of the current kinetic method.

  14. MIMO transmit scheme based on morphological perceptron with competitive learning.

    PubMed

    Valente, Raul Ambrozio; Abrão, Taufik

    2016-08-01

    This paper proposes a new multi-input multi-output (MIMO) transmit scheme aided by artificial neural network (ANN). The morphological perceptron with competitive learning (MP/CL) concept is deployed as a decision rule in the MIMO detection stage. The proposed MIMO transmission scheme is able to achieve double spectral efficiency; hence, in each time-slot the receiver decodes two symbols at a time instead one as Alamouti scheme. Other advantage of the proposed transmit scheme with MP/CL-aided detector is its polynomial complexity according to modulation order, while it becomes linear when the data stream length is greater than modulation order. The performance of the proposed scheme is compared to the traditional MIMO schemes, namely Alamouti scheme and maximum-likelihood MIMO (ML-MIMO) detector. Also, the proposed scheme is evaluated in a scenario with variable channel information along the frame. Numerical results have shown that the diversity gain under space-time coding Alamouti scheme is partially lost, which slightly reduces the bit-error rate (BER) performance of the proposed MP/CL-NN MIMO scheme. Copyright © 2016 Elsevier Ltd. All rights reserved.

  15. Parallelization of implicit finite difference schemes in computational fluid dynamics

    NASA Technical Reports Server (NTRS)

    Decker, Naomi H.; Naik, Vijay K.; Nicoules, Michel

    1990-01-01

    Implicit finite difference schemes are often the preferred numerical schemes in computational fluid dynamics, requiring less stringent stability bounds than the explicit schemes. Each iteration in an implicit scheme involves global data dependencies in the form of second and higher order recurrences. Efficient parallel implementations of such iterative methods are considerably more difficult and non-intuitive. The parallelization of the implicit schemes that are used for solving the Euler and the thin layer Navier-Stokes equations and that require inversions of large linear systems in the form of block tri-diagonal and/or block penta-diagonal matrices is discussed. Three-dimensional cases are emphasized and schemes that minimize the total execution time are presented. Partitioning and scheduling schemes for alleviating the effects of the global data dependencies are described. An analysis of the communication and the computation aspects of these methods is presented. The effect of the boundary conditions on the parallel schemes is also discussed.

  16. Semi-Numerical Studies of the Three-Meter Spherical Couette Experiment Utilizing Data Assimilation

    NASA Astrophysics Data System (ADS)

    Burnett, S. C.; Rojas, R.; Perevalov, A.; Lathrop, D. P.

    2017-12-01

    The model of the Earth's magnetic field has been investigated in recent years through experiments and numerical models. At the University of Maryland, experimental studies are implemented in a three-meter spherical Couette device filled with liquid sodium. The inner and outer spheres of this apparatus mimic the planet's inner core and core-mantle boundary, respectively. These experiments incorporate high velocity flows with Reynolds numbers 108. In spherical Couette geometry, the numerical scheme applied to this work features finite difference methods in the radial direction and pseudospectral spherical harmonic transforms elsewhere [Schaeffer, N. G3 (2013)]. Adding to the numerical model, data assimilation integrates the experimental outer-layer magnetic field measurements. This semi-numerical model can then be compared to the experimental results as well as forecasting magnetic field changes. Data assimilation makes it possible to get estimates of internal motions of the three-meter experiment that would otherwise be intrusive or impossible to obtain in experiments or too computationally expensive with a purely numerical code. If we can provide accurate models of the three-meter device, it is possible to attempt to model the geomagnetic field. We gratefully acknowledge the support of NSF Grant No. EAR1417148 & DGE1322106.

  17. Finite-volume application of high order ENO schemes to multi-dimensional boundary-value problems

    NASA Technical Reports Server (NTRS)

    Casper, Jay; Dorrepaal, J. Mark

    1990-01-01

    The finite volume approach in developing multi-dimensional, high-order accurate essentially non-oscillatory (ENO) schemes is considered. In particular, a two dimensional extension is proposed for the Euler equation of gas dynamics. This requires a spatial reconstruction operator that attains formal high order of accuracy in two dimensions by taking account of cross gradients. Given a set of cell averages in two spatial variables, polynomial interpolation of a two dimensional primitive function is employed in order to extract high-order pointwise values on cell interfaces. These points are appropriately chosen so that correspondingly high-order flux integrals are obtained through each interface by quadrature, at each point having calculated a flux contribution in an upwind fashion. The solution-in-the-small of Riemann's initial value problem (IVP) that is required for this pointwise flux computation is achieved using Roe's approximate Riemann solver. Issues to be considered in this two dimensional extension include the implementation of boundary conditions and application to general curvilinear coordinates. Results of numerical experiments are presented for qualitative and quantitative examination. These results contain the first successful application of ENO schemes to boundary value problems with solid walls.

  18. Effects of Mesh Irregularities on Accuracy of Finite-Volume Discretization Schemes

    NASA Technical Reports Server (NTRS)

    Diskin, Boris; Thomas, James L.

    2012-01-01

    The effects of mesh irregularities on accuracy of unstructured node-centered finite-volume discretizations are considered. The focus is on an edge-based approach that uses unweighted least-squares gradient reconstruction with a quadratic fit. For inviscid fluxes, the discretization is nominally third order accurate on general triangular meshes. For viscous fluxes, the scheme is an average-least-squares formulation that is nominally second order accurate and contrasted with a common Green-Gauss discretization scheme. Gradient errors, truncation errors, and discretization errors are separately studied according to a previously introduced comprehensive methodology. The methodology considers three classes of grids: isotropic grids in a rectangular geometry, anisotropic grids typical of adapted grids, and anisotropic grids over a curved surface typical of advancing layer grids. The meshes within the classes range from regular to extremely irregular including meshes with random perturbation of nodes. Recommendations are made concerning the discretization schemes that are expected to be least sensitive to mesh irregularities in applications to turbulent flows in complex geometries.

  19. Accurate numerical solution of the Helmholtz equation by iterative Lanczos reduction.

    PubMed

    Ratowsky, R P; Fleck, J A

    1991-06-01

    The Lanczos recursion algorithm is used to determine forward-propagating solutions for both the paraxial and Helmholtz wave equations for longitudinally invariant refractive indices. By eigenvalue analysis it is demonstrated that the method gives extremely accurate solutions to both equations.

  20. Accurate adiabatic singlet-triplet gaps in atoms and molecules employing the third-order spin-flip algebraic diagrammatic construction scheme for the polarization propagator

    DOE Office of Scientific and Technical Information (OSTI.GOV)

    Lefrancois, Daniel; Dreuw, Andreas, E-mail: dreuw@uni-heidelberg.de; Rehn, Dirk R.

    For the calculation of adiabatic singlet-triplet gaps (STG) in diradicaloid systems the spin-flip (SF) variant of the algebraic diagrammatic construction (ADC) scheme for the polarization propagator in third order perturbation theory (SF-ADC(3)) has been applied. Due to the methodology of the SF approach the singlet and triplet states are treated on an equal footing since they are part of the same determinant subspace. This leads to a systematically more accurate description of, e.g., diradicaloid systems than with the corresponding non-SF single-reference methods. Furthermore, using analytical excited state gradients at ADC(3) level, geometry optimizations of the singlet and triplet states weremore » performed leading to a fully consistent description of the systems, leading to only small errors in the calculated STGs ranging between 0.6 and 2.4 kcal/mol with respect to experimental references.« less

  1. A comparative study of advanced shock-capturing schemes applied to Burgers' equation

    NASA Technical Reports Server (NTRS)

    Yang, H. Q.; Przekwas, A. J.

    1992-01-01

    A systematic evaluation is conducted of all extant numerical schemes for nonlinear scalar transport problems, and several advanced shock-capturing schemes are used to solve the nonlinear Burgers' equation in order to characterize their ability to resolve the sharp discontinuity, expansion zone, and propagation and collision features of shocks. For discontinuous functions, the Warming-Beam scheme generates preshock wiggles, while the Lax-Wendroff scheme generates postshock ones. Such limiters as the MUSCL or the superbee are more compressive than minimod or monotonic limiters. The performance of such TVD schemes as the upwind, the symmetric, and the Roe-Sweby, resemble each other.

  2. Physiology driven adaptivity for the numerical solution of the bidomain equations.

    PubMed

    Whiteley, Jonathan P

    2007-09-01

    Previous work [Whiteley, J. P. IEEE Trans. Biomed. Eng. 53:2139-2147, 2006] derived a stable, semi-implicit numerical scheme for solving the bidomain equations. This scheme allows the timestep used when solving the bidomain equations numerically to be chosen by accuracy considerations rather than stability considerations. In this study we modify this scheme to allow an adaptive numerical solution in both time and space. The spatial mesh size is determined by the gradient of the transmembrane and extracellular potentials while the timestep is determined by the values of: (i) the fast sodium current; and (ii) the calcium release from junctional sarcoplasmic reticulum to myoplasm current. For two-dimensional simulations presented here, combining the numerical algorithm in the paper cited above with the adaptive algorithm presented here leads to an increase in computational efficiency by a factor of around 250 over previous work, together with significantly less computational memory being required. The speedup for three-dimensional simulations is likely to be more impressive.

  3. Designing Adaptive Low-Dissipative High Order Schemes for Long-Time Integrations. Chapter 1

    NASA Technical Reports Server (NTRS)

    Yee, Helen C.; Sjoegreen, B.; Mansour, Nagi N. (Technical Monitor)

    2001-01-01

    A general framework for the design of adaptive low-dissipative high order schemes is presented. It encompasses a rather complete treatment of the numerical approach based on four integrated design criteria: (1) For stability considerations, condition the governing equations before the application of the appropriate numerical scheme whenever it is possible; (2) For consistency, compatible schemes that possess stability properties, including physical and numerical boundary condition treatments, similar to those of the discrete analogue of the continuum are preferred; (3) For the minimization of numerical dissipation contamination, efficient and adaptive numerical dissipation control to further improve nonlinear stability and accuracy should be used; and (4) For practical considerations, the numerical approach should be efficient and applicable to general geometries, and an efficient and reliable dynamic grid adaptation should be used if necessary. These design criteria are, in general, very useful to a wide spectrum of flow simulations. However, the demand on the overall numerical approach for nonlinear stability and accuracy is much more stringent for long-time integration of complex multiscale viscous shock/shear/turbulence/acoustics interactions and numerical combustion. Robust classical numerical methods for less complex flow physics are not suitable or practical for such applications. The present approach is designed expressly to address such flow problems, especially unsteady flows. The minimization of employing very fine grids to overcome the production of spurious numerical solutions and/or instability due to under-resolved grids is also sought. The incremental studies to illustrate the performance of the approach are summarized. Extensive testing and full implementation of the approach is forthcoming. The results shown so far are very encouraging.

  4. A Novel Iterative Scheme for the Very Fast and Accurate Solution of Non-LTE Radiative Transfer Problems

    NASA Astrophysics Data System (ADS)

    Trujillo Bueno, J.; Fabiani Bendicho, P.

    1995-12-01

    Iterative schemes based on Gauss-Seidel (G-S) and optimal successive over-relaxation (SOR) iteration are shown to provide a dramatic increase in the speed with which non-LTE radiation transfer (RT) problems can be solved. The convergence rates of these new RT methods are identical to those of upper triangular nonlocal approximate operator splitting techniques, but the computing time per iteration and the memory requirements are similar to those of a local operator splitting method. In addition to these properties, both methods are particularly suitable for multidimensional geometry, since they neither require the actual construction of nonlocal approximate operators nor the application of any matrix inversion procedure. Compared with the currently used Jacobi technique, which is based on the optimal local approximate operator (see Olson, Auer, & Buchler 1986), the G-S method presented here is faster by a factor 2. It gives excellent smoothing of the high-frequency error components, which makes it the iterative scheme of choice for multigrid radiative transfer. This G-S method can also be suitably combined with standard acceleration techniques to achieve even higher performance. Although the convergence rate of the optimal SOR scheme developed here for solving non-LTE RT problems is much higher than G-S, the computing time per iteration is also minimal, i.e., virtually identical to that of a local operator splitting method. While the conventional optimal local operator scheme provides the converged solution after a total CPU time (measured in arbitrary units) approximately equal to the number n of points per decade of optical depth, the time needed by this new method based on the optimal SOR iterations is only √n/2√2. This method is competitive with those that result from combining the above-mentioned Jacobi and G-S schemes with the best acceleration techniques. Contrary to what happens with the local operator splitting strategy currently in use, these novel

  5. Three-dimensional cascaded lattice Boltzmann method: Improved implementation and consistent forcing scheme

    NASA Astrophysics Data System (ADS)

    Fei, Linlin; Luo, Kai H.; Li, Qing

    2018-05-01

    The cascaded or central-moment-based lattice Boltzmann method (CLBM) proposed in [Phys. Rev. E 73, 066705 (2006), 10.1103/PhysRevE.73.066705] possesses very good numerical stability. However, two constraints exist in three-dimensional (3D) CLBM simulations. First, the conventional implementation for 3D CLBM involves cumbersome operations and requires much higher computational cost compared to the single-relaxation-time (SRT) LBM. Second, it is a challenge to accurately incorporate a general force field into the 3D CLBM. In this paper, we present an improved method to implement CLBM in 3D. The main strategy is to adopt a simplified central moment set and carry out the central-moment-based collision operator based on a general multi-relaxation-time (GMRT) framework. Next, the recently proposed consistent forcing scheme for CLBM [Fei and Luo, Phys. Rev. E 96, 053307 (2017), 10.1103/PhysRevE.96.053307] is extended to incorporate a general force field into 3D CLBM. Compared with the recently developed nonorthogonal CLBM [Rosis, Phys. Rev. E 95, 013310 (2017), 10.1103/PhysRevE.95.013310], our implementation is proved to reduce the computational cost significantly. The inconsistency of adopting the discrete equilibrium distribution functions in the nonorthogonal CLBM is analyzed and validated. The 3D CLBM developed here in conjunction with the consistent forcing scheme is verified through numerical simulations of several canonical force-driven flows, highlighting very good properties in terms of accuracy, convergence, and consistency with the nonslip rule. Finally, the techniques developed here for 3D CLBM can be applied to make the implementation and execution of 3D MRT-LBM more efficient.

  6. Studies of Inviscid Flux Schemes for Acoustics and Turbulence Problems

    NASA Technical Reports Server (NTRS)

    Morris, Chris

    2013-01-01

    Five different central difference schemes, based on a conservative differencing form of the Kennedy and Gruber skew-symmetric scheme, were compared with six different upwind schemes based on primitive variable reconstruction and the Roe flux. These eleven schemes were tested on a one-dimensional acoustic standing wave problem, the Taylor-Green vortex problem and a turbulent channel flow problem. The central schemes were generally very accurate and stable, provided the grid stretching rate was kept below 10%. As near-DNS grid resolutions, the results were comparable to reference DNS calculations. At coarser grid resolutions, the need for an LES SGS model became apparent. There was a noticeable improvement moving from CD-2 to CD-4, and higher-order schemes appear to yield clear benefits on coarser grids. The UB-7 and CU-5 upwind schemes also performed very well at near-DNS grid resolutions. The UB-5 upwind scheme does not do as well, but does appear to be suitable for well-resolved DNS. The UF-2 and UB-3 upwind schemes, which have significant dissipation over a wide spectral range, appear to be poorly suited for DNS or LES.

  7. Assembling mesoscopic particles by various optical schemes

    NASA Astrophysics Data System (ADS)

    Fournier, Jean-Marc; Rohner, Johann; Jacquot, Pierre; Johann, Robert; Mias, Solon; Salathé, René-P.

    2005-08-01

    Shaping optical fields is the key issue in the control of optical forces that pilot the manipulation of mesoscopic polarizable dielectric particles. The latter can be positioned according to endless configurations. The scope of this paper is to review and discuss several unusual designs which produce what we think are among some of the most interesting arrangements. The simplest schemes result from interference between two or several coherent light beams, leading to periodic as well as pseudo-periodic arrays of optical traps. Complex assemblages of traps can be created with holographic-type set-ups; this case is widely used by the trapping community. Clusters of traps can also be configured through interferometric-type set-ups or by generating external standing waves by diffractive elements. The particularly remarkable possibilities of the Talbot effect to generate three-dimensional optical lattices and several schemes of self-organization represent further very interesting means for trapping. They will also be described and discussed. in this paper. The mechanisms involved in those trapping schemes do not require the use of high numerical aperture optics; by avoiding the need for bulky microscope objectives, they allow for more physical space around the trapping area to perform experiments. Moreover, very large regular arrays of traps can be manufactured, opening numerous possibilities for new applications.

  8. A 3D staggered-grid finite difference scheme for poroelastic wave equation

    NASA Astrophysics Data System (ADS)

    Zhang, Yijie; Gao, Jinghuai

    2014-10-01

    Three dimensional numerical modeling has been a viable tool for understanding wave propagation in real media. The poroelastic media can better describe the phenomena of hydrocarbon reservoirs than acoustic and elastic media. However, the numerical modeling in 3D poroelastic media demands significantly more computational capacity, including both computational time and memory. In this paper, we present a 3D poroelastic staggered-grid finite difference (SFD) scheme. During the procedure, parallel computing is implemented to reduce the computational time. Parallelization is based on domain decomposition, and communication between processors is performed using message passing interface (MPI). Parallel analysis shows that the parallelized SFD scheme significantly improves the simulation efficiency and 3D decomposition in domain is the most efficient. We also analyze the numerical dispersion and stability condition of the 3D poroelastic SFD method. Numerical results show that the 3D numerical simulation can provide a real description of wave propagation.

  9. A Multiserver Biometric Authentication Scheme for TMIS using Elliptic Curve Cryptography.

    PubMed

    Chaudhry, Shehzad Ashraf; Khan, Muhammad Tawab; Khan, Muhammad Khurram; Shon, Taeshik

    2016-11-01

    Recently several authentication schemes are proposed for telecare medicine information system (TMIS). Many of such schemes are proved to have weaknesses against known attacks. Furthermore, numerous such schemes cannot be used in real time scenarios. Because they assume a single server for authentication across the globe. Very recently, Amin et al. (J. Med. Syst. 39(11):180, 2015) designed an authentication scheme for secure communication between a patient and a medical practitioner using a trusted central medical server. They claimed their scheme to extend all security requirements and emphasized the efficiency of their scheme. However, the analysis in this article proves that the scheme designed by Amin et al. is vulnerable to stolen smart card and stolen verifier attacks. Furthermore, their scheme is having scalability issues along with inefficient password change and password recovery phases. Then we propose an improved scheme. The proposed scheme is more practical, secure and lightweight than Amin et al.'s scheme. The security of proposed scheme is proved using the popular automated tool ProVerif.

  10. An approach toward the numerical evaluation of multi-loop Feynman diagrams

    NASA Astrophysics Data System (ADS)

    Passarino, Giampiero

    2001-12-01

    A scheme for systematically achieving accurate numerical evaluation of multi-loop Feynman diagrams is developed. This shows the feasibility of a project aimed to produce a complete calculation for two-loop predictions in the Standard Model. As a first step an algorithm, proposed by F.V. Tkachov and based on the so-called generalized Bernstein functional relation, is applied to one-loop multi-leg diagrams with particular emphasis to the presence of infrared singularities, to the problem of tensorial reduction and to the classification of all singularities of a given diagram. Successively, the extension of the algorithm to two-loop diagrams is examined. The proposed solution consists in applying the functional relation to the one-loop sub-diagram which has the largest number of internal lines. In this way the integrand can be made smooth, a part from a factor which is a polynomial in xS, the vector of Feynman parameters needed for the complementary sub-diagram with the smallest number of internal lines. Since the procedure does not introduce new singularities one can distort the xS-integration hyper-contour into the complex hyper-plane, thus achieving numerical stability. The algorithm is then modified to deal with numerical evaluation around normal thresholds. Concise and practical formulas are assembled and presented, numerical results and comparisons with the available literature are shown and discussed for the so-called sunset topology.

  11. An Accurate Direction Finding Scheme Using Virtual Antenna Array via Smartphones

    PubMed Central

    Wang, Xiaopu; Xiong, Yan; Huang, Wenchao

    2016-01-01

    With the development of localization technologies, researchers solve the indoor localization problems using diverse methods and equipment. Most localization techniques require either specialized devices or fingerprints, which are inconvenient for daily use. Therefore, we propose and implement an accurate, efficient and lightweight system for indoor direction finding using common smartphones and loudspeakers. Our method is derived from a key insight: By moving a smartphone in regular patterns, we can effectively emulate the sensitivity and functionality of a Uniform Antenna Array to estimate the angle of arrival of the target signal. Specifically, a user only needs to hold his smartphone still in front of him, and then rotate his body around 360∘ duration with the smartphone at an approximate constant velocity. Then, our system can provide accurate directional guidance and lead the user to their destinations (normal loudspeakers we preset in the indoor environment transmitting high frequency acoustic signals) after a few measurements. Major challenges in implementing our system are not only imitating a virtual antenna array by ordinary smartphones but also overcoming the detection difficulties caused by the complex indoor environment. In addition, we leverage the gyroscope of the smartphone to reduce the impact of a user’s motion pattern change to the accuracy of our system. In order to get rid of the multipath effect, we leverage multiple signal classification to calculate the direction of the target signal, and then design and deploy our system in various indoor scenes. Extensive comparative experiments show that our system is reliable under various circumstances. PMID:27801866

  12. An Accurate Direction Finding Scheme Using Virtual Antenna Array via Smartphones.

    PubMed

    Wang, Xiaopu; Xiong, Yan; Huang, Wenchao

    2016-10-29

    With the development of localization technologies, researchers solve the indoor localization problems using diverse methods and equipment. Most localization techniques require either specialized devices or fingerprints, which are inconvenient for daily use. Therefore, we propose and implement an accurate, efficient and lightweight system for indoor direction finding using common smartphones and loudspeakers. Our method is derived from a key insight: By moving a smartphone in regular patterns, we can effectively emulate the sensitivity and functionality of a Uniform Antenna Array to estimate the angle of arrival of the target signal. Specifically, a user only needs to hold his smartphone still in front of him, and then rotate his body around 360 ∘ duration with the smartphone at an approximate constant velocity. Then, our system can provide accurate directional guidance and lead the user to their destinations (normal loudspeakers we preset in the indoor environment transmitting high frequency acoustic signals) after a few measurements. Major challenges in implementing our system are not only imitating a virtual antenna array by ordinary smartphones but also overcoming the detection difficulties caused by the complex indoor environment. In addition, we leverage the gyroscope of the smartphone to reduce the impact of a user's motion pattern change to the accuracy of our system. In order to get rid of the multipath effect, we leverage multiple signal classification to calculate the direction of the target signal, and then design and deploy our system in various indoor scenes. Extensive comparative experiments show that our system is reliable under various circumstances.

  13. Multigrid time-accurate integration of Navier-Stokes equations

    NASA Technical Reports Server (NTRS)

    Arnone, Andrea; Liou, Meng-Sing; Povinelli, Louis A.

    1993-01-01

    Efficient acceleration techniques typical of explicit steady-state solvers are extended to time-accurate calculations. Stability restrictions are greatly reduced by means of a fully implicit time discretization. A four-stage Runge-Kutta scheme with local time stepping, residual smoothing, and multigridding is used instead of traditional time-expensive factorizations. Some applications to natural and forced unsteady viscous flows show the capability of the procedure.

  14. A divergence-cleaning scheme for cosmological SPMHD simulations

    NASA Astrophysics Data System (ADS)

    Stasyszyn, F. A.; Dolag, K.; Beck, A. M.

    2013-01-01

    In magnetohydrodynamics (MHD), the magnetic field is evolved by the induction equation and coupled to the gas dynamics by the Lorentz force. We perform numerical smoothed particle magnetohydrodynamics (SPMHD) simulations and study the influence of a numerical magnetic divergence. For instabilities arising from {nabla }\\cdot {boldsymbol B} related errors, we find the hyperbolic/parabolic cleaning scheme suggested by Dedner et al. to give good results and prevent numerical artefacts from growing. Additionally, we demonstrate that certain current SPMHD implementations of magnetic field regularizations give rise to unphysical instabilities in long-time simulations. We also find this effect when employing Euler potentials (divergenceless by definition), which are not able to follow the winding-up process of magnetic field lines properly. Furthermore, we present cosmological simulations of galaxy cluster formation at extremely high resolution including the evolution of magnetic fields. We show synthetic Faraday rotation maps and derive structure functions to compare them with observations. Comparing all the simulations with and without divergence cleaning, we are able to confirm the results of previous simulations performed with the standard implementation of MHD in SPMHD at normal resolution. However, at extremely high resolution, a cleaning scheme is needed to prevent the growth of numerical {nabla }\\cdot {boldsymbol B} errors at small scales.

  15. Numerical Analysis of Dusty-Gas Flows

    NASA Astrophysics Data System (ADS)

    Saito, T.

    2002-02-01

    This paper presents the development of a numerical code for simulating unsteady dusty-gas flows including shock and rarefaction waves. The numerical results obtained for a shock tube problem are used for validating the accuracy and performance of the code. The code is then extended for simulating two-dimensional problems. Since the interactions between the gas and particle phases are calculated with the operator splitting technique, we can choose numerical schemes independently for the different phases. A semi-analytical method is developed for the dust phase, while the TVD scheme of Harten and Yee is chosen for the gas phase. Throughout this study, computations are carried out on SGI Origin2000, a parallel computer with multiple of RISC based processors. The efficient use of the parallel computer system is an important issue and the code implementation on Origin2000 is also described. Flow profiles of both the gas and solid particles behind the steady shock wave are calculated by integrating the steady conservation equations. The good agreement between the pseudo-stationary solutions and those from the current numerical code validates the numerical approach and the actual coding. The pseudo-stationary shock profiles can also be used as initial conditions of unsteady multidimensional simulations.

  16. Study of stability of the difference scheme for the model problem of the gaslift process

    NASA Astrophysics Data System (ADS)

    Temirbekov, Nurlan; Turarov, Amankeldy

    2017-09-01

    The paper studies a model of the gaslift process where the motion in a gas-lift well is described by partial differential equations. The system describing the studied process consists of equations of motion, continuity, equations of thermodynamic state, and hydraulic resistance. A two-layer finite-difference Lax-Vendroff scheme is constructed for the numerical solution of the problem. The stability of the difference scheme for the model problem is investigated using the method of a priori estimates, the order of approximation is investigated, the algorithm for numerical implementation of the gaslift process model is given, and the graphs are presented. The development and investigation of difference schemes for the numerical solution of systems of equations of gas dynamics makes it possible to obtain simultaneously exact and monotonic solutions.

  17. New transmission scheme to enhance throughput of DF relay network using rate and power adaptation

    NASA Astrophysics Data System (ADS)

    Taki, Mehrdad; Heshmati, Milad

    2017-09-01

    This paper presents a new transmission scheme for a decode and forward (DF) relay network using continuous power adaptation while independent average power constraints are provisioned for each node. To have analytical insight, the achievable throughputs are analysed using continuous adaptation of the rates and the powers. As shown by numerical evaluations, a considerable outperformance is seen by continuous power adaptation compared to the case where constant powers are utilised. Also for practical systems, a new throughput maximised transmission scheme is developed using discrete rate adaptation (adaptive modulation and coding) and continuous transmission power adaptation. First a 2-hop relay network is considered and then the scheme is extended for an N-hop network. Numerical evaluations show the efficiency of the designed schemes.

  18. Low-Dissipation Advection Schemes Designed for Large Eddy Simulations of Hypersonic Propulsion Systems

    NASA Technical Reports Server (NTRS)

    White, Jeffrey A.; Baurle, Robert A.; Fisher, Travis C.; Quinlan, Jesse R.; Black, William S.

    2012-01-01

    The 2nd-order upwind inviscid flux scheme implemented in the multi-block, structured grid, cell centered, finite volume, high-speed reacting flow code VULCAN has been modified to reduce numerical dissipation. This modification was motivated by the desire to improve the codes ability to perform large eddy simulations. The reduction in dissipation was accomplished through a hybridization of non-dissipative and dissipative discontinuity-capturing advection schemes that reduces numerical dissipation while maintaining the ability to capture shocks. A methodology for constructing hybrid-advection schemes that blends nondissipative fluxes consisting of linear combinations of divergence and product rule forms discretized using 4th-order symmetric operators, with dissipative, 3rd or 4th-order reconstruction based upwind flux schemes was developed and implemented. A series of benchmark problems with increasing spatial and fluid dynamical complexity were utilized to examine the ability of the candidate schemes to resolve and propagate structures typical of turbulent flow, their discontinuity capturing capability and their robustness. A realistic geometry typical of a high-speed propulsion system flowpath was computed using the most promising of the examined schemes and was compared with available experimental data to demonstrate simulation fidelity.

  19. Combining symmetry breaking and restoration with configuration interaction: A highly accurate many-body scheme applied to the pairing Hamiltonian

    NASA Astrophysics Data System (ADS)

    Ripoche, J.; Lacroix, D.; Gambacurta, D.; Ebran, J.-P.; Duguet, T.

    2017-01-01

    internucleon coupling defining the pairing Hamiltonian and driving the normal-to-superfluid quantum phase transition. The presently proposed method offers the advantage of automatic access to the low-lying spectroscopy, which it does with high accuracy. Conclusions: The numerical cost of the newly designed variational method is polynomial (N6) in system size. This method achieves unprecedented accuracy for the ground-state correlation energy, effective pairing gap, and one-body entropy as well as for the excitation energy of low-lying states of the attractive pairing Hamiltonian. This constitutes a sufficiently strong motivation to envision its application to realistic nuclear Hamiltonians in view of providing a complementary, accurate, and versatile ab initio description of mid-mass open-shell nuclei in the future.

  20. Evaluating radiative transfer schemes treatment of vegetation canopy architecture in land surface models

    NASA Astrophysics Data System (ADS)

    Braghiere, Renato; Quaife, Tristan; Black, Emily

    2016-04-01

    Incoming shortwave radiation is the primary source of energy driving the majority of the Earth's climate system. The partitioning of shortwave radiation by vegetation into absorbed, reflected, and transmitted terms is important for most of biogeophysical processes, including leaf temperature changes and photosynthesis, and it is currently calculated by most of land surface schemes (LSS) of climate and/or numerical weather prediction models. The most commonly used radiative transfer scheme in LSS is the two-stream approximation, however it does not explicitly account for vegetation architectural effects on shortwave radiation partitioning. Detailed three-dimensional (3D) canopy radiative transfer schemes have been developed, but they are too computationally expensive to address large-scale related studies over long time periods. Using a straightforward one-dimensional (1D) parameterisation proposed by Pinty et al. (2006), we modified a two-stream radiative transfer scheme by including a simple function of Sun zenith angle, so-called "structure factor", which does not require an explicit description and understanding of the complex phenomena arising from the presence of vegetation heterogeneous architecture, and it guarantees accurate simulations of the radiative balance consistently with 3D representations. In order to evaluate the ability of the proposed parameterisation in accurately represent the radiative balance of more complex 3D schemes, a comparison between the modified two-stream approximation with the "structure factor" parameterisation and state-of-art 3D radiative transfer schemes was conducted, following a set of virtual scenarios described in the RAMI4PILPS experiment. These experiments have been evaluating the radiative balance of several models under perfectly controlled conditions in order to eliminate uncertainties arising from an incomplete or erroneous knowledge of the structural, spectral and illumination related canopy characteristics typical