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Sample records for accurate numerical scheme

  1. Orbital Advection by Interpolation: A Fast and Accurate Numerical Scheme for Super-Fast MHD Flows

    SciTech Connect

    Johnson, B M; Guan, X; Gammie, F

    2008-04-11

    In numerical models of thin astrophysical disks that use an Eulerian scheme, gas orbits supersonically through a fixed grid. As a result the timestep is sharply limited by the Courant condition. Also, because the mean flow speed with respect to the grid varies with position, the truncation error varies systematically with position. For hydrodynamic (unmagnetized) disks an algorithm called FARGO has been developed that advects the gas along its mean orbit using a separate interpolation substep. This relaxes the constraint imposed by the Courant condition, which now depends only on the peculiar velocity of the gas, and results in a truncation error that is more nearly independent of position. This paper describes a FARGO-like algorithm suitable for evolving magnetized disks. Our method is second order accurate on a smooth flow and preserves {del} {center_dot} B = 0 to machine precision. The main restriction is that B must be discretized on a staggered mesh. We give a detailed description of an implementation of the code and demonstrate that it produces the expected results on linear and nonlinear problems. We also point out how the scheme might be generalized to make the integration of other supersonic/super-fast flows more efficient. Although our scheme reduces the variation of truncation error with position, it does not eliminate it. We show that the residual position dependence leads to characteristic radial variations in the density over long integrations.

  2. A high order accurate difference scheme for complex flow fields

    SciTech Connect

    Dexun Fu; Yanwen Ma

    1997-06-01

    A high order accurate finite difference method for direct numerical simulation of coherent structure in the mixing layers is presented. The reason for oscillation production in numerical solutions is analyzed. It is caused by a nonuniform group velocity of wavepackets. A method of group velocity control for the improvement of the shock resolution is presented. In numerical simulation the fifth-order accurate upwind compact difference relation is used to approximate the derivatives in the convection terms of the compressible N-S equations, a sixth-order accurate symmetric compact difference relation is used to approximate the viscous terms, and a three-stage R-K method is used to advance in time. In order to improve the shock resolution the scheme is reconstructed with the method of diffusion analogy which is used to control the group velocity of wavepackets. 18 refs., 12 figs., 1 tab.

  3. Second-order accurate difference schemes on highly irregular meshes

    SciTech Connect

    Manteuffel, T.A.; White, A.B. Jr.

    1988-01-01

    In this paper compact-as-possible second-order accurate difference schemes will be constructed for boundary-value problems of arbitrary order on highly irregular meshes. It will be shown that for equations of order (K) these schemes will have truncation error of order (3/endash/K). This phenomena is known as supraconvergence. 7 refs.

  4. 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.

  5. A numerical scheme for ionizing shock waves

    SciTech Connect

    Aslan, Necdet . E-mail: naslan@yeditepe.edu.tr; Mond, Michael

    2005-12-10

    A two-dimensional (2D) visual computer code to solve the steady state (SS) or transient shock problems including partially ionizing plasma is presented. Since the flows considered are hypersonic and the resulting temperatures are high, the plasma is partially ionized. Hence the plasma constituents are electrons, ions and neutral atoms. It is assumed that all the above species are in thermal equilibrium, namely, that they all have the same temperature. The ionization degree is calculated from Saha equation as a function of electron density and pressure by means of a nonlinear Newton type root finding algorithms. The code utilizes a wave model and numerical fluctuation distribution (FD) scheme that runs on structured or unstructured triangular meshes. This scheme is based on evaluating the mesh averaged fluctuations arising from a number of waves and distributing them to the nodes of these meshes in an upwind manner. The physical properties (directions, strengths, etc.) of these wave patterns are obtained by a new wave model: ION-A developed from the eigen-system of the flux Jacobian matrices. Since the equation of state (EOS) which is used to close up the conservation laws includes electronic effects, it is a nonlinear function and it must be inverted by iterations to determine the ionization degree as a function of density and temperature. For the time advancement, the scheme utilizes a multi-stage Runge-Kutta (RK) algorithm with time steps carefully evaluated from the maximum possible propagation speed in the solution domain. The code runs interactively with the user and allows to create different meshes to use different initial and boundary conditions and to see changes of desired physical quantities in the form of color and vector graphics. The details of the visual properties of the code has been published before (see [N. Aslan, A visual fluctuation splitting scheme for magneto-hydrodynamics with a new sonic fix and Euler limit, J. Comput. Phys. 197 (2004) 1

  6. Filtered schemes for Hamilton-Jacobi equations: A simple construction of convergent accurate difference schemes

    NASA Astrophysics Data System (ADS)

    Oberman, Adam M.; Salvador, Tiago

    2015-03-01

    We build a simple and general class of finite difference schemes for first order Hamilton-Jacobi (HJ) Partial Differential Equations. These filtered schemes are convergent to the unique viscosity solution of the equation. The schemes are accurate: we implement second, third and fourth order accurate schemes in one dimension and second order accurate schemes in two dimensions, indicating how to build higher order ones. They are also explicit, which means they can be solved using the fast sweeping method. The accuracy of the method is validated with computational results for the eikonal equation and other HJ equations in one and two dimensions, using filtered schemes made from standard centered differences, higher order upwinding and ENO interpolation.

  7. 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.

  8. Uniformly high order accurate essentially non-oscillatory schemes 3

    NASA Technical Reports Server (NTRS)

    Harten, A.; Engquist, B.; Osher, S.; Chakravarthy, S. R.

    1986-01-01

    In this paper (a third in a series) the construction and the analysis of essentially non-oscillatory shock capturing methods for the approximation of hyperbolic conservation laws are presented. Also presented is a hierarchy of high order accurate schemes which generalizes Godunov's scheme and its second order accurate MUSCL extension to arbitrary order of accuracy. The design involves an essentially non-oscillatory piecewise polynomial 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. The reconstruction algorithm is derived from a new interpolation technique that when applied to piecewise smooth data gives high-order accuracy whenever the function is smooth but avoids a Gibbs phenomenon at discontinuities. Unlike standard finite difference methods this procedure uses an adaptive stencil of grid points and consequently the resulting schemes are highly nonlinear.

  9. Fourth-Order Accurate IDO Scheme Using Gradient-Staggered Interpolation

    NASA Astrophysics Data System (ADS)

    Imai, Yohsuke; Aoki, Takayuki

    An Interpolated Differential Operator (IDO) scheme using a new interpolation function is proposed. The gradient of the dependent variable is calculated at the position shifted by a half grid size from that of the physical value. A fourth-order Hermite-interpolation function is constructed locally using both the value and the gradient defined at staggered positions. The numerical solutions for the Poisson, diffusion, advection and wave equations have fourth-order accuracy in space. In particular, for the Poisson and diffusion equations, the Gradient-Staggered (G-S) IDO scheme shows better accuracy than the original IDO scheme. As a practical application, the Direct Numerical Simulation (DNS) for two-dimensional isotropic homogeneous turbulence is examined and a comparable result with that of the original IDO scheme is obtained. The G-S IDO scheme clearly contributes to high-accurate computations for solving partial differential equations in computational mechanics.

  10. Uniformly second-order-accurate essentially nonoscillatory schemes for the Euler equations

    NASA Astrophysics Data System (ADS)

    Yang, J. Y.

    1990-12-01

    Two time-level explicit and implicit finite-difference shock-capturing schemes based on the characteristic flux difference splitting method and the modified flux approach with the essentially nonoscillatory (ENO) property of Harten and Osher have been developed for the two-dimensional Euler equations. The methods are conservative, uniformly second-order accurate in time and space, even at local extrema. General coordinate systems are used to treat complex geometries. Standard alternating direction implicit approximate factorization is used for constructing implicit schemes. Numerical results have been obtained for unsteady shock wave reflection around general two-dimensional blunt bodies and for steady transonic flows over a circular arc bump in a channel. Properties of ENO schemes as applied to two-dimensional flows with multiple embedded discontinuities are discussed. Comparisons of the performance between the present ENO schemes and the previous total variation diminishing schemes is also included.

  11. Numerical Schemes for Rough Parabolic Equations

    SciTech Connect

    Deya, Aurelien

    2012-04-15

    This paper is devoted to the study of numerical approximation schemes for a class of parabolic equations on (0,1) perturbed by a non-linear rough signal. It is the continuation of Deya (Electron. J. Probab. 16:1489-1518, 2011) and Deya et al. (Probab. Theory Relat. Fields, to appear), where the existence and uniqueness of a solution has been established. The approach combines rough paths methods with standard considerations on discretizing stochastic PDEs. The results apply to a geometric 2-rough path, which covers the case of the multidimensional fractional Brownian motion with Hurst index H>1/3.

  12. 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.

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

    NASA Technical Reports Server (NTRS)

    Kim, Hyun D.; Liu, Nan-Suey

    1993-01-01

    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.

  14. 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.

  15. Practical Schemes for Accurate Forces in Quantum Monte Carlo.

    PubMed

    Moroni, S; Saccani, S; Filippi, C

    2014-11-11

    While the computation of interatomic forces has become a well-established practice within variational Monte Carlo (VMC), the use of the more accurate Fixed-Node Diffusion Monte Carlo (DMC) method is still largely limited to the computation of total energies on structures obtained at a lower level of theory. Algorithms to compute exact DMC forces have been proposed in the past, and one such scheme is also put forward in this work, but remain rather impractical due to their high computational cost. As a practical route to DMC forces, we therefore revisit here an approximate method, originally developed in the context of correlated sampling and named here the Variational Drift-Diffusion (VD) approach. We thoroughly investigate its accuracy by checking the consistency between the approximate VD force and the derivative of the DMC potential energy surface for the SiH and C2 molecules and employ a wide range of wave functions optimized in VMC to assess its robustness against the choice of trial function. We find that, for all but the poorest wave function, the discrepancy between force and energy is very small over all interatomic distances, affecting the equilibrium bond length obtained with the VD forces by less than 0.004 au. Furthermore, when the VMC forces are approximate due to the use of a partially optimized wave function, the DMC forces have smaller errors and always lead to an equilibrium distance in better agreement with the experimental value. We also show that the cost of computing the VD forces is only slightly larger than the cost of calculating the DMC energy. Therefore, the VD approximation represents a robust and efficient approach to compute accurate DMC forces, superior to the VMC counterparts.

  16. An accurate scheme to solve cluster dynamics equations using a Fokker-Planck approach

    NASA Astrophysics Data System (ADS)

    Jourdan, T.; Stoltz, G.; Legoll, F.; Monasse, L.

    2016-10-01

    We present a numerical method to accurately simulate particle size distributions within the formalism of rate equation cluster dynamics. This method is based on a discretization of the associated Fokker-Planck equation. We show that particular care has to be taken to discretize the advection part of the Fokker-Planck equation, in order to avoid distortions of the distribution due to numerical diffusion. For this purpose we use the Kurganov-Noelle-Petrova scheme coupled with the monotonicity-preserving reconstruction MP5, which leads to very accurate results. The interest of the method is highlighted in the case of loop coarsening in aluminum. We show that the choice of the models to describe the energetics of loops does not significantly change the normalized loop distribution, while the choice of the models for the absorption coefficients seems to have a significant impact on it.

  17. Simple Numerical Schemes for the Korteweg-deVries Equation

    SciTech Connect

    C. J. McKinstrie; M. V. Kozlov

    2000-12-01

    Two numerical schemes, which simulate the propagation of dispersive non-linear waves, are described. The first is a split-step Fourier scheme for the Korteweg-de Vries (KdV) equation. The second is a finite-difference scheme for the modified KdV equation. The stability and accuracy of both schemes are discussed. These simple schemes can be used to study a wide variety of physical processes that involve dispersive nonlinear waves.

  18. Application of second-order-accurate Total Variation Diminishing (TVD) schemes to the Euler equations in general geometries

    NASA Technical Reports Server (NTRS)

    Yee, H. C.; Kutler, P.

    1983-01-01

    A one-parameter family of explicit and implicit second-order-accurate, entropy satisfying, total variation diminishing (TVD) schemes was developed by Harten. These TVD schemes were the property of not generating spurious oscillations for one-dimensional nonlinear scalar hyperbolic conservation laws and constant coefficient hyperbolic systems. Application of these methods to one- and two-dimensional fluid flows containing shocks (in Cartesian coordinates) yields highly accurate nonoscillatory numerical solutions. The goal of this work is to expand these methods to the multidimensional Euler equations in generalized coordinate systems. Some numerical results of shock waves impinging on cylindrical bodies are compared with MacCormack's method.

  19. 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.

  20. Multi-dimensional high-order numerical schemes for Lagrangian hydrodynamics

    SciTech Connect

    Dai, William W; Woodward, Paul R

    2009-01-01

    An approximate solver for multi-dimensional Riemann problems at grid points of unstructured meshes, and a numerical scheme for multi-dimensional hydrodynamics have been developed in this paper. The solver is simple, and is developed only for the use in numerical schemes for hydrodynamics. The scheme is truely multi-dimensional, is second order accurate in both space and time, and satisfies conservation laws exactly for mass, momentum, and total energy. The scheme has been tested through numerical examples involving strong shocks. It has been shown that the scheme offers the principle advantages of high-order Codunov schemes; robust operation in the presence of very strong shocks and thin shock fronts.

  1. Geometrically invariant and high capacity image watermarking scheme using accurate radial transform

    NASA Astrophysics Data System (ADS)

    Singh, Chandan; Ranade, Sukhjeet K.

    2013-12-01

    Angular radial transform (ART) is a region based descriptor and possesses many attractive features such as rotation invariance, low computational complexity and resilience to noise which make them more suitable for invariant image watermarking than that of many transform domain based image watermarking techniques. In this paper, we introduce ART for fast and geometrically invariant image watermarking scheme with high embedding capacity. We also develop an accurate and fast framework for the computation of ART coefficients based on Gaussian quadrature numerical integration, 8-way symmetry/anti-symmetry properties and recursive relations for the calculation of sinusoidal kernel functions. ART coefficients so computed are then used for embedding the binary watermark using dither modulation. Experimental studies reveal that the proposed watermarking scheme not only provides better robustness against geometric transformations and other signal processing distortions, but also has superior advantages over the existing ones in terms of embedding capacity, speed and visual imperceptibility.

  2. Numerical schemes for a model for nonlinear dispersive waves

    NASA Technical Reports Server (NTRS)

    Bona, J. L.; Pritchard, W. G.; Scott, L. R.

    1985-01-01

    A description is given of a number of numerical schemes to solve an evolution equation (Korteweg-deVries) that arises when modelling the propagation of water waves in a channel. The discussion also includes the results of numerical experiments made with each of the schemes. It is suggested, on the basis of these experiments, that one of the schemes may have (discrete) solitary-wave solutions.

  3. 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.

  4. 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.

  5. Highly Accurate Schemes for Wave Propagation Systems: Application in Aeroacoustics

    NASA Astrophysics Data System (ADS)

    Bartoli, Nathalie; Mazet, Pierre-Alain; Mouysset, Vincent; Rogier, François

    2010-09-01

    The Discontinuous Galerkin (DG) method is considered for computational aeroacoustic. A software has been developed to make it possible to test a large variety of configurations (non-conform grid, variable polynomial order). To deal with instationary phenomena involved by some shear flows, a compromise between time computation and accuracy is deduced from some numerical experiments.

  6. High-order accurate physical-constraints-preserving finite difference WENO schemes for special relativistic hydrodynamics

    NASA Astrophysics Data System (ADS)

    Wu, Kailiang; Tang, Huazhong

    2015-10-01

    The paper develops high-order accurate physical-constraints-preserving finite difference WENO schemes for special relativistic hydrodynamical (RHD) equations, built on the local Lax-Friedrichs splitting, the WENO reconstruction, the physical-constraints-preserving flux limiter, and the high-order strong stability preserving time discretization. They are extensions of the positivity-preserving finite difference WENO schemes for the non-relativistic Euler equations [20]. However, developing physical-constraints-preserving methods for the RHD system becomes much more difficult than the non-relativistic case because of the strongly coupling between the RHD equations, no explicit formulas of the primitive variables and the flux vectors with respect to the conservative vector, and one more physical constraint for the fluid velocity in addition to the positivity of the rest-mass density and the pressure. The key is to prove the convexity and other properties of the admissible state set and discover a concave function with respect to the conservative vector instead of the pressure which is an important ingredient to enforce the positivity-preserving property for the non-relativistic case. Several one- and two-dimensional numerical examples are used to demonstrate accuracy, robustness, and effectiveness of the proposed physical-constraints-preserving schemes in solving RHD problems with large Lorentz factor, or strong discontinuities, or low rest-mass density or pressure etc.

  7. A Second-Order Accurate, Component-Wise TVD Scheme for Nonlinear, Hyperbolic Conservation Laws

    NASA Astrophysics Data System (ADS)

    Yu, Heng; Liu, Yu-Ping

    2001-10-01

    In this paper, we present a two-step, component-wise TVD scheme for nonlinear, hyperbolic conservation laws, which is obtained by combining the schemes of Mac Cormack and Warming-Beam. The scheme does not necessitate the characteristic decompositions of the usual TVD schemes. It employs component-wise limiting; hence the programming is much simpler, especially for complicated coupled systems. For Euler systems of conservation laws, we found the scheme is two times faster in computation than the usual TVD schemes based on field-by-field decomposition limiting. A lot of numerical results show primarily the value of the new method.

  8. Numerical simulation of shock wave diffraction by TVD schemes

    NASA Technical Reports Server (NTRS)

    Young, Victor Y. C.; Yee, H. C.

    1987-01-01

    An upwind total variation diminishing (TVD) scheme and a predictor-corrector symmetric TVD scheme were used to numerically simulate the blast wave diffraction on a stationary object. The objective is to help design an optimum configuration so that lateral motion is minimized and at the same time vortex shedding and flow separation are reduced during a blast wave encounter. Results are presented for a generic configuration for both a coarse grid and a fine grid to illustrate the global and local diffraction flow fields. Numerical experiments for the shock wave reflection on a wedge are also included to validate the current approach. Numerical study indicated that these TVD schemes are more stable and produced higher shock resolution than classical shock capturing methods such as the explicit MacCormack scheme.

  9. Accurate numerical solution of compressible, linear stability equations

    NASA Technical Reports Server (NTRS)

    Malik, M. R.; Chuang, S.; Hussaini, M. Y.

    1982-01-01

    The present investigation is concerned with a fourth order accurate finite difference method and its application to the study of the temporal and spatial stability of the three-dimensional compressible boundary layer flow on a swept wing. This method belongs to the class of compact two-point difference schemes discussed by White (1974) and Keller (1974). The method was apparently first used for solving the two-dimensional boundary layer equations. Attention is given to the governing equations, the solution technique, and the search for eigenvalues. A general purpose subroutine is employed for solving a block tridiagonal system of equations. The computer time can be reduced significantly by exploiting the special structure of two matrices.

  10. 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.

  11. Earthquake ground motion prediction for real sedimentary basins: which numerical schemes are applicable?

    NASA Astrophysics Data System (ADS)

    Moczo, P.; Kristek, J.; Galis, M.; Pazak, P.

    2009-12-01

    Numerical prediction of earthquake ground motion in sedimentary basins and valleys often has to account for P-wave to S-wave speed ratios (Vp/Vs) as large as 5 and even larger, mainly in sediments below groundwater level. The ratio can attain values larger than 10 in unconsolidated sediments (e.g. in Ciudad de México). In a process of developing 3D optimally-accurate finite-difference schemes we encountered a serious problem with accuracy in media with large Vp/Vs ratio. This led us to investigate the very fundamental reasons for the inaccuracy. In order to identify the very basic inherent aspects of the numerical schemes responsible for their behavior with varying Vp/Vs ratio, we restricted to the most basic 2nd-order 2D numerical schemes on a uniform grid in a homogeneous medium. Although basic in the specified sense, the schemes comprise the decisive features for accuracy of wide class of numerical schemes. We investigated 6 numerical schemes: finite-difference_displacement_conventional grid (FD_D_CG) finite-element_Lobatto integration (FE_L) finite-element_Gauss integration (FE_G) finite-difference_displacement-stress_partly-staggered grid (FD_DS_PSG) finite-difference_displacement-stress_staggered grid (FD_DS_SG) finite-difference_velocity-stress_staggered grid (FD_VS_SG) We defined and calculated local errors of the schemes in amplitude and polarization. Because different schemes use different time steps, they need different numbers of time levels to calculate solution for a desired time window. Therefore, we normalized errors for a unit time. The normalization allowed for a direct comparison of errors of different schemes. Extensive numerical calculations for wide ranges of values of the Vp/Vs ratio, spatial sampling ratio, stability ratio, and entire range of directions of propagation with respect to the spatial grid led to interesting and surprising findings. Accuracy of FD_D_CG, FE_L and FE_G strongly depends on Vp/Vs ratio. The schemes are not

  12. Efficient energy stable numerical schemes for a phase field moving contact line model

    NASA Astrophysics Data System (ADS)

    Shen, Jie; Yang, Xiaofeng; Yu, Haijun

    2015-03-01

    In this paper, we present two efficient energy stable schemes to solve a phase field model incorporating moving contact line. The model is a coupled system that consists of incompressible Navier-Stokes equations with a generalized Navier boundary condition and Cahn-Hilliard equation in conserved form. In both schemes the projection method is used to deal with the Navier-Stokes equations and stabilization approach is used for the non-convex Ginzburg-Landau bulk potential. By some subtle explicit-implicit treatments, we obtain a linear coupled energy stable scheme for systems with dynamic contact line conditions and a linear decoupled energy stable scheme for systems with static contact line conditions. An efficient spectral-Galerkin spatial discretization method is implemented to verify the accuracy and efficiency of proposed schemes. Numerical results show that the proposed schemes are very efficient and accurate.

  13. Navier-Stokes simulations of blade-vortex interaction using high-order accurate upwind schemes

    NASA Technical Reports Server (NTRS)

    Rai, Man Mohan

    1987-01-01

    Conventional, spatially second-order-accurate, finite-difference schemes are much too dissipative for calculations involving vortices that travel large distances (relative to some measure of the size of the vortex). This study presents a fifth-order-accurate upwind-biased scheme that preserves vortex structure for much longer times than existing second-order-accurate central and upwind difference schemes. Vortex calculations demonstrating this aspect of the fifth-order scheme are also presented. The method is then applied to the blade-vortex interaction problem. Results for strong interactions wherein the vortex impinges directly on the airfoil or a shock associated with the airfoil are presented. None of these calculations required any modeling of the shape, size, and trajectory of the interacting vortex.

  14. 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.

  15. A practical numerical scheme for the ternary Cahn-Hilliard system with a logarithmic free energy

    NASA Astrophysics Data System (ADS)

    Jeong, Darae; Kim, Junseok

    2016-01-01

    We consider a practically stable finite difference method for the ternary Cahn-Hilliard system with a logarithmic free energy modeling the phase separation of a three-component mixture. The numerical scheme is based on a linear unconditionally gradient stable scheme by Eyre and is solved by an efficient and accurate multigrid method. The logarithmic function has a singularity at zero. To remove the singularity, we regularize the function near zero by using a quadratic polynomial approximation. We perform a convergence test, a linear stability analysis, and a robustness test of the ternary Cahn-Hilliard equation. We observe that our numerical solutions are convergent, consistent with the exact solutions of linear stability analysis, and stable with practically large enough time steps. Using the proposed numerical scheme, we also study the temporal evolution of morphology patterns during phase separation in one-, two-, and three-dimensional spaces.

  16. Optimal monotonization of a high-order accurate bicompact scheme for the nonstationary multidimensional transport equation

    NASA Astrophysics Data System (ADS)

    Aristova, E. N.; Rogov, B. V.; Chikitkin, A. V.

    2016-06-01

    A hybrid scheme is proposed for solving the nonstationary inhomogeneous transport equation. The hybridization procedure is based on two baseline schemes: (1) a bicompact one that is fourth-order accurate in all space variables and third-order accurate in time and (2) a monotone first-order accurate scheme from the family of short characteristic methods with interpolation over illuminated faces. It is shown that the first-order accurate scheme has minimal dissipation, so it is called optimal. The solution of the hybrid scheme depends locally on the solutions of the baseline schemes at each node of the space-time grid. A monotonization procedure is constructed continuously and uniformly in all mesh cells so as to keep fourth-order accuracy in space and third-order accuracy in time in domains where the solution is smooth, while maintaining a high level of accuracy in domains of discontinuous solution. Due to its logical simplicity and uniformity, the algorithm is well suited for supercomputer simulation.

  17. 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

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

    NASA Astrophysics Data System (ADS)

    Sagiyama, K.; Rudraraju, S.; Garikipati, K.

    2016-11-01

    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 scale 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.

  19. Towards numerically accurate many-body perturbation theory: Short-range correlation effects

    SciTech Connect

    Gulans, Andris

    2014-10-28

    The example of the uniform electron gas is used for showing that the short-range electron correlation is difficult to handle numerically, while it noticeably contributes to the self-energy. Nonetheless, in condensed-matter applications studied with advanced methods, such as the GW and random-phase approximations, it is common to neglect contributions due to high-momentum (large q) transfers. Then, the short-range correlation is poorly described, which leads to inaccurate correlation energies and quasiparticle spectra. To circumvent this problem, an accurate extrapolation scheme is proposed. It is based on an analytical derivation for the uniform electron gas presented in this paper, and it provides an explanation why accurate GW quasiparticle spectra are easy to obtain for some compounds and very difficult for others.

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

    SciTech Connect

    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.

  1. Accurate Orbital Integration of the General Three-body Problem Based on the d'Alembert-type Scheme

    NASA Astrophysics Data System (ADS)

    Minesaki, Yukitaka

    2013-03-01

    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.

  2. 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.

  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. 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.

  5. Quantitative evaluation of numerical integration schemes for Lagrangian particle dispersion models

    NASA Astrophysics Data System (ADS)

    Ramli, Huda Mohd.; Esler, J. Gavin

    2016-07-01

    A rigorous methodology for the evaluation of integration schemes for Lagrangian particle dispersion models (LPDMs) is presented. A series of one-dimensional test problems are introduced, for which the Fokker-Planck equation is solved numerically using a finite-difference discretisation in physical space and a Hermite function expansion in velocity space. Numerical convergence errors in the Fokker-Planck equation solutions are shown to be much less than the statistical error associated with a practical-sized ensemble (N = 106) of LPDM solutions; hence, the former can be used to validate the latter. The test problems are then used to evaluate commonly used LPDM integration schemes. The results allow for optimal time-step selection for each scheme, given a required level of accuracy. The following recommendations are made for use in operational models. First, if computational constraints require the use of moderate to long time steps, it is more accurate to solve the random displacement model approximation to the LPDM rather than use existing schemes designed for long time steps. Second, useful gains in numerical accuracy can be obtained, at moderate additional computational cost, by using the relatively simple "small-noise" scheme of Honeycutt.

  6. PDE-based Morphology for Matrix Fields: Numerical Solution Schemes

    NASA Astrophysics Data System (ADS)

    Burgeth, Bernhard; Breuß, Michael; Didas, Stephan; Weickert, Joachim

    Tensor fields are important in digital imaging and computer vision. Hence there is a demand for morphological operations to perform e.g. shape analysis, segmentation or enhancement procedures. Recently, fundamental morphological concepts have been transferred to the setting of fields of symmetric positive definite matrices, which are symmetric rank two tensors. This has been achieved by a matrix-valued extension of the nonlinear morphological partial differential equations (PDEs) for dilation and erosion known for grey scale images. Having these two basic operations at our disposal, more advanced morphological operators such as top hats or morphological derivatives for matrix fields with symmetric, positive semidefinite matrices can be constructed. The approach realises a proper coupling of the matrix channels rather than treating them independently. However, from the algorithmic side the usual scalar morphological PDEs are transport equations that require special upwind-schemes or novel high-accuracy predictor-corrector approaches for their adequate numerical treatment. In this chapter we propose the non-trivial extension of these schemes to the matrix-valued setting by exploiting the special algebraic structure available for symmetric matrices. Furthermore we compare the performance and juxtapose the results of these novel matrix-valued high-resolution-type (HRT) numerical schemes by considering top hats and morphological derivatives applied to artificial and real world data sets.

  7. Numerical dissipation control in high order shock-capturing schemes for LES of low speed flows

    NASA Astrophysics Data System (ADS)

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

    2016-02-01

    The Yee & Sjögreen adaptive numerical dissipation control in high order scheme (High Order Filter Methods for Wide Range of Compressible Flow Speeds, ICOSAHOM 09, 2009) is further improved for DNS and LES of shock-free turbulence and low speed turbulence with shocklets. There are vastly different requirements in the minimization of numerical dissipation for accurate turbulence simulations of different compressible flow types and flow speeds. Traditionally, the method of choice for shock-free turbulence and low speed turbulence are by spectral, high order central or high order compact schemes with high order linear filters. With a proper control of a local flow sensor, appropriate amount of numerical dissipation in high order shock-capturing schemes can have spectral-like accuracy for compressible low speed turbulent flows. The development of the method includes an adaptive flow sensor with automatic selection on the amount of numerical dissipation needed at each flow location for more accurate DNS and LES simulations with less tuning of parameters for flows with a wide range of flow speed regime during the time-accurate evolution, e.g., time varying random forcing. An automatic selection of the different flow sensors catered to the different flow types is constructed. A Mach curve and high-frequency oscillation indicators are used to reduce the tuning of parameters in controlling the amount of shock-capturing numerical dissipation to be employed for shock-free turbulence, low speed turbulence and turbulence with strong shocks. In Kotov et al. (High Order Numerical Methods for LES of Turbulent Flows with Shocks, ICCFD8, Chengdu, Sichuan, China, July 14-18, 2014) the LES of a turbulent flow with a strong shock by the Yee & Sjögreen scheme indicated a good agreement with the filtered DNS data. A work in progress for the application of the adaptive flow sensor for compressible turbulence with time-varying random forcing is forthcoming. The present study examines the

  8. A solution accurate, efficient and stable unsplit staggered mesh scheme for three dimensional magnetohydrodynamics

    NASA Astrophysics Data System (ADS)

    Lee, Dongwook

    2013-06-01

    In this paper, we extend the unsplit staggered mesh scheme (USM) for 2D magnetohydrodynamics (MHD) [D. Lee, A.E. Deane, An unsplit staggered mesh scheme for multidimensional magnetohydrodynamics, J. Comput. Phys. 228 (2009) 952-975] to a full 3D MHD scheme. The scheme is a finite-volume Godunov method consisting of a constrained transport (CT) method and an efficient and accurate single-step, directionally unsplit multidimensional data reconstruction-evolution algorithm, which extends Colella's original 2D corner transport upwind (CTU) method [P. Colella, Multidimensional upwind methods for hyperbolic conservation laws, J. Comput. Phys. 87 (1990) 446-466]. We present two types of data reconstruction-evolution algorithms for 3D: (1) a reduced CTU scheme and (2) a full CTU scheme. The reduced 3D CTU scheme is a variant of a simple 3D extension of Collela's 2D CTU method and is considered as a direct extension from the 2D USM scheme. The full 3D CTU scheme is our primary 3D solver which includes all multidimensional cross-derivative terms for stability. The latter method is logically analogous to the 3D unsplit CTU method by Saltzman [J. Saltzman, An unsplit 3D upwind method for hyperbolic conservation laws, J. Comput. Phys. 115 (1994) 153-168]. The major novelties in our algorithms are twofold. First, we extend the reduced CTU scheme to the full CTU scheme which is able to run with CFL numbers close to unity. Both methods utilize the transverse update technique developed in the 2D USM algorithm to account for transverse fluxes without solving intermediate Riemann problems, which in turn gives cost-effective 3D methods by reducing the total number of Riemann solves. The proposed algorithms are simple and efficient especially when including multidimensional MHD terms that maintain in-plane magnetic field dynamics. Second, we introduce a new CT scheme that makes use of proper upwind information in taking averages of electric fields. Our 3D USM schemes can be easily

  9. Numerical solution of a semilinear elliptic equation via difference scheme

    NASA Astrophysics Data System (ADS)

    Beigmohammadi, Elif Ozturk; Demirel, Esra

    2016-08-01

    We consider the Bitsadze-Samarskii type nonlocal boundary value problem { -d/2v (t ) d t2 +B v (t ) =h (t ,v (t ) ) ,0 scheme. The numerical results are computed by MATLAB.

  10. Numerical evolution of multiple black holes with accurate initial data

    SciTech Connect

    Galaviz, Pablo; Bruegmann, Bernd; Cao Zhoujian

    2010-07-15

    We present numerical evolutions of three equal-mass black holes using the moving puncture approach. We calculate puncture initial data for three black holes solving the constraint equations by means of a high-order multigrid elliptic solver. Using these initial data, we show the results for three black hole evolutions with sixth-order waveform convergence. We compare results obtained with the BAM and AMSS-NCKU codes with previous results. The approximate analytic solution to the Hamiltonian constraint used in previous simulations of three black holes leads to different dynamics and waveforms. We present some numerical experiments showing the evolution of four black holes and the resulting gravitational waveform.

  11. 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.

  12. 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. PMID:27070155

  13. 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.

  14. 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

  15. Accurate scoring of non-uniform sampling schemes for quantitative NMR

    PubMed Central

    Aoto, Phillip C.; Fenwick, R. Bryn; Kroon, Gerard J. A.; Wright, Peter E.

    2014-01-01

    Non-uniform sampling (NUS) in NMR spectroscopy is a recognized and powerful tool to minimize acquisition time. Recent advances in reconstruction methodologies are paving the way for the use of NUS in quantitative applications, where accurate measurement of peak intensities is crucial. The presence or absence of NUS artifacts in reconstructed spectra ultimately determines the success of NUS in quantitative NMR. The quality of reconstructed spectra from NUS acquired data is dependent upon the quality of the sampling scheme. Here we demonstrate that the best performing sampling schemes make up a very small percentage of the total randomly generated schemes. A scoring method is found to accurately predict the quantitative similarity between reconstructed NUS spectra and those of fully sampled spectra. We present an easy-to-use protocol to batch generate and rank optimal Poisson-gap NUS schedules for use with 2D NMR with minimized noise and accurate signal reproduction, without the need for the creation of synthetic spectra. PMID:25063954

  16. Efficient Schemes for Reducing Numerical Dispersion in ModelingMultiphase Transport through Porous and Fractured Media

    SciTech Connect

    Wu, Yu-Shu; Forsyth, Peter A.

    2006-04-13

    Numerical issues with modeling transport of chemicals or solute in realistic large-scale subsurface systems have been a serious concern, even with the continual progress made in both simulation algorithms and computer hardware in the past few decades. The problem remains and becomes even more difficult when dealing with chemical transport in a multiphase flow system using coarse, multidimensional regular or irregular grids, because of the known effects of numerical dispersion associated with moving plume fronts. We have investigated several total-variation-diminishing (TVD) or flux-limiter schemes by implementing and testing them in the T2R3D code, one of the TOUGH2 family of codes. The objectives of this paper are (1) to investigate the possibility of applying these TVD schemes, using multi-dimensional irregular unstructured grids, and (2) to help select more accurate spatial averaging methods for simulating chemical transport given a numerical grid or spatial discretization. We present an application example to show that such TVD schemes are able to effectively reduce numerical dispersion.

  17. 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.

  18. Third-order accurate entropy-stable schemes for initial-boundary-value conservation laws

    NASA Astrophysics Data System (ADS)

    Svärd, Magnus

    2012-08-01

    We consider initial-boundary-value conservation laws with the objective to obtain high-order approximations. We study two different approaches to obtain third-order accuracy, local entropy stability and a global bound on the entropy. The results are applicable to, for example the Euler equations of gas dynamics, for which we present numerical results demonstrating the robustness and accuracy of the scheme.

  19. Accurate numerical simulation of short fiber optical parametric amplifiers.

    PubMed

    Marhic, M E; Rieznik, A A; Kalogerakis, G; Braimiotis, C; Fragnito, H L; Kazovsky, L G

    2008-03-17

    We improve the accuracy of numerical simulations for short fiber optical parametric amplifiers (OPAs). Instead of using the usual coarse-step method, we adopt a model for birefringence and dispersion which uses fine-step variations of the parameters. We also improve the split-step Fourier method by exactly treating the nonlinear ellipse rotation terms. We find that results obtained this way for two-pump OPAs can be significantly different from those obtained by using the usual coarse-step fiber model, and/or neglecting ellipse rotation terms.

  20. A numerical study of a class of TVD schemes for compressible mixing layers

    NASA Technical Reports Server (NTRS)

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

    1989-01-01

    At high Mach numbers the two-dimensional time-developing mixing layer develops shock waves, positioned around large-scale vortical structures. A suitable numerical method has to be able to capture the inherent instability of the flow, leading to the roll-up of vortices, and also must be able to capture shock waves when they develop. Standard schemes for low speed turbulent flows, for example spectral methods, rely on resolution of all flow-features and cannot handle shock waves, which become too thin at any realistic Reynolds number. The performance of a class of second-order explicit total variation diminishing (TVD) schemes on a compressible mixing layer problem was studied. The basic idea is to capture the physics of the flow correctly, by resolving down to the smallest turbulent length scales, without resorting to turbulence or sub-grid scale modeling, and at the same time capture shock waves without spurious oscillations. The present study indicates that TVD schemes can capture the shocks accurately when they form, but (without resorting to a finer grid) have poor accuracy in computing the vortex growth. The solution accuracy depends on the choice of limiter. However a larger number of grid points are in general required to resolve the correct vortex growth. The low accuracy in computing time-dependent problems containing shock waves as well as vortical structures is partly due to the inherent shock-capturing property of all TVD schemes. In order to capture shock waves without spurious oscillations these schemes reduce to first-order near extrema and indirectly produce clipping phenomena, leading to inaccuracy in the computation of vortex growth. Accurate simulation of unsteady turbulent fluid flows with shock waves will require further development of efficient, uniformly higher than second-order accurate, shock-capturing methods.

  1. Numerical issues for coupling biological models with isopycnal mixing schemes

    NASA Astrophysics Data System (ADS)

    Gnanadesikan, Anand

    1999-01-01

    In regions of sloping isopycnals, isopycnal mixing acting in conjunction with biological cycling can produce patterns in the nutrient field which have negative values of tracer in light water and unrealistically large values of tracer in dense water. Under certain circumstances, these patterns can start to grow unstably. This paper discusses why such behavior occurs. Using a simple four-box model, it demonstrates that the instability appears when the isopycnal slopes exceed the grid aspect ratio ( Δz/ Δx). In contrast to other well known instabilities of the CFL type, this instability does not depend on the time step or time-stepping scheme. Instead it arises from a fundamental incompatibility between two requirements for isopycnal mixing schemes, namely that they should produce no net flux of passive tracer across an isopycnal and everywhere reduce tracer extrema. In order to guarantee no net flux of tracer across an isopycnal, some upgradient fluxes across certain parts of an isopycnal are required to balance downgradient fluxes across other parts of the isopycnal. However, these upgradient fluxes can cause local maxima in the nutrient field to become self-reinforcing. Although this is less of a problem in larger domains, there is still a strong tendency for isopycnal mixing to overconcentrate tracer in the dense water. The introduction of eddy-induced advection is shown to be capable of counteracting the upgradient fluxes of nutrient which cause problems, stabilizing the solution. The issue is not simply a numerical curiosity. When used in a GCM, different parameterizations of eddy mixing result in noticeably different distributions of nutrient and large differences in biological production. While much of this is attributable to differences in convection and circulation, the numerical errors described here may also play an important role in runs with isopycnal mixing alone.

  2. 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.

  3. A numerical scheme for coastal morphodynamic modelling on unstructured grids

    NASA Astrophysics Data System (ADS)

    Guerin, Thomas; Bertin, Xavier; Dodet, Guillaume

    2016-08-01

    Over the last decade, modelling systems based on unstructured grids have been appearing increasingly attractive to investigate the dynamics of coastal zones. However, the resolution of the sediment continuity equation to simulate bed evolution is a complex problem which often leads to the development of numerical oscillations. To overcome this problem, addition of artificial diffusion or bathymetric filters are commonly employed methods, although these techniques can potentially over-smooth the bathymetry. This study aims to present a numerical scheme based on the Weighted Essentially Non-Oscillatory (WENO) formalism to solve the bed continuity equation on unstructured grids in a finite volume formulation. The new solution is compared against a classical method, which combines a basic node-centered finite volume method with artificial diffusion, for three idealized test cases. This comparison reveals that a higher accuracy is obtained with our new method while the addition of diffusion appears inappropriate mainly due to the arbitrary choice of the diffusion coefficient. Moreover, the increased computation time associated with the WENO-based method to solve the bed continuity equation is negligible when considering a fully-coupled simulation with tides and waves. Finally, the application of the new method to the pluri-monthly evolution of an idealized inlet subjected to tides and waves shows the development of realistic bed features (e.g. secondary flood channels, ebb-delta sandbars, or oblique sandbars at the adjacent beaches), that are smoothed or nonexistent when using additional diffusion.

  4. 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.

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

    PubMed

    Pershin, Anton; Szalay, Péter G

    2015-08-21

    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, it 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. PMID:26298117

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

    SciTech Connect

    Pershin, Anton; Szalay, Péter G.

    2015-08-21

    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, it 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.

  7. 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

  8. 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.

  9. Efficient numerical schemes for viscoplastic avalanches. Part 1: The 1D case

    SciTech Connect

    Fernández-Nieto, Enrique D.

    2014-05-01

    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. We derived such schemes and numerical experiments are presented to show their performances.

  10. Numerical study of chemically reacting flows using an LU scheme

    NASA Technical Reports Server (NTRS)

    Shuen, Jian Shun; Yoon, Seokkwan

    1988-01-01

    A new computational fluid dynamic code has been developed for the study of mixing and chemical reactions in the flow fields of ramjets and scramjets. The code employs an implicit finite volume, lower-upper symmetric successive overrelaxation scheme for solving the complete two-dimensional Navier-Stokes equations and species transport equations in a fully-coupled and very efficient manner. The combustion processes are modeled by an 8-species, 14-step finite rate chemistry model whereas turbulence is simulated by a Baldwin-Lomax algebraic model. The validity of the code is demonstrated by comparing the numerical calculations with both experimental data and previous calculations of a cold flow helium injection into a straight channel and premixed hydrogen-air reacting flows in a ramped duct. The code is then used to calculate the mixing and chemical reactions of a hydrogen jet transversely injected into a supersonic airstream. Results are presented describing the flow field, the recirculation regions in front and behind the injector, and the chemical reactions.

  11. 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.

  12. 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.

  13. On the very accurate numerical evaluation of the Generalized Fermi-Dirac Integrals

    NASA Astrophysics Data System (ADS)

    Mohankumar, N.; Natarajan, A.

    2016-10-01

    We indicate a new and a very accurate algorithm for the evaluation of the Generalized Fermi-Dirac Integral with a relative error less than 10-20. The method involves Double Exponential, Trapezoidal and Gauss-Legendre quadratures. For the residue correction of the Gauss-Legendre scheme, a simple and precise continued fraction algorithm is used.

  14. Numerical Modeling of Deep Mantle Convection: Advection and Diffusion Schemes for Marker Methods

    NASA Astrophysics Data System (ADS)

    Mulyukova, Elvira; Dabrowski, Marcin; Steinberger, Bernhard

    2013-04-01

    that we use for this study, the velocity field is discretised using second order triangular elements, which gives second order accuracy of interpolation from grid-nodes to markers. A fourth order Runge-Kutta solver is used to compute marker-trajectories. We reevaluate the velocity field for each of the intermediate steps of the ODE-solver, rendering our advection scheme to be fourth-order accurate in time. We compare two different approaches for performing the thermal diffusion step. In the first, more conventional approach, the energy equation is solved on a static grid. For this grid, we use first-order triangular elements and a higher resolution than for the velocity-grid, to compensate for the lower order elements. The temperature field is transferred between grid-nodes and markers, and a subgrid diffusion correction step (Gerya and Yuen, 2003) is included to account for the different spatial resolutions of the markers and the grid. In the second approach, the energy equation is solved directly on markers. To do this, we compute a constrained Delaunay triangulation, with markers as nodes, at every time step. We wish to resolve the large range of spatial scales of the solution at lowest possible computational cost. In several existing codes this is achieved with dynamically adaptive meshes, which use high resolution in regions with high solution gradients, and vice versa. The numerical scheme used in this study can be extended to include a similar feature, by regenerating the thermal and mechanical grids in the course of computation, adapting them to the temperature and chemistry fields carried by the markers. We present the results of thermochemical convection simulations obtained using the schemes outlined above, as well as the results of the numerical benchmarks commonly used in the geodynamics community. The quality of the solutions, as well as the computational cost of our schemes, are discussed.

  15. 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...

  16. Finite volume schemes optimized for low numerical dispersion and their aeroacoustic applications

    NASA Astrophysics Data System (ADS)

    Nance, Douglas Vinson

    1997-11-01

    The field of computational aeroacoustics is concerned with the calculation of acoustic fluctuations in an aerodynamic flow field. Moreover, it is desirable to resolve the spectral content and directivity of the aeroacoustic field with high accuracy. For the purposes of the designer, it is preferable to endow a computational fluid dynamics code with some capability for predicting aeroacoustic information. If the prediction algorithm can be written within the current flow solver's structure, the costly acquisition of a new code is not necessary. In an effort to provide designers with this option, a new finite volume methodology is developed in the present work. Three families of upwind, finite volume schemes are developed and demonstrated for a series of aeroacoustics problems. These new low dispersion finite volume schemes are designed to mitigate numerical dispersion and dissipation errors in the computational space while achieving high formal orders of accuracy. Variable extrapolation stands as the framework for these methods. In this case, the cell face variables are interpolated from cell nodes by using a procedure that optimizes the stencil representation of flow field properties in terms of sinusoidal waves. This procedure renders an accurate representation of these properties for a higher range of numerical wavenumbers. In addition, an unsteady, farfield boundary treatment is proposed. This low reflectivity farfield boundary treatment is designed as an integral part of the finite volume discretization procedure. This technique is very robust and causes only minimal reflection at the farfield boundary. The low dispersion finite volume schemes have been applied to a number of aeroacoustics problems. The numerical results are shown and compared either to exact solutions or to the results computed by other schemes. Good agreement with the exact solutions is evident. Results are also shown for the problem of laminar vortex- shedding from a circular cylinder. The

  17. IDO Scheme for Accurate Computation of Seismic Waves I. Plane-Wave Response of a Vertically Heterogeneous Medium

    NASA Astrophysics Data System (ADS)

    Ohkawauchi, K.; Takenaka, H.

    2006-12-01

    We propose a new method for the calculation of seismic wave propagation using the interpolated differential operator (IDO, Aoki,1997) which is a numerical method for solving the partial differential equations and is based on a high accurate interpolation of the profile for the independent variables over a local area. It improves the accuracy of wave computation with high accuracy because the local interpolation can represent high order behavior of wave field between grid points. In addition, locality of this approach makes possible treatment of boundary conditions exactly. In this study, we address computation of plane-wave responses of vertically heterogeneous structure models. We then solve the elastodynamic equation for plane wave derived by Tanaka and Takenaka (2005). The equations to be solved in our method are not only velocity-stress equations but also the corresponding ones integrated over each cell between adjacent grid points. We use two staggered-grid systems which can be non-uniform, and then discretize the governing equations using a finite-difference scheme of second-order accurate in time, and the second-order Hermite interpolation in space. In this method, the second-order Hermite interpolation of particle velocity or stress is obtained from the values at the adjacent two grid points and the integration value at the cell between the grid points. The time marching of the original and integrated quantities are proceeded, and in the following time step the quantities are computed on the alternative grid system to that used in the current time step. In implementation of a free-surface boundary condition, all field quantities locate just on the free surface. Their computational accuracy is the same order as those in the other spatial domain. We also implement the interface condition in a similarly way to the free surface condition. We used some simple models to test the scheme. The results showed that the waveforms calculated by our method fit the

  18. A benchmark study of numerical schemes for one-dimensional arterial blood flow modelling.

    PubMed

    Boileau, Etienne; Nithiarasu, Perumal; Blanco, Pablo J; Müller, Lucas O; Fossan, Fredrik Eikeland; Hellevik, Leif Rune; Donders, Wouter P; Huberts, Wouter; Willemet, Marie; Alastruey, Jordi

    2015-10-01

    Haemodynamical simulations using one-dimensional (1D) computational models exhibit many of the features of the systemic circulation under normal and diseased conditions. Recent interest in verifying 1D numerical schemes has led to the development of alternative experimental setups and the use of three-dimensional numerical models to acquire data not easily measured in vivo. In most studies to date, only one particular 1D scheme is tested. In this paper, we present a systematic comparison of six commonly used numerical schemes for 1D blood flow modelling: discontinuous Galerkin, locally conservative Galerkin, Galerkin least-squares finite element method, finite volume method, finite difference MacCormack method and a simplified trapezium rule method. Comparisons are made in a series of six benchmark test cases with an increasing degree of complexity. The accuracy of the numerical schemes is assessed by comparison with theoretical results, three-dimensional numerical data in compatible domains with distensible walls or experimental data in a network of silicone tubes. Results show a good agreement among all numerical schemes and their ability to capture the main features of pressure, flow and area waveforms in large arteries. All the information used in this study, including the input data for all benchmark cases, experimental data where available and numerical solutions for each scheme, is made publicly available online, providing a comprehensive reference data set to support the development of 1D models and numerical schemes.

  19. An accurate numerical solution to the Saint-Venant-Hirano model for mixed-sediment morphodynamics in rivers

    NASA Astrophysics Data System (ADS)

    Stecca, Guglielmo; Siviglia, Annunziato; Blom, Astrid

    2016-07-01

    We present an accurate numerical approximation to the Saint-Venant-Hirano model for mixed-sediment morphodynamics in one space dimension. Our solution procedure originates from the fully-unsteady matrix-vector formulation developed in [54]. The principal part of the problem is solved by an explicit Finite Volume upwind method of the path-conservative type, by which all the variables are updated simultaneously in a coupled fashion. The solution to the principal part is embedded into a splitting procedure for the treatment of frictional source terms. The numerical scheme is extended to second-order accuracy and includes a bookkeeping procedure for handling the evolution of size stratification in the substrate. We develop a concept of balancedness for the vertical mass flux between the substrate and active layer under bed degradation, which prevents the occurrence of non-physical oscillations in the grainsize distribution of the substrate. We suitably modify the numerical scheme to respect this principle. We finally verify the accuracy in our solution to the equations, and its ability to reproduce one-dimensional morphodynamics due to streamwise and vertical sorting, using three test cases. In detail, (i) we empirically assess the balancedness of vertical mass fluxes under degradation; (ii) we study the convergence to the analytical linearised solution for the propagation of infinitesimal-amplitude waves [54], which is here employed for the first time to assess a mixed-sediment model; (iii) we reproduce Ribberink's E8-E9 flume experiment [46].

  20. 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.

  1. Accurate thermochemistry of hydrocarbon radicals via an extended generalized bond separation reaction scheme.

    PubMed

    Wodrich, Matthew D; Corminboeuf, Clémence; Wheeler, Steven E

    2012-04-01

    Detailed knowledge of hydrocarbon radical thermochemistry is critical for understanding diverse chemical phenomena, ranging from combustion processes to organic reaction mechanisms. Unfortunately, experimental thermochemical data for many radical species tend to have large errors or are lacking entirely. Here we develop procedures for deriving high-quality thermochemical data for hydrocarbon radicals by extending Wheeler et al.'s "generalized bond separation reaction" (GBSR) scheme (J. Am. Chem. Soc., 2009, 131, 2547). Moreover, we show that the existing definition of hyperhomodesmotic reactions is flawed. This is because transformation reactions, in which one molecule each from the predefined sets of products and reactants can be converted to a different product and reactant molecule, are currently allowed. This problem is corrected via a refined definition of hyperhomodesmotic reactions in which there are equal numbers of carbon-carbon bond types inclusive of carbon hybridization and number of hydrogens attached. Ab initio and density functional theory (DFT) computations using the expanded GBSRs are applied to a newly derived test set of 27 hydrocarbon radicals (HCR27). Greatly reduced errors in computed reaction enthalpies are seen for hyperhomodesmotic and other highly balanced reactions classes, which benefit from increased matching of hybridization and bonding requirements. The best performing DFT methods for hyperhomodesmotic reactions, M06-2X and B97-dDsC, give average deviations from benchmark computations of only 0.31 and 0.44 (±0.90 and ±1.56 at the 95% confidence level) kcal/mol, respectively, over the test set. By exploiting the high degree of error cancellation provided by hyperhomodesmotic reactions, accurate thermochemical data for hydrocarbon radicals (e.g., enthalpies of formation) can be computed using relatively inexpensive computational methods.

  2. Towards improved numerical schemes of turbulent lateral dispersion

    NASA Astrophysics Data System (ADS)

    Kämpf, Jochen; Cox, Darren

    2016-10-01

    This paper focuses on an alternative approach of lateral turbulent dispersion, proposed by Benoit Cushman-Roisin in 2008, that is based on a linear increase of the width of dispersing patches in a field of isotropic horizontal turbulence. In the open ocean, this Richardson-like dispersion regime is a well-observed feature on sub-mesoscale length scales from 10 to 100 km. In this work, we successfully validate and calibrate the new diffusion scheme using Lagrangian particles and Eulerian tracer in turbulent velocity fields simulated with the shallow-water equations. In discretized form, the new diffusion scheme exclusively relies on specification of a turbulent velocity scale that, unlike the turbulent diffusivity of Fickian approaches, is well defined through statistical properties of the turbulent flow.

  3. 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.

  4. On some numerical scheme of solving diffraction problem on open and closed screens

    SciTech Connect

    Ryzhakov, Gleb V.

    2015-03-10

    In the paper, the problem of diffraction on thin ideally conductive screens is reduced to vector hypersingular integral equation with integral treated in the sense of finite Hadamard value. An numerical scheme to solve the equation is introduced. The scheme is based on piecewise approximation of unknown function. The advantage of the scheme is that integral of singular part is reduced to contour integral which can be analytically calculated so numerical calculation are significantly accelerated. Several examples of resulting numerical experiments are given in comparison with known theoretical and experimental data.

  5. The numerical viscosity of entropy stable schemes for systems of conservation laws. I

    NASA Technical Reports Server (NTRS)

    Tadmor, Eitan

    1987-01-01

    Discrete approximations to hyperbolic systems of conservation laws are studied. The amount of numerical viscosity present in such schemes is quantified and related to their entropy stability by means of comparison.To this end, conservative schemes which are also entropy-conservative are constructed. These entropy-conservative schemes enjoy second-order accuracy; moreover, they can be interpreted as piecewise-linear finite-element methods, and hence can be formulated on various mesh configurations. It is then shown that conservative schemes are entropy stable, if and (for three-point schemes) only they contain more viscosity than that present in the above-mentioned entropy-conservative ones.

  6. SEAWAT 2000: modelling unstable flow and sensitivity to discretization levels and numerical schemes

    NASA Astrophysics Data System (ADS)

    Al-Maktoumi, A.; Lockington, D. A.; Volker, R. E.

    2007-09-01

    A systematic analysis shows how results from the finite difference code SEAWAT are sensitive to choice of grid dimension, time step, and numerical scheme for unstable flow problems. Guidelines to assist in selecting appropriate combinations of these factors are suggested. While the SEAWAT code has been tested for a wide range of problems, the sensitivity of results to spatial and temporal discretization levels and numerical schemes has not been studied in detail for unstable flow problems. Here, the Elder-Voss-Souza benchmark problem has been used to systematically explore the sensitivity of SEAWAT output to spatio-temporal resolution and numerical solver choice. A grid size of 0.38 and 0.60% of the total domain length and depth respectively is found to be fine enough to deliver results with acceptable accuracy for most of the numerical schemes when Courant number (Cr) is 0.1. All numerical solvers produced similar results for extremely fine meshes; however, some schemes converged faster than others. For instance, the 3rd-order total variation-diminishing method (TVD3) scheme converged at a much coarser mesh than the standard finite difference methods (SFDM) upstream weighting (UW) scheme. The sensitivity of the results to Cr number depends on the numerical scheme as expected.

  7. Linear Properties of Numerical Schemes for the Shallow Water Equations

    NASA Astrophysics Data System (ADS)

    Eldred, C.; Randall, D. A.

    2013-12-01

    The shallow water equations provide a useful analogue of fully compressible Euler equations since they have similar conservation laws, many of the same types of waves and a similar (quasi-) balanced state. There has been extensive work exploring the linear properties (balanced states and propagating modes) of various schemes for the shallow water equations on uniform grids, but comparatively little work for non-uniform grids (especially in the case of finite difference and finite volume methods). With the simplifications associated with uniform grids, analytic results for the dispersion relationship and other linear properties can be obtained. However, such grids are not necessarily representative of the actual grids used in dynamical cores on the sphere. Using the Atmospheric Dynamical Core Testbed (ADCoT) built on top of Morphe, the linear properties of various popular finite-difference and finite-volume schemes are examined on both uniform and non-uniform grids (such as the cubed sphere, triangular geodesic and hexagonal-pentagonal geodesic grids).

  8. 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

  9. Finite-difference scheme for the numerical solution of the Schroedinger equation

    NASA Technical Reports Server (NTRS)

    Mickens, Ronald E.; Ramadhani, Issa

    1992-01-01

    A finite-difference scheme for numerical integration of the Schroedinger equation is constructed. Asymptotically (r goes to infinity), the method gives the exact solution correct to terms of order r exp -2.

  10. An improved snow cover scheme for high-resolution numerical weather prediction models.

    NASA Astrophysics Data System (ADS)

    Bellaire, S.; Sauter, T.; Rotach, M. W.

    2015-12-01

    Numerical weather prediction (NWP) is the core of any operational weather service. The horizontal and vertical resolution of numerical weather prediction models strongly increased during the last decades. However, numerical weather prediction in complex terrain is still challenging, because the underlying physics in the majority of subgrid-scale parameterizations have been developed for flat or idealized terrain. Weather prediction in alpine countries - such as Austria or Switzerland - is not only challenged by complex topography, furthermore, for a good part of the year the ground is snow covered influencing boundary layer processes such as turbulence and radiation. Currently, most NWP models predict the formation and evolution of the seasonal mountain snow cover in a simplified way, i.e. often a single layer model. We validated the performance of the currently implemented snow cover scheme of the COSMO model (Consortium for Small-scale Modelling) in terms of the snow surface temperature, a key parameter for the evolution of the snow cover, as well as snow height. Snow surface temperature and snow height from 120 alpine weather stations located across the Swiss Alps were compared to the corresponding COSMO output. Surface temperature was found to be overestimated especially during the night (up to 10 °C, RMSE = 6.0 °C). Snow height tends to be underestimated during the ablation phase, i.e. the COSMO model becomes snow-free too early. A new multi-layer snow module, which minimizes the energy balance equation with regard to snow surface temperature and then iteratively solves the heat equation has been implemented, predicting the daily cycle of the snow surface temperature accurately (RMSE = 1.8 °C). Furthermore, by implementing densification, melt-freeze processes and water transport snow height, especially during the ablation phase, was found to be in good agreement with the observations. Our suggested snow scheme shows promising potential not only for

  11. 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.

  12. 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).

  13. 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.

  14. High resolution schemes for hyperbolic conservation laws

    NASA Technical Reports Server (NTRS)

    Harten, A.

    1983-01-01

    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 accurate 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. Numerical experiments are presented to demonstrate the performance of these new schemes.

  15. The numerical viscosity of entropy stable schemes for systems of conservation laws

    NASA Technical Reports Server (NTRS)

    Tadmor, E.

    1985-01-01

    Discrete approximations to hyperbolic systems of conservation laws are studied. The amount of numerical viscosity present in such schemes, is quantified and related to their entropy stability by means of comparison. To this end, conservative schemes which are also entropy conservative are constructed. These entropy conservative schemes enjoy second-order accuracy; moreover, they admit a particular interpretation within the finite-element frameworks, and hence can be formulated on various mesh configurations. It is then shown that conservative schemes are entropy stable if and only if they contain more viscosity than the mentioned above entropy conservative ones.

  16. 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.

  17. 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

  18. Numerical Compression Schemes for Proteomics Mass Spectrometry Data*

    PubMed Central

    Teleman, Johan; Dowsey, Andrew W.; Gonzalez-Galarza, Faviel F.; Perkins, Simon; Pratt, Brian; Röst, Hannes L.; Malmström, Lars; Malmström, Johan; Jones, Andrew R.; Deutsch, Eric W.; Levander, Fredrik

    2014-01-01

    The open XML format mzML, used for representation of MS data, is pivotal for the development of platform-independent MS analysis software. Although conversion from vendor formats to mzML must take place on a platform on which the vendor libraries are available (i.e. Windows), once mzML files have been generated, they can be used on any platform. However, the mzML format has turned out to be less efficient than vendor formats. In many cases, the naïve mzML representation is fourfold or even up to 18-fold larger compared with the original vendor file. In disk I/O limited setups, a larger data file also leads to longer processing times, which is a problem given the data production rates of modern mass spectrometers. In an attempt to reduce this problem, we here present a family of numerical compression algorithms called MS-Numpress, intended for efficient compression of MS data. To facilitate ease of adoption, the algorithms target the binary data in the mzML standard, and support in main proteomics tools is already available. Using a test set of 10 representative MS data files we demonstrate typical file size decreases of 90% when combined with traditional compression, as well as read time decreases of up to 50%. It is envisaged that these improvements will be beneficial for data handling within the MS community. PMID:24677029

  19. A Haptic Feedback Scheme to Accurately Position a Virtual Wrist Prosthesis Using a Three-Node Tactor Array.

    PubMed

    Erwin, Andrew; Sup, Frank C

    2015-01-01

    In this paper, a novel haptic feedback scheme, used for accurately positioning a 1DOF virtual wrist prosthesis through sensory substitution, is presented. The scheme employs a three-node tactor array and discretely and selectively modulates the stimulation frequency of each tactor to relay 11 discrete haptic stimuli to the user. Able-bodied participants were able to move the virtual wrist prosthesis via a surface electromyography based controller. The participants evaluated the feedback scheme without visual or audio feedback and relied solely on the haptic feedback alone to correctly position the hand. The scheme was evaluated through both normal (perpendicular) and shear (lateral) stimulations applied on the forearm. Normal stimulations were applied through a prototype device previously developed by the authors while shear stimulations were generated using an ubiquitous coin motor vibrotactor. Trials with no feedback served as a baseline to compare results within the study and to the literature. The results indicated that using normal and shear stimulations resulted in accurately positioning the virtual wrist, but were not significantly different. Using haptic feedback was substantially better than no feedback. The results found in this study are significant since the feedback scheme allows for using relatively few tactors to relay rich haptic information to the user and can be learned easily despite a relatively short amount of training. Additionally, the results are important for the haptic community since they contradict the common conception in the literature that normal stimulation is inferior to shear. From an ergonomic perspective normal stimulation has the potential to benefit upper limb amputees since it can operate at lower frequencies than shear-based vibrotactors while also generating less noise. Through further tuning of the novel haptic feedback scheme and normal stimulation device, a compact and comfortable sensory substitution device for upper

  20. 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.

  1. Quantification of numerical diffusivity due to TVD schemes in the advection equation

    NASA Astrophysics Data System (ADS)

    Bidadi, Shreyas; Rani, Sarma L.

    2014-03-01

    In this study, the numerical diffusivity νnum inherent to the Roe-MUSCL scheme has been quantified for the scalar advection equation. The Roe-MUSCL scheme employed is a combination of: (1) the standard extension of the original Roe's formulation to the advection equation, and (2) van Leer's Monotone Upwind Scheme for Conservation Laws (MUSCL) technique that applies a linear variable reconstruction in a cell along with a scaled limiter function. An explicit expression is derived for the numerical diffusivity in terms of the limiter function, the distance between the cell centers on either side of a face, and the face-normal velocity. The numerical diffusivity formulation shows that a scaled limiter function is more appropriate for MUSCL in order to consistently recover the central-differenced flux at the maximum value of the limiter. The significance of the scaling factor is revealed when the Roe-MUSCL scheme, originally developed for 1-D scenarios, is applied to 2-D scalar advection problems. It is seen that without the scaling factor, the MUSCL scheme may not necessarily be monotonic in multi-dimensional scenarios. Numerical diffusivities of the minmod, superbee, van Leer and Barth-Jesperson TVD limiters were quantified for four problems: 1-D advection of a step function profile, and 2-D advection of step, sinusoidal, and double-step profiles. For all the cases, it is shown that the superbee scheme provides the lowest numerical diffusivity that is also most confined to the vicinity of the discontinuity. The minmod scheme is the most diffusive, as well as active in regions away from high gradients. As expected, the grid resolution study demonstrates that the magnitude and the spatial extent of the numerical diffusivity decrease with increasing resolution.

  2. 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.

  3. Final Report for "Accurate Numerical Models of the Secondary Electron Yield from Grazing-incidence Collisions".

    SciTech Connect

    Seth A Veitzer

    2008-10-21

    Effects of stray electrons are a main factor limiting performance of many accelerators. Because heavy-ion fusion (HIF) accelerators will operate in regimes of higher current and with walls much closer to the beam than accelerators operating today, stray electrons might have a large, detrimental effect on the performance of an HIF accelerator. A primary source of stray electrons is electrons generated when halo ions strike the beam pipe walls. There is some research on these types of secondary electrons for the HIF community to draw upon, but this work is missing one crucial ingredient: the effect of grazing incidence. The overall goal of this project was to develop the numerical tools necessary to accurately model the effect of grazing incidence on the behavior of halo ions in a HIF accelerator, and further, to provide accurate models of heavy ion stopping powers with applications to ICF, WDM, and HEDP experiments.

  4. An Analysis of Two Schemes to Numerically Solve the Stochastic Collection Growth Equation.

    NASA Astrophysics Data System (ADS)

    de Almeida, Fausto Carlos; Dennett, Roger D.

    1980-12-01

    Two schemes for the numerical solution of the stochastic collection growth equation for cloud drops are compared. Their numerical approaches are different. One (the Berry/Reinhardt method) emphasizes accuracy; the other (the Bleck method) emphasizes speed. Our analysis shows that for applications where the number of solutions (time steps) does not exceed 104 the accuracy-oriented scheme is faster. For larger, repetitive applications, such as a comprehensive cloud model, an objective analysis can be made on the merits of exchanging accuracy for computational time.

  5. Efficient and accurate numerical methods for the Klein-Gordon-Schroedinger equations

    SciTech Connect

    Bao, Weizhu . E-mail: bao@math.nus.edu.sg; Yang, Li . E-mail: yangli@nus.edu.sg

    2007-08-10

    In this paper, we present efficient, unconditionally stable and accurate numerical methods for approximations of the Klein-Gordon-Schroedinger (KGS) equations with/without damping terms. The key features of our methods are based on: (i) the application of a time-splitting spectral discretization for a Schroedinger-type equation in KGS (ii) the utilization of Fourier pseudospectral discretization for spatial derivatives in the Klein-Gordon equation in KGS (iii) the adoption of solving the ordinary differential equations (ODEs) in phase space analytically under appropriate chosen transmission conditions between different time intervals or applying Crank-Nicolson/leap-frog for linear/nonlinear terms for time derivatives. The numerical methods are either explicit or implicit but can be solved explicitly, unconditionally stable, and of spectral accuracy in space and second-order accuracy in time. Moreover, they are time reversible and time transverse invariant when there is no damping terms in KGS, conserve (or keep the same decay rate of) the wave energy as that in KGS without (or with a linear) damping term, keep the same dynamics of the mean value of the meson field, and give exact results for the plane-wave solution. Extensive numerical tests are presented to confirm the above properties of our numerical methods for KGS. Finally, the methods are applied to study solitary-wave collisions in one dimension (1D), as well as dynamics of a 2D problem in KGS.

  6. Size-extensivity-corrected multireference configuration interaction schemes to accurately predict bond dissociation energies of oxygenated hydrocarbons

    SciTech Connect

    Oyeyemi, Victor B.; Krisiloff, David B.; Keith, John A.; Libisch, Florian; Pavone, Michele; Carter, Emily A.

    2014-01-28

    Oxygenated hydrocarbons play important roles in combustion science as renewable fuels and additives, but many details about their combustion chemistry remain poorly understood. Although many methods exist for computing accurate electronic energies of molecules at equilibrium geometries, a consistent description of entire combustion reaction potential energy surfaces (PESs) requires multireference correlated wavefunction theories. Here we use bond dissociation energies (BDEs) as a foundational metric to benchmark methods based on multireference configuration interaction (MRCI) for several classes of oxygenated compounds (alcohols, aldehydes, carboxylic acids, and methyl esters). We compare results from multireference singles and doubles configuration interaction to those utilizing a posteriori and a priori size-extensivity corrections, benchmarked against experiment and coupled cluster theory. We demonstrate that size-extensivity corrections are necessary for chemically accurate BDE predictions even in relatively small molecules and furnish examples of unphysical BDE predictions resulting from using too-small orbital active spaces. We also outline the specific challenges in using MRCI methods for carbonyl-containing compounds. The resulting complete basis set extrapolated, size-extensivity-corrected MRCI scheme produces BDEs generally accurate to within 1 kcal/mol, laying the foundation for this scheme's use on larger molecules and for more complex regions of combustion PESs.

  7. Size-extensivity-corrected multireference configuration interaction schemes to accurately predict bond dissociation energies of oxygenated hydrocarbons

    NASA Astrophysics Data System (ADS)

    Oyeyemi, Victor B.; Krisiloff, David B.; Keith, John A.; Libisch, Florian; Pavone, Michele; Carter, Emily A.

    2014-01-01

    Oxygenated hydrocarbons play important roles in combustion science as renewable fuels and additives, but many details about their combustion chemistry remain poorly understood. Although many methods exist for computing accurate electronic energies of molecules at equilibrium geometries, a consistent description of entire combustion reaction potential energy surfaces (PESs) requires multireference correlated wavefunction theories. Here we use bond dissociation energies (BDEs) as a foundational metric to benchmark methods based on multireference configuration interaction (MRCI) for several classes of oxygenated compounds (alcohols, aldehydes, carboxylic acids, and methyl esters). We compare results from multireference singles and doubles configuration interaction to those utilizing a posteriori and a priori size-extensivity corrections, benchmarked against experiment and coupled cluster theory. We demonstrate that size-extensivity corrections are necessary for chemically accurate BDE predictions even in relatively small molecules and furnish examples of unphysical BDE predictions resulting from using too-small orbital active spaces. We also outline the specific challenges in using MRCI methods for carbonyl-containing compounds. The resulting complete basis set extrapolated, size-extensivity-corrected MRCI scheme produces BDEs generally accurate to within 1 kcal/mol, laying the foundation for this scheme's use on larger molecules and for more complex regions of combustion PESs.

  8. A numerical method for solving the Vlasov-Poisson equation based on the conservative IDO scheme

    NASA Astrophysics Data System (ADS)

    Imadera, Kenji; Kishimoto, Yasuaki; Saito, Daisuke; Li, Jiquan; Utsumi, Takayuki

    2009-12-01

    We have applied the conservative form of the Interpolated Differential Operator (IDO-CF) scheme in order to solve the Vlasov-Poisson equation, which is one of the multi-moment schemes. Through numerical tests of the nonlinear Landau damping and two-stream instability, we compared the present scheme with other schemes such as the Spline and CIP ones. We mainly investigated the conservation property of the L1-norm, energy, entropy and phase space area for each scheme, and demonstrated that the IDO-CF scheme is capable of performing stable long time scale simulation while maintaining high accuracy. The scheme is based on an Eulerian approach, and it can thus be directly used for Fokker-Planck, high dimensional Vlasov-Poisson and also guiding-center drift simulations, aiming at particular problems of plasma physics. The benchmark tests for such simulations have shown that the IDO-CF scheme is superior in keeping the conservation properties without causing serious phase error.

  9. Numerical Simulation of Laser-Driven Rayleigh-Taylor Instability using TVD MUSCL Scheme

    NASA Astrophysics Data System (ADS)

    Nagatomo, Hideo; Ohnishi, Naofumo; Takeuchi, Hajime; Takabe, Hideaki; Mima, Kunioki

    1996-11-01

    For the inertial confinement fusion, it is important to simulate and predict the hydrodynamic instabilities. The numerical simulation of the laser-driven Rayleigh-Taylor instability was performed by using a newly developed numerical code which include the two temperature plasma effect and the equation of state. This code is robust and less dissipative because the scheme is based on flux vector splitting method. Furthermore, this method is coupled with high-order MUSCL TVD scheme which enable to capture the shock, the vortices and the contact discontinuity clearly. In the two temperature model, the relaxation of the ion and electron temperature is considered. Cowan ion equation and Thomas-Fermi fitting formula for electron are applied to the equation of state. The dependence on the equation of state will be discussed in this presentation. Also, some numerical results which are solved by the other numerical codes will be shown for the comparison.

  10. A numerical study of ENO and TVD schemes for shock capturing

    NASA Technical Reports Server (NTRS)

    Chang, Shih-Hung; Liou, Meng-Sing

    1988-01-01

    The numerical performance of a second-order upwind-based total variation diminishing (TVD) scheme and that of a uniform second-order essentially non-oscillatory (ENO) scheme for shock capturing are compared. The TVD scheme used is a modified version of Liou, using the flux-difference splitting (FDS) of Roe and his superbee function as the limiter. The construction of the basic ENO scheme is based on Harten, Engquist, Osher, and Chakravarthy, and the 2-D extensions are obtained by using a Strang-type of fractional-step time-splitting method. Numerical results presented include both steady and unsteady, 1-D and 2-D calculations. All the chosen test problems have exact solutions so that numerical performance can be measured by comparing the computer results to them. For 1-D calculations, the standard shock-tube problems of Sod and Lax are chosen. A very strong shock-tube problem, with the initial density ratio of 400 to 1 and pressure ratio of 500 to 1, is also used to study the behavior of the two schemes. For 2-D calculations, the shock wave reflection problems are adopted for testing. The cases presented in this report include flows with Mach numbers of 2.9, 5.0, and 10.0.

  11. RELAP5 two-phase fluid model and numerical scheme for economic LWR system simulation

    SciTech Connect

    Ransom, V.H.; Wagner, R.J.; Trapp, J.A.

    1981-01-01

    The RELAP5 two-phase fluid model and the associated numerical scheme are summarized. The experience accrued in development of a fast running light water reactor system transient analysis code is reviewed and example of the code application are given.

  12. Numerical calculation of tidal current with UTOPIA scheme for advection and application to Osaka Bay

    NASA Astrophysics Data System (ADS)

    Komoda, Jun; Matsuyama, Masaji

    UTOPIA scheme was applied to advection term for the numerical calculation of tide and tidal current to reproduce the strong tidal current realistically. Numerical model is constructed by boundary-fitted coordinate method vertically using Arakawa A grid in space. The new method is designed to suppress a numerical oscillation usually induced by Arakawa A grid. UTOPIA scheme was confirmed to be suitable to express a strong current around complicated topography. This model was applied to the tidal calculation for M2 constituent in Osaka Bay with two narrow straits, i.e., Akashi and Tomogashima straits. The tidal currents obtained in this model agree with them observed at monitoring stations, and the four eddies in the bay were also reproduced as the residual currents, i.e., tide induced transient eddy (TITE). The generation, growth and lifetime of the eddies also were investigated.

  13. A second order in time, uniquely solvable, unconditionally stable numerical scheme for Cahn-Hilliard-Navier-Stokes equation

    NASA Astrophysics Data System (ADS)

    Han, Daozhi; Wang, Xiaoming

    2015-06-01

    We propose a novel second order in time numerical scheme for Cahn-Hilliard-Navier-Stokes phase field model with matched density. The scheme is based on second order convex-splitting for the Cahn-Hilliard equation and pressure-projection for the Navier-Stokes equation. We show that the scheme is mass-conservative, satisfies a modified energy law and is therefore unconditionally stable. Moreover, we prove that the scheme is unconditionally uniquely solvable at each time step by exploring the monotonicity associated with the scheme. Thanks to the simple coupling of the scheme, we design an efficient Picard iteration procedure to further decouple the computation of Cahn-Hilliard equation and Navier-Stokes equation. We implement the scheme by the mixed finite element method. Ample numerical experiments are performed to validate the accuracy and efficiency of the numerical scheme.

  14. A novel numerical technique to obtain an accurate solution to the Thomas-Fermi equation

    NASA Astrophysics Data System (ADS)

    Parand, Kourosh; Yousefi, Hossein; Delkhosh, Mehdi; Ghaderi, Amin

    2016-07-01

    In this paper, a new algorithm based on the fractional order of rational Euler functions (FRE) is introduced to study the Thomas-Fermi (TF) model which is a nonlinear singular ordinary differential equation on a semi-infinite interval. This problem, using the quasilinearization method (QLM), converts to the sequence of linear ordinary differential equations to obtain the solution. For the first time, the rational Euler (RE) and the FRE have been made based on Euler polynomials. In addition, the equation will be solved on a semi-infinite domain without truncating it to a finite domain by taking FRE as basic functions for the collocation method. This method reduces the solution of this problem to the solution of a system of algebraic equations. We demonstrated that the new proposed algorithm is efficient for obtaining the value of y'(0) , y(x) and y'(x) . Comparison with some numerical and analytical solutions shows that the present solution is highly accurate.

  15. Recommendations for accurate numerical blood flow simulations of stented intracranial aneurysms.

    PubMed

    Janiga, Gábor; Berg, Philipp; Beuing, Oliver; Neugebauer, Mathias; Gasteiger, Rocco; Preim, Bernhard; Rose, Georg; Skalej, Martin; Thévenin, Dominique

    2013-06-01

    The number of scientific publications dealing with stented intracranial aneurysms is rapidly increasing. Powerful computational facilities are now available; an accurate computational modeling of hemodynamics in patient-specific configurations is, however, still being sought. Furthermore, there is still no general agreement on the quantities that should be computed and on the most adequate analysis for intervention support. In this article, the accurate representation of patient geometry is first discussed, involving successive improvements. Concerning the second step, the mesh required for the numerical simulation is especially challenging when deploying a stent with very fine wire structures. Third, the description of the fluid properties is a major challenge. Finally, a founded quantitative analysis of the simulation results is obviously needed to support interventional decisions. In the present work, an attempt has been made to review the most important steps for a high-quality computational fluid dynamics computation of virtually stented intracranial aneurysms. In consequence, this leads to concrete recommendations, whereby the obtained results are not discussed for their medical relevance but for the evaluation of their quality. This investigation might hopefully be helpful for further studies considering stent deployment in patient-specific geometries, in particular regarding the generation of the most appropriate computational model. PMID:23729530

  16. The numerical simulations of explosion and implosion in air: use of a modified Harten's TVD scheme

    NASA Astrophysics Data System (ADS)

    Liu, T. G.; Khoo, B. C.; Yeo, K. S.

    1999-10-01

    Numerical simulations of explosion and implosion in air are carried out with a modified Harten's TVD scheme. The new scheme has a high resolution for contact discontinuities in addition to maintaining the good features of Harten's TVD scheme. In the numerical experiment of spherical explosion in air, the second shock wave (which does not exist in the one-dimensional shock tube problem) and its subsequent implosion on the origin have been successfully captured. The positions of the main shock wave, the contact discontinuity and the second shock wave have shown satisfactory agreement with those predicted from previous analysis. The numerical results are also compared with those obtained experimentally. Finally, simulations of a cylindrical explosion and implosion in air are carried out. Results of the cylindrical implosion in air are compared with those of previous work, including the interaction of the reflected main shock wave with the contact discontinuity and the formation of a second shock wave. All these attest to the successful use of the modified Harten's TVD scheme for the simulations of shock waves arising from explosion and implosion. Copyright

  17. 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.

  18. 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).

  19. Keeping the edge: an accurate numerical method to solve the stream power law

    NASA Astrophysics Data System (ADS)

    Campforts, B.; Govers, G.

    2015-12-01

    Bedrock rivers set the base level of surrounding hill slopes and mediate the dynamic interplay between mountain building and denudation. The propensity of rivers to preserve pulses of increased tectonic uplift also allows to reconstruct long term uplift histories from longitudinal river profiles. An accurate reconstruction of river profile development at different timescales is therefore essential. Long term river development is typically modeled by means of the stream power law. Under specific conditions this equation can be solved analytically but numerical Finite Difference Methods (FDMs) are most frequently used. Nonetheless, FDMs suffer from numerical smearing, especially at knickpoint zones which are key to understand transient landscapes. Here, we solve the stream power law by means of a Finite Volume Method (FVM) which is Total Variation Diminishing (TVD). Total volume methods are designed to simulate sharp discontinuities making them very suitable to model river incision. In contrast to FDMs, the TVD_FVM is well capable of preserving knickpoints as illustrated for the fast propagating Niagara falls. Moreover, we show that the TVD_FVM performs much better when reconstructing uplift at timescales exceeding 100 Myr, using Eastern Australia as an example. Finally, uncertainty associated with parameter calibration is dramatically reduced when the TVD_FVM is applied. Therefore, the use of a TVD_FVM to understand long term landscape evolution is an important addition to the toolbox at the disposition of geomorphologists.

  20. 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). PMID:26430979

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

    NASA Astrophysics Data System (ADS)

    Pizzocri, D.; Rabiti, C.; Luzzi, L.; Barani, T.; Van Uffelen, P.; Pastore, G.

    2016-09-01

    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 the 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 paper, 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, combined with 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 PolyPole-1 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.

  2. 2D numerical simulation of the MEP energy-transport model with a finite difference scheme

    SciTech Connect

    Romano, V. . E-mail: romano@dmi.unict.it

    2007-02-10

    A finite difference scheme of Scharfetter-Gummel type is used to simulate a consistent energy-transport model for electron transport in semiconductors devices, free of any fitting parameters, formulated on the basis of the maximum entropy principle. Simulations of silicon n{sup +}-n-n{sup +} diodes, 2D-MESFET and 2D-MOSFET and comparisons with the results obtained by a direct simulation of the Boltzmann transport equation and with other energy-transport models, known in the literature, show the validity of the model and the robustness of the numerical scheme.

  3. A Comparison of Higher-Order Weak Numerical Schemes for Stopped Stochastic Differential Equations

    NASA Astrophysics Data System (ADS)

    Bernal, Francisco; Acebróon, Juan A.

    2016-09-01

    We review, implement, and compare numerical integration schemes for spatially bounded diffusions stopped at the boundary which possess a convergence rate of the discretization error with respect to the timestep $h$ higher than ${\\cal O}(\\sqrt{h})$. We address specific implementation issues of the most general-purpose of such schemes. They have been coded into a single Matlab program and compared, according to their accuracy and computational cost, on a wide range of problems in up to ${\\mathbb R}^{48}$. The paper is self-contained and the code will be made freely downloadable.

  4. Towards an accurate understanding of UHMWPE visco-dynamic behaviour for numerical modelling of implants.

    PubMed

    Quinci, Federico; Dressler, Matthew; Strickland, Anthony M; Limbert, Georges

    2014-04-01

    Considerable progress has been made in understanding implant wear and developing numerical models to predict wear for new orthopaedic devices. However any model of wear could be improved through a more accurate representation of the biomaterial mechanics, including time-varying dynamic and inelastic behaviour such as viscosity and plastic deformation. In particular, most computational models of wear of UHMWPE implement a time-invariant version of Archard's law that links the volume of worn material to the contact pressure between the metal implant and the polymeric tibial insert. During in-vivo conditions, however, the contact area is a time-varying quantity and is therefore dependent upon the dynamic deformation response of the material. From this observation one can conclude that creep deformations of UHMWPE may be very important to consider when conducting computational wear analyses, in stark contrast to what can be found in the literature. In this study, different numerical modelling techniques are compared with experimental creep testing on a unicondylar knee replacement system in a physiologically representative context. Linear elastic, plastic and time-varying visco-dynamic models are benchmarked using literature data to predict contact deformations, pressures and areas. The aim of this study is to elucidate the contributions of viscoelastic and plastic effects on these surface quantities. It is concluded that creep deformations have a significant effect on the contact pressure measured (experiment) and calculated (computational models) at the surface of the UHMWPE unicondylar insert. The use of a purely elastoplastic constitutive model for UHMWPE lead to compressive deformations of the insert which are much smaller than those predicted by a creep-capturing viscoelastic model (and those measured experimentally). This shows again the importance of including creep behaviour into a constitutive model in order to predict the right level of surface deformation

  5. Towards an accurate understanding of UHMWPE visco-dynamic behaviour for numerical modelling of implants.

    PubMed

    Quinci, Federico; Dressler, Matthew; Strickland, Anthony M; Limbert, Georges

    2014-04-01

    Considerable progress has been made in understanding implant wear and developing numerical models to predict wear for new orthopaedic devices. However any model of wear could be improved through a more accurate representation of the biomaterial mechanics, including time-varying dynamic and inelastic behaviour such as viscosity and plastic deformation. In particular, most computational models of wear of UHMWPE implement a time-invariant version of Archard's law that links the volume of worn material to the contact pressure between the metal implant and the polymeric tibial insert. During in-vivo conditions, however, the contact area is a time-varying quantity and is therefore dependent upon the dynamic deformation response of the material. From this observation one can conclude that creep deformations of UHMWPE may be very important to consider when conducting computational wear analyses, in stark contrast to what can be found in the literature. In this study, different numerical modelling techniques are compared with experimental creep testing on a unicondylar knee replacement system in a physiologically representative context. Linear elastic, plastic and time-varying visco-dynamic models are benchmarked using literature data to predict contact deformations, pressures and areas. The aim of this study is to elucidate the contributions of viscoelastic and plastic effects on these surface quantities. It is concluded that creep deformations have a significant effect on the contact pressure measured (experiment) and calculated (computational models) at the surface of the UHMWPE unicondylar insert. The use of a purely elastoplastic constitutive model for UHMWPE lead to compressive deformations of the insert which are much smaller than those predicted by a creep-capturing viscoelastic model (and those measured experimentally). This shows again the importance of including creep behaviour into a constitutive model in order to predict the right level of surface deformation

  6. 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.

  7. Theoretical and numerical comparison of 3D numerical schemes for their accuracy with respect to P-wave to S-wave speed ratio

    NASA Astrophysics Data System (ADS)

    Moczo, P.; Kristek, J.; Galis, M.; Chaljub, E.; Chen, X.; Zhang, Z.

    2012-04-01

    Numerical modeling of earthquake ground motion in sedimentary basins and valleys often has to account for the P-wave to S-wave speed ratios (VP/VS) as large as five and even larger, mainly in sediments below groundwater level. The ratio can attain values larger than 10 - the unconsolidated lake sediments in Ciudad de México are a good example. At the same time, accuracy of the numerical schemes with respect to VP/VS has not been sufficiently analyzed. The numerical schemes are often applied without adequate check of the accuracy. We present theoretical analysis and numerical comparison of 18 3D numerical time-domain explicit schemes for modeling seismic motion for their accuracy with the varying VP/VS. The schemes are based on the finite-difference, spectral-element, finite-element and discontinuous-Galerkin methods. All schemes are presented in a unified form. Theoretical analysis compares accuracy of the schemes in terms of local errors in amplitude and vector difference. In addition to the analysis we compare numerically simulated seismograms with exact solutions for canonical configurations. We compare accuracy of the schemes in terms of the local errors, grid dispersion and full wavefield simulations with respect to the structure of the numerical schemes.

  8. Numerical investigation of BB-AMR scheme using entropy production as refinement criterion

    NASA Astrophysics Data System (ADS)

    Altazin, Thomas; Ersoy, Mehmet; Golay, Frédéric; Sous, Damien; Yushchenko, Lyudmyla

    2016-03-01

    In this work, a parallel finite volume scheme on unstructured meshes is applied to fluid flow for multidimensional hyperbolic system of conservation laws. It is based on a block-based adaptive mesh refinement strategy which allows quick meshing and easy parallelisation. As a continuation and as an extension of a previous work, the useful numerical density of entropy production is used as mesh refinement criterion combined with a local time-stepping method to preserve the computational time. Then, we numerically investigate its efficiency through several test cases with a confrontation with exact solution or experimental data.

  9. A numerical scheme for optimal transition paths of stochastic chemical kinetic systems

    SciTech Connect

    Liu Di

    2008-10-01

    We present a new framework for finding the optimal transition paths of metastable stochastic chemical kinetic systems with large system size. The optimal transition paths are identified to be the most probable paths according to the Large Deviation Theory of stochastic processes. Dynamical equations for the optimal transition paths are derived using the variational principle. A modified Minimum Action Method (MAM) is proposed as a numerical scheme to solve the optimal transition paths. Applications to Gene Regulatory Networks such as the toggle switch model and the Lactose Operon Model in Escherichia coli are presented as numerical examples.

  10. Toward a consistent framework for high order mesh refinement schemes in numerical relativity

    NASA Astrophysics Data System (ADS)

    Mongwane, Bishop

    2015-05-01

    It has now become customary in the field of numerical relativity to couple high order finite difference schemes to mesh refinement algorithms. To this end, different modifications to the standard Berger-Oliger adaptive mesh refinement algorithm have been proposed. In this work we present a fourth order stable mesh refinement scheme with sub-cycling in time for numerical relativity. We do not use buffer zones to deal with refinement boundaries but explicitly specify boundary data for refined grids. We argue that the incompatibility of the standard mesh refinement algorithm with higher order Runge Kutta methods is a manifestation of order reduction phenomena, caused by inconsistent application of boundary data in the refined grids. Our scheme also addresses the problem of spurious reflections that are generated when propagating waves cross mesh refinement boundaries. We introduce a transition zone on refined levels within which the phase velocity of propagating modes is allowed to decelerate in order to smoothly match the phase velocity of coarser grids. We apply the method to test problems involving propagating waves and show a significant reduction in spurious reflections.

  11. Topological invariants for interacting topological insulators. I. Efficient numerical evaluation scheme and implementations

    NASA Astrophysics Data System (ADS)

    He, Yuan-Yao; Wu, Han-Qing; Meng, Zi Yang; Lu, Zhong-Yi

    2016-05-01

    The aim of this series of two papers is to discuss topological invariants for interacting topological insulators (TIs). In the first paper (I), we provide a paradigm of efficient numerical evaluation scheme for topological invariants, in which we demystify the procedures and techniques employed in calculating Z2 invariant and spin Chern number via zero-frequency single-particle Green's function in quantum Monte Carlo (QMC) simulations. Here we introduce an interpolation process to overcome the ubiquitous finite-size effect, so that the calculated spin Chern number shows ideally quantized values. We also show that making use of symmetry properties of the underlying systems can greatly reduce the computational effort. To demonstrate the effectiveness of our numerical evaluation scheme, especially the interpolation process, for calculating topological invariants, we apply it on two independent two-dimensional models of interacting topological insulators. In the subsequent paper (II), we apply the scheme developed here to wider classes of models of interacting topological insulators, for which certain limitation of constructing topological invariant via single-particle Green's functions will be presented.

  12. The stability of numerical boundary treatments for compact high-order finite-difference schemes

    NASA Technical Reports Server (NTRS)

    Carpenter, Mark H.; Gottlieb, David; Abarbanel, Saul

    1991-01-01

    The stability characteristics of various compact fourth and sixth order spatial operators are assessed using the theory of Gustafsson, Kreiss and Sundstrom (G-K-S) for the semi-discrete Initial Boundary Value Problem (IBVP). These results are then generalized to the fully discrete case using a recently developed theory of Kreiss. In all cases, favorable comparisons are obtained between the G-K-S theory, eigenvalue determination, and numerical simulation. The conventional definition of stability is then sharpened to include only those spatial discretizations that are asymptotically stable. It is shown that many of the higher order schemes which are G-K-S stable are not asymptotically stable. A series of compact fourth and sixth order schemes, which are both asymptotically and G-K-S stable for the scalar case, are then developed.

  13. 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.

  14. A new numerical scheme for computer simulation of multiple cracking in ceramic films during constrained sintering

    NASA Astrophysics Data System (ADS)

    Li, Fan; Pan, Jingzhe; Cocks, Alan

    2012-04-01

    Heterogeneities in a green film made from a powder compact is considered to be one of the major reasons for the generation of sintering cracks. Stresses are generated in a film due to the constraint of the substrate. Instabilities in the sintering process can occur at sites of these heterogeneities resulting in the generation of multiple cracks, which can propagate through the thickness of the film. The classical finite element method is fundamentally ill-suited to studying this multiple-cracking problem. This paper presents a simple and robust numerical method for the computer modelling of sintering and multiple cracking. The method is based on the so-called material point method, which was initially developed for large deformation problems in plasticity. A parallel computing algorithm is implemented and a simple scheme for modelling the initiation and propagation of multiple cracks is proposed. The numerical scheme is then validated by simulating a simple geometric problem for which an analytical solution can be obtained. Finally, the robust performance of the numerical method is demonstrated by modelling the sintering response of a film which contains different types of heterogeneities.

  15. Accurate Intermolecular Interactions at Dramatically Reduced Cost and a Many-Body Energy Decomposition Scheme for XPol+SAPT

    NASA Astrophysics Data System (ADS)

    Lao, Ka Un; Herbert, John M.

    2013-06-01

    An efficient, monomer-based electronic structure method is introduced for computing non-covalent interactions in molecular and ionic clusters. It builds upon our ``explicit polarization" (XPol) with pairwise-additive symmetry-adapted perturbation theory (SAPT) using the Kohn-Sham (KS) version of SAPT, but replaces the problematic and expensive sum-over-states dispersion terms with empirical potentials. This modification reduces the scaling from {O}(N^5) to {O}(N^3) and also facilitates the use of Kohn-Sham density functional theory (KS-DFT) as a low-cost means to capture intramolecular electron correlation. Accurate binding energies are obtained for benchmark databases of dimer binding energies, and potential energy curves are also captured accurately, for a variety of challenging systems. As compared to traditional DFT-SAPT or SAPT(DFT) methods, it removes the limitation to dimers and extends SAPT-based methodology to many-body systems. For many-body systems such as water clusters and halide-water cluster anions, the new method is superior to established density-functional methods for non-covalent interactions. We suggest that using different asymptotic corrections for different monomers is necessary to get good binding energies in general, as DFT-SAPT or SAPT(DFT), especially for hydrogen-bonded complexes. We also introduce a decomposition scheme for the interaction energy that extends traditional SAPT energy decomposition analysis to systems containing more than two monomers, and we find that the various energy components (electrostatic, exchange, induction, and dispersion) are in very good agreement with high-level SAPT benchmarks for dimers. For (H_2O)_6, the many-body contribution to the interaction energy agrees well with that obtained from traditional Kitaura-Morokuma energy decomposition analysis.

  16. A time-accurate adaptive grid method and the numerical simulation of a shock-vortex interaction

    NASA Technical Reports Server (NTRS)

    Bockelie, Michael J.; Eiseman, Peter R.

    1990-01-01

    A time accurate, general purpose, adaptive grid method is developed that is suitable for multidimensional steady and unsteady numerical simulations. The grid point movement is performed in a manner that generates smooth grids which resolve the severe solution gradients and the sharp transitions in the solution gradients. The temporal coupling of the adaptive grid and the PDE solver is performed with a grid prediction correction method that is simple to implement and ensures the time accuracy of the grid. Time accurate solutions of the 2-D Euler equations for an unsteady shock vortex interaction demonstrate the ability of the adaptive method to accurately adapt the grid to multiple solution features.

  17. Accurate numerical forward model for optimal retracking of SIRAL2 SAR echoes over open ocean

    NASA Astrophysics Data System (ADS)

    Phalippou, L.; Demeestere, F.

    2011-12-01

    The SAR mode of SIRAL-2 on board Cryosat-2 has been designed to measure primarily sea-ice and continental ice (Wingham et al. 2005). In 2005, K. Raney (KR, 2005) pointed out the improvements brought by SAR altimeter for open ocean. KR results were mostly based on 'rule of thumb' considerations on speckle noise reduction due to the higher PRF and to speckle decorrelation after SAR processing. In 2007, Phalippou and Enjolras (PE,2007) provided the theoretical background for optimal retracking of SAR echoes over ocean with a focus on the forward modelling of the power-waveforms. The accuracies of geophysical parameters (range, significant wave heights, and backscattering coefficient) retrieved from SAR altimeter data were derived accounting for SAR echo shape and speckle noise accurate modelling. The step forward to optimal retracking using numerical forward model (NFM) was also pointed out. NFM of the power waveform avoids analytical approximation, a warranty to minimise the geophysical dependent biases in the retrieval. NFM have been used for many years, in operational meteorology in particular, for retrieving temperature and humidity profiles from IR and microwave radiometers as the radiative transfer function is complex (Eyre, 1989). So far this technique was not used in the field of ocean conventional altimetry as analytical models (e.g. Brown's model for instance) were found to give sufficient accuracy. However, although NFM seems desirable even for conventional nadir altimetry, it becomes inevitable if one wish to process SAR altimeter data as the transfer function is too complex to be approximated by a simple analytical function. This was clearly demonstrated in PE 2007. The paper describes the background to SAR data retracking over open ocean. Since PE 2007 improvements have been brought to the forward model and it is shown that the altimeter on-ground and in flight characterisation (e.g antenna pattern range impulse response, azimuth impulse response

  18. Physical and Numerical Model Studies of Cross-flow Turbines Towards Accurate Parameterization in Array Simulations

    NASA Astrophysics Data System (ADS)

    Wosnik, M.; Bachant, P.

    2014-12-01

    Cross-flow turbines, often referred to as vertical-axis turbines, show potential for success in marine hydrokinetic (MHK) and wind energy applications, ranging from small- to utility-scale installations in tidal/ocean currents and offshore wind. As turbine designs mature, the research focus is shifting from individual devices to the optimization of turbine arrays. It would be expensive and time-consuming to conduct physical model studies of large arrays at large model scales (to achieve sufficiently high Reynolds numbers), and hence numerical techniques are generally better suited to explore the array design parameter space. However, since the computing power available today is not sufficient to conduct simulations of the flow in and around large arrays of turbines with fully resolved turbine geometries (e.g., grid resolution into the viscous sublayer on turbine blades), the turbines' interaction with the energy resource (water current or wind) needs to be parameterized, or modeled. Models used today--a common model is the actuator disk concept--are not able to predict the unique wake structure generated by cross-flow turbines. This wake structure has been shown to create "constructive" interference in some cases, improving turbine performance in array configurations, in contrast with axial-flow, or horizontal axis devices. Towards a more accurate parameterization of cross-flow turbines, an extensive experimental study was carried out using a high-resolution turbine test bed with wake measurement capability in a large cross-section tow tank. The experimental results were then "interpolated" using high-fidelity Navier--Stokes simulations, to gain insight into the turbine's near-wake. The study was designed to achieve sufficiently high Reynolds numbers for the results to be Reynolds number independent with respect to turbine performance and wake statistics, such that they can be reliably extrapolated to full scale and used for model validation. The end product of

  19. A Class of TVD Type Combined Numerical Scheme for MHD Equations With a Survey About Numerical Methods in Solar Wind Simulations

    NASA Astrophysics Data System (ADS)

    Feng, Xueshang; Wu, S. T.; Wei, Fengsi; Fan, Quanlin

    2003-04-01

    It has been believed that three-dimensional, numerical, magnetohydrodynamic (MHD) modelling must play a crucial role in a seamless forecasting system. This system refers to space weather originating on the sun; propagation of disturbances through the solar wind and interplanetary magnetic field (IMF), and thence, transmission into the magnetosphere, ionosphere, and thermosphere. This role comes as no surprise to numerical modelers that participate in the numerical modelling of atmospheric environments as well as the meteorological conditions at Earth. Space scientists have paid great attention to operational numerical space weather prediction models. To this purpose practical progress has been made in the past years. Here first is reviewed the progress of the numerical methods in solar wind modelling. Then, based on our discussion, a new numerical scheme of total variation diminishing (TVD) type for magnetohydrodynamic equations in spherical coordinates is proposed by taking into account convergence, stability and resolution. This new MHD model is established by solving the fluid equations of MHD system with a modified Lax-Friedrichs scheme and the magnetic induction equations with MacCormack II scheme for the purpose of developing a combined scheme of quick convergence as well as of TVD property. To verify the validation of the scheme, the propagation of one-dimensional MHD fast and slow shock problem is discussed with the numerical results conforming to the existing results obtained by the piece-wise parabolic method (PPM). Finally, some conclusions are made.

  20. Multiscale/fractional step schemes for the numerical simulation of the rotating shallow water flows with complex periodic topography

    NASA Astrophysics Data System (ADS)

    Jauberteau, F.; Temam, R. M.; Tribbia, J.

    2014-08-01

    In this paper, we study several multiscale/fractional step schemes for the numerical solution of the rotating shallow water equations with complex topography. We consider the case of periodic boundary conditions (f-plane model). Spatial discretization is obtained using a Fourier spectral Galerkin method. For the schemes presented in this paper we consider two approaches. The first approach (multiscale schemes) is based on topography scale separation and the numerical time integration is function of the scales. The second approach is based on a splitting of the operators, and the time integration method is function of the operator considered (fractional step schemes). The numerical results obtained are compared with the explicit reference scheme (Leap-Frog scheme). With these multiscale/fractional step schemes the objective is to propose new schemes giving numerical results similar to those obtained using only one uniform fine grid N×N and a time step Δt, but with a CPU time near the CPU time needed when using only one coarse grid N1×N1, N1Δt.

  1. Lagrangian model of zooplankton dispersion: numerical schemes comparisons and parameter sensitivity tests

    NASA Astrophysics Data System (ADS)

    Qiu, Zhongfeng; Doglioli, Andrea M.; He, Yijun; Carlotti, Francois

    2011-03-01

    This paper presents two comparisons or tests for a Lagrangian model of zooplankton dispersion: numerical schemes and time steps. Firstly, we compared three numerical schemes using idealized circulations. Results show that the precisions of the advanced Adams-Bashfold-Moulton (ABM) method and the Runge-Kutta (RK) method were in the same order and both were much higher than that of the Euler method. Furthermore, the advanced ABM method is more efficient than the RK method in computational memory requirements and time consumption. We therefore chose the advanced ABM method as the Lagrangian particle-tracking algorithm. Secondly, we performed a sensitivity test for time steps, using outputs of the hydrodynamic model, Symphonie. Results show that the time step choices depend on the fluid response time that is related to the spatial resolution of velocity fields. The method introduced by Oliveira et al. in 2002 is suitable for choosing time steps of Lagrangian particle-tracking models, at least when only considering advection.

  2. Comparing numerical integration schemes for time-continuous car-following models

    NASA Astrophysics Data System (ADS)

    Treiber, Martin; Kanagaraj, Venkatesan

    2015-02-01

    When simulating trajectories by integrating time-continuous car-following models, standard integration schemes such as the fourth-order Runge-Kutta method (RK4) are rarely used while the simple Euler method is popular among researchers. We compare four explicit methods both analytically and numerically: Euler's method, ballistic update, Heun's method (trapezoidal rule), and the standard RK4. As performance metrics, we plot the global discretization error as a function of the numerical complexity. We tested the methods on several time-continuous car-following models in several multi-vehicle simulation scenarios with and without discontinuities such as stops or a discontinuous behavior of an external leader. We find that the theoretical advantage of RK4 (consistency order 4) only plays a role if both the acceleration function of the model and the trajectory of the leader are sufficiently often differentiable. Otherwise, we obtain lower (and often fractional) consistency orders. Although, to our knowledge, Heun's method has never been used for integrating car-following models, it turns out to be the best scheme for many practical situations. The ballistic update always prevails over Euler's method although both are of first order.

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

    NASA Astrophysics Data System (ADS)

    Ku, S.; Hager, R.; Chang, C. S.; Kwon, J. M.; Parker, S. E.

    2016-06-01

    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 provide 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.

  4. Solution of population balance equations in applications with fine particles: Mathematical modeling and numerical schemes

    NASA Astrophysics Data System (ADS)

    Nguyen, T. T.; Laurent, F.; Fox, R. O.; Massot, M.

    2016-11-01

    The accurate description and robust simulation, at relatively low cost, of global quantities (e.g. number density or volume fraction) as well as the size distribution of a population of fine particles in a carrier fluid is still a major challenge for many applications. For this purpose, two types of methods are investigated for solving the population balance equation with aggregation, continuous particle size change (growth and size reduction), and nucleation: the extended quadrature method of moments (EQMOM) based on the work of Yuan et al. [52] and a hybrid method (TSM) between the sectional and moment methods, considering two moments per section based on the work of Laurent et al. [30]. For both methods, the closure employs a continuous reconstruction of the number density function of the particles from its moments, thus allowing evaluation of all the unclosed terms in the moment equations, including the negative flux due to the disappearance of particles. Here, new robust and efficient algorithms are developed for this reconstruction step and two kinds of reconstruction are tested for each method. Moreover, robust and accurate numerical methods are developed, ensuring the realizability of the moments. The robustness is ensured with efficient and tractable algorithms despite the numerous couplings and various algebraic constraints thanks to a tailored overall strategy. EQMOM and TSM are compared to a sectional method for various simple but relevant test cases, showing their ability to describe accurately the fine-particle population with a much lower number of variables. These results demonstrate the efficiency of the modeling and numerical choices, and their potential for the simulation of real-world applications.

  5. Numerical simulation of Stokes flow around particles via a hybrid Finite Difference-Boundary Integral scheme

    NASA Astrophysics Data System (ADS)

    Bhattacharya, Amitabh

    2013-11-01

    An efficient algorithm for simulating Stokes flow around particles is presented here, in which a second order Finite Difference method (FDM) is coupled to a Boundary Integral method (BIM). This method utilizes the strong points of FDM (i.e. localized stencil) and BIM (i.e. accurate representation of particle surface). Specifically, in each iteration, the flow field away from the particles is solved on a Cartesian FDM grid, while the traction on the particle surface (given the the velocity of the particle) is solved using BIM. The two schemes are coupled by matching the solution in an intermediate region between the particle and surrounding fluid. We validate this method by solving for flow around an array of cylinders, and find good agreement with Hasimoto's (J. Fluid Mech. 1959) analytical results.

  6. 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.

  7. Third-order-accurate numerical methods for efficient, large time-step solutions of mixed linear and nonlinear problems

    SciTech Connect

    Cobb, J.W.

    1995-02-01

    There is an increasing need for more accurate numerical methods for large-scale nonlinear magneto-fluid turbulence calculations. These methods should not only increase the current state of the art in terms of accuracy, but should also continue to optimize other desired properties such as simplicity, minimized computation, minimized memory requirements, and robust stability. This includes the ability to stably solve stiff problems with long time-steps. This work discusses a general methodology for deriving higher-order numerical methods. It also discusses how the selection of various choices can affect the desired properties. The explicit discussion focuses on third-order Runge-Kutta methods, including general solutions and five examples. The study investigates the linear numerical analysis of these methods, including their accuracy, general stability, and stiff stability. Additional appendices discuss linear multistep methods, discuss directions for further work, and exhibit numerical analysis results for some other commonly used lower-order methods.

  8. Spectrally accurate numerical solution of the single-particle Schrödinger equation

    NASA Astrophysics Data System (ADS)

    Batcho, P. F.

    1998-06-01

    We have formulated a three-dimensional fully numerical (i.e., chemical basis-set free) method and applied it to the solution of the single-particle Schrödinger equation. The numerical method combines the rapid ``exponential'' convergence rates of spectral methods with the geometric flexibility of finite-element methods and can be viewed as an extension of the spectral element method. Singularities associated with multicenter systems are efficiently integrated by a Duffy transformation and the discrete operator is formulated by a variational statement. The method is applicable to molecular modeling for quantum chemical calculations on polyatomic systems. The complete system is shown to be efficiently inverted by the preconditioned conjugate gradient method and exponential convergence rates in numerical approximations are demonstrated for suitable benchmark problems including the hydrogenlike orbitals of nitrogen.

  9. Numerical Study for the Three-Dimensional Rayleigh Taylor Instability through the TVD/AC Scheme and Parallel Computation

    NASA Astrophysics Data System (ADS)

    Li, X. L.; Jin, B. X.; Glimm, J.

    1996-07-01

    The Rayleigh-Taylor instability is a gravity driven instability of a contact surface between fluids of different densities. The growth of this instability is sensitive to numerical or physical mass diffusion. For this reason, high resolution of the contact discontinuity is particularly important. In this paper, we address this problem using a second-order TVD finite difference scheme with artificial compression. We describe our numerical simulations of the 3D Rayleigh-Taylor instability using this scheme. The numerical solutions are compared to (a) the exact 2D solution in the linear regime and (b) numerical solutions using the TVD scheme and the front tracking method. The computational program is used to study the evolution of a single bubble and 3D bubble merger, i.e., the nonlinear evolution of a single mode and the process of nonlinear mode-mode interaction.

  10. 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.

  11. 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.

  12. A numerical scheme and some theoretical aspects for the cylindrically and spherically symmetric sine-Gordon equations

    NASA Astrophysics Data System (ADS)

    Nguyen, Lu Trong Khiem

    2016-07-01

    A finite difference formula based on the predictor-corrector technique is presented to integrate the cylindrically and spherically symmetric sine-Gordon equations numerically. Based on various numerical observations, one property of the waves of kink type is conjectured and used to explain their returning effect. Several numerical experiments are carried out and they are in excellent agreement with the existing results. In addition, the corresponding modulation solution for the two-dimensional ring-shaped kink is extended to that in three-dimension. Both numerical and theoretical aspects are utilized to verify the reliability of the proposed numerical scheme and thus the analytical modulation solutions.

  13. Numerical Computation of a Continuous-thrust State Transition Matrix Incorporating Accurate Hardware and Ephemeris Models

    NASA Technical Reports Server (NTRS)

    Ellison, Donald; Conway, Bruce; Englander, Jacob

    2015-01-01

    A significant body of work exists showing that providing a nonlinear programming (NLP) solver with expressions for the problem constraint gradient substantially increases the speed of program execution and can also improve the robustness of convergence, especially for local optimizers. Calculation of these derivatives is often accomplished through the computation of spacecraft's state transition matrix (STM). If the two-body gravitational model is employed as is often done in the context of preliminary design, closed form expressions for these derivatives may be provided. If a high fidelity dynamics model, that might include perturbing forces such as the gravitational effect from multiple third bodies and solar radiation pressure is used then these STM's must be computed numerically. We present a method for the power hardward model and a full ephemeris model. An adaptive-step embedded eight order Dormand-Prince numerical integrator is discussed and a method for the computation of the time of flight derivatives in this framework is presented. The use of these numerically calculated derivatieves offer a substantial improvement over finite differencing in the context of a global optimizer. Specifically the inclusion of these STM's into the low thrust missiondesign tool chain in use at NASA Goddard Spaceflight Center allows for an increased preliminary mission design cadence.

  14. 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.

  15. 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.

  16. 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.

  17. Gravitational waveforms from binary neutron star mergers with high-order weighted-essentially-nonoscillatory schemes in numerical relativity

    NASA Astrophysics Data System (ADS)

    Bernuzzi, Sebastiano; Dietrich, Tim

    2016-09-01

    The theoretical modeling of gravitational waveforms from binary neutron star mergers requires precise numerical relativity simulations. Assessing convergence of the numerical data and building the error budget is currently challenging due to the low accuracy of general-relativistic hydrodynamics schemes and to the grid resolutions that can be employed in (3 +1 )-dimensional simulations. In this work, we explore the use of high-order weighted-essentially-nonoscillatory (WENO) schemes in neutron star merger simulations and investigate the accuracy of the waveforms obtained with such methods. We find that high-order WENO schemes can be robustly employed for simulating the inspiral-merger phase and they significantly improve the assessment of the waveform's error budget with respect to finite-volume methods. High-order WENO schemes can be thus efficiently used for high-quality waveform production, and in future large-scale investigations of the binary parameter space.

  18. Numerical Methodology for Coupled Time-Accurate Simulations of Primary and Secondary Flowpaths in Gas Turbines

    NASA Technical Reports Server (NTRS)

    Przekwas, A. J.; Athavale, M. M.; Hendricks, R. C.; Steinetz, B. M.

    2006-01-01

    Detailed information of the flow-fields in the secondary flowpaths and their interaction with the primary flows in gas turbine engines is necessary for successful designs with optimized secondary flow streams. Present work is focused on the development of a simulation methodology for coupled time-accurate solutions of the two flowpaths. The secondary flowstream is treated using SCISEAL, an unstructured adaptive Cartesian grid code developed for secondary flows and seals, while the mainpath flow is solved using TURBO, a density based code with capability of resolving rotor-stator interaction in multi-stage machines. An interface is being tested that links the two codes at the rim seal to allow data exchange between the two codes for parallel, coupled execution. A description of the coupling methodology and the current status of the interface development is presented. Representative steady-state solutions of the secondary flow in the UTRC HP Rig disc cavity are also presented.

  19. Towards more accurate numerical modeling of impedance based high frequency harmonic vibration

    NASA Astrophysics Data System (ADS)

    Lim, Yee Yan; Kiong Soh, Chee

    2014-03-01

    The application of smart materials in various fields of engineering has recently become increasingly popular. For instance, the high frequency based electromechanical impedance (EMI) technique employing smart piezoelectric materials is found to be versatile in structural health monitoring (SHM). Thus far, considerable efforts have been made to study and improve the technique. Various theoretical models of the EMI technique have been proposed in an attempt to better understand its behavior. So far, the three-dimensional (3D) coupled field finite element (FE) model has proved to be the most accurate. However, large discrepancies between the results of the FE model and experimental tests, especially in terms of the slope and magnitude of the admittance signatures, continue to exist and are yet to be resolved. This paper presents a series of parametric studies using the 3D coupled field finite element method (FEM) on all properties of materials involved in the lead zirconate titanate (PZT) structure interaction of the EMI technique, to investigate their effect on the admittance signatures acquired. FE model updating is then performed by adjusting the parameters to match the experimental results. One of the main reasons for the lower accuracy, especially in terms of magnitude and slope, of previous FE models is the difficulty in determining the damping related coefficients and the stiffness of the bonding layer. In this study, using the hysteretic damping model in place of Rayleigh damping, which is used by most researchers in this field, and updated bonding stiffness, an improved and more accurate FE model is achieved. The results of this paper are expected to be useful for future study of the subject area in terms of research and application, such as modeling, design and optimization.

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

    SciTech Connect

    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.

  1. Fast and accurate numerical method for predicting gas chromatography retention time.

    PubMed

    Claumann, Carlos Alberto; Wüst Zibetti, André; Bolzan, Ariovaldo; Machado, Ricardo A F; Pinto, Leonel Teixeira

    2015-08-01

    Predictive modeling for gas chromatography compound retention depends on the retention factor (ki) and on the flow of the mobile phase. Thus, different approaches for determining an analyte ki in column chromatography have been developed. The main one is based on the thermodynamic properties of the component and on the characteristics of the stationary phase. These models can be used to estimate the parameters and to optimize the programming of temperatures, in gas chromatography, for the separation of compounds. Different authors have proposed the use of numerical methods for solving these models, but these methods demand greater computational time. Hence, a new method for solving the predictive modeling of analyte retention time is presented. This algorithm is an alternative to traditional methods because it transforms its attainments into root determination problems within defined intervals. The proposed approach allows for tr calculation, with accuracy determined by the user of the methods, and significant reductions in computational time; it can also be used to evaluate the performance of other prediction methods.

  2. The use of experimental bending tests to more accurate numerical description of TBC damage process

    NASA Astrophysics Data System (ADS)

    Sadowski, T.; Golewski, P.

    2016-04-01

    Thermal barrier coatings (TBCs) have been extensively used in aircraft engines to protect critical engine parts such as blades and combustion chambers, which are exposed to high temperatures and corrosive environment. The blades of turbine engines are additionally exposed to high mechanical loads. These loads are created by the high rotational speed of the rotor (30 000 rot/min), causing the tensile and bending stresses. Therefore, experimental testing of coated samples is necessary in order to determine strength properties of TBCs. Beam samples with dimensions 50×10×2 mm were used in those studies. The TBC system consisted of 150 μm thick bond coat (NiCoCrAlY) and 300 μm thick top coat (YSZ) made by APS (air plasma spray) process. Samples were tested by three-point bending test with various loads. After bending tests, the samples were subjected to microscopic observation to determine the quantity of cracks and their depth. The above mentioned results were used to build numerical model and calibrate material data in Abaqus program. Brittle cracking damage model was applied for the TBC layer, which allows to remove elements after reaching criterion. Surface based cohesive behavior was used to model the delamination which may occur at the boundary between bond coat and top coat.

  3. A Second-order Divergence-constrained Multidimensional Numerical Scheme for Relativistic Two-fluid Electrodynamics

    NASA Astrophysics Data System (ADS)

    Amano, Takanobu

    2016-11-01

    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 exactly 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.

  4. Comparison of ice-phase microphysical parameterization schemes using numerical simulations of tropical convection

    NASA Technical Reports Server (NTRS)

    Mccumber, Michael; Tao, Wei-Kuo; Simpson, Joanne; Penc, Richard; Soong, Su-Tzai

    1991-01-01

    The performance of several ice parameterizations has been evaluated through a numerical cloud model. Ice effects using different schemes are contrasted with each other and with an ice-free control by incorporating them into the cloud model and by applying them to simulations of tropical squall systems. The latter are simulated in 2D so that a large domain can be used to incorporate a complete anvil. Nonsquall-type convective lines are simulated in 3D owing to their smaller horizontal scale. It is concluded that inclusion of ice microphysics in the cloud model enhanced the agreement of the simulated convection with some features of observed convection, including the proportion of surface rainfall in the anvil region and the intensity and structure of the radar brightband near the melting level in the anvil. In the experiments with bulk microphysics, three ice categories produced much better results than two ice categories, which in turn was better than no ice. For the tropical squall-type and nonsquall-type systems the optimal mix was ice, snow, and graupel.

  5. Analysis and Dynamically Consistent Numerical Schemes for the SIS Model and Related Reaction Diffusion Equation

    NASA Astrophysics Data System (ADS)

    Lubuma, J. M.-S.; Mureithi, E.; Terefe, Y. A.

    2011-11-01

    The classical SIS epidemiological model is extended in two directions: (a) The number of adequate contacts per infective in unit time is assumed to be a function of the total population in such a way that this number grows less rapidly as the total population increases; (b) A diffusion term is added to the SIS model and this leads to a reaction diffusion equation, which governs the spatial spread of the disease. With the parameter R0 representing the basic reproduction number, it is shown that R0 = 1 is a forward bifurcation for the model (a), with the disease-free equilibrium being globally asymptotic stable when R0 is less than 1. In the case when R0 is greater than 1, traveling wave solutions are found for the model (b). Nonstandard finite difference (NSFD) schemes that replicate the dynamics of the continuous models are presented. In particular, for the model (a), a nonstandard version of the Runge-Kutta method having high order of convergence is investigated. Numerical experiments that support the theory are provided.

  6. 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.

  7. 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

  8. 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

  9. 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

  10. 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.

  11. 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.

  12. 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.

  13. A numerical scheme for modelling reacting flow with detailed chemistry and transport.

    SciTech Connect

    Knio, Omar M.; Najm, Habib N.; Paul, Phillip H.

    2003-09-01

    An efficient projection scheme is developed for the simulation of reacting flow with detailed kinetics and transport. The scheme is based on a zero-Mach-number formulation of the compressible conservation equations for an ideal gas mixture. It is a modified version of the stiff operator-split scheme developed by Knio, Najm & Wyckoff (1999, J. Comput. Phys. 154, 428). Similar to its predecessor, the new scheme relies on Strang splitting of the discrete evolution equations, where diffusion is integrated in two half steps that are symmetrically distributed around a single stiff step for the reaction source terms. The diffusive half-step is integrated using an explicit single-step, multistage, Runge-Kutta-Chebyshev (RKC) method, which replaces the explicit, multi-step, fractional sub-step approach used in the previous formulation. This modification maintains the overall second-order convergence properties of the scheme and enhances the efficiency of the computations by taking advantage of the extended real-stability region of the RKC scheme. Two additional efficiency-enhancements are also explored, based on an extrapolation procedure for the transport coefficients and on the use of approximate Jacobian data evaluated on a coarse mesh. By including these enhancement schemes, performance tests using 2D computations with a detailed C{sub 1}C{sub 2} methane-air mechanism and a detailed mixture-averaged transport model indicate that speedup factors of about 15 are achieved over the previous split-stiff scheme.

  14. Dynamic design, numerical solution and effective verification of acceleration-level obstacle-avoidance scheme for robot manipulators

    NASA Astrophysics Data System (ADS)

    Xiao, Lin; Zhang, Yunong

    2016-03-01

    For avoiding obstacles and joint physical constraints of robot manipulators, this paper proposes and investigates a novel obstacle avoidance scheme (termed the acceleration-level obstacle-avoidance scheme). The scheme is based on a new obstacle-avoidance criterion that is designed by using the gradient neural network approach for the first time. In addition, joint physical constraints such as joint-angle limits, joint-velocity limits and joint-acceleration limits are incorporated into such a scheme, which is further reformulated as a quadratic programming (QP). Two important 'bridge' theorems are established so that such a QP can be converted equivalently to a linear variational inequality and then equivalently to a piecewise-linear projection equation (PLPE). A numerical algorithm based on a PLPE is thus developed and applied for an online solution of the resultant QP. Four path-tracking tasks based on the PA10 robot in the presence of point and window-shaped obstacles demonstrate and verify the effectiveness and accuracy of the acceleration-level obstacle-avoidance scheme. Besides, the comparisons between the non-obstacle-avoidance and obstacle-avoidance results further validate the superiority of the proposed scheme.

  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. A hybrid numerical prediction scheme for solar radiation estimation in un-gauged catchments.

    NASA Astrophysics Data System (ADS)

    Shamim, M. A.; Bray, M.; Ishak, A. M.; Remesan, R.; Han, D.

    2009-09-01

    The importance of solar radiation on earth's surface is depicted in its wide range of applications in the fields of meteorology, agricultural sciences, engineering, hydrology, crop water requirements, climatic changes and energy assessment. It is quite random in nature as it has to go through different processes of assimilation and dispersion while on its way to earth. Compared to other meteorological parameters, solar radiation is quite infrequently measured, for example, the worldwide ratio of stations collecting solar radiation to those collecting temperature is 1:500 (Badescu, 2008). Researchers, therefore, have to rely on indirect techniques of estimation that include nonlinear models, artificial intelligence (e.g. neural networks), remote sensing and numerical weather predictions (NWP). This study proposes a hybrid numerical prediction scheme for solar radiation estimation in un-gauged catchments. It uses the PSU/NCAR's Mesoscale Modelling system (MM5) (Grell et al., 1995) to parameterise the cloud effect on extraterrestrial radiation by dividing the atmosphere into four layers of very high (6-12 km), high (3-6 km), medium (1.5-3) and low (0-1.5) altitudes from earth. It is believed that various cloud forms exist within each of these layers. An hourly time series of upper air pressure and relative humidity data sets corresponding to all of these layers is determined for the Brue catchment, southwest UK, using MM5. Cloud Index (CI) was then determined using (Yang and Koike, 2002): 1 p?bi [ (Rh - Rh )] ci =------- max 0.0,---------cri dp pbi - ptipti (1- Rhcri) where, pbi and pti represent the air pressure at the top and bottom of each layer and Rhcri is the critical value of relative humidity at which a certain cloud type is formed. Output from a global clear sky solar radiation model (MRM v-5) (Kambezidis and Psiloglu, 2008) is used along with meteorological datasets of temperature and precipitation and astronomical information. The analysis is aided by the

  17. Numerical simulation by TVD schemes of complex shock reflections from airfoils at high angle of attack. [Total Variation Diminishing

    NASA Technical Reports Server (NTRS)

    Moon, Young J.; Yee, H. C.

    1987-01-01

    The shock-capturing capability of total variation diminishing (TVD) schemes is demonstrated for a more realistic complex shock-diffraction problem for which the experimental data are available. Second-order explicit upwind and symmetric TVD schemes are used to solve the time-dependent Euler equations of gas dynamics for the interaction of a blast wave with an airfoil at high angle-of-attack. The test cases considered are a time-dependent moving curved-shock wave and a contant moving planar-shock wave impinging at an angle-of-attack 30 deg on a NACA 0018 airfoil. Good agreement is obtained between isopycnic contours computed by the TVD schemes and those from experimental interferograms. No drastic difference in flow-field structure is found between the curved- and planar-shock wave cases, except for a difference in density level near the lower surface of the airfoil. Computation for cases with higher shock Mach numbers is also possible. Numerical experiments show that the symmetric TVD scheme is less sensitive to the boundary conditions treatment than the upwind scheme.

  18. A numerical resolution study of high order essentially non-oscillatory schemes applied to incompressible flow

    NASA Technical Reports Server (NTRS)

    Weinan, E.; Shu, Chi-Wang

    1994-01-01

    High order essentially non-oscillatory (ENO) schemes, originally designed for compressible flow and in general for hyperbolic conservation laws, are applied to incompressible Euler and Navier-Stokes equations with periodic boundary conditions. The projection to divergence-free velocity fields is achieved by fourth-order central differences through fast Fourier transforms (FFT) and a mild high-order filtering. The objective of this work is to assess the resolution of ENO schemes for large scale features of the flow when a coarse grid is used and small scale features of the flow, such as shears and roll-ups, are not fully resolved. It is found that high-order ENO schemes remain stable under such situations and quantities related to large scale features, such as the total circulation around the roll-up region, are adequately resolved.

  19. A numerical resolution study of high order essentially non-oscillatory schemes applied to incompressible flow

    NASA Technical Reports Server (NTRS)

    Weinan, E.; Shu, Chi-Wang

    1992-01-01

    High order essentially non-oscillatory (ENO) schemes, originally designed for compressible flow and in general for hyperbolic conservation laws, are applied to incompressible Euler and Navier-Stokes equations with periodic boundary conditions. The projection to divergence-free velocity fields is achieved by fourth order central differences through Fast Fourier Transforms (FFT) and a mild high-order filtering. The objective of this work is to assess the resolution of ENO schemes for large scale features of the flow when a coarse grid is used and small scale features of the flow, such as shears and roll-ups, are not fully resolved. It is found that high-order ENO schemes remain stable under such situations and quantities related to large-scale features, such as the total circulation around the roll-up region, are adequately resolved.

  20. Accurate adiabatic singlet-triplet gaps in atoms and molecules employing the third-order spin-flip algebraic diagrammatic construction scheme for the polarization propagator

    NASA Astrophysics Data System (ADS)

    Lefrancois, Daniel; Rehn, Dirk R.; Dreuw, Andreas

    2016-08-01

    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 were 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.

  1. Accurate adiabatic singlet-triplet gaps in atoms and molecules employing the third-order spin-flip algebraic diagrammatic construction scheme for the polarization propagator.

    PubMed

    Lefrancois, Daniel; Rehn, Dirk R; Dreuw, Andreas

    2016-08-28

    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 were 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. PMID:27586899

  2. On one numerical scheme of the solution of a three-dimensional problem of diffraction of an electromagnetic wave on thin ideally conductive screens

    SciTech Connect

    Ryzhakov, G. V.

    2014-11-12

    In the paper, the problem of diffraction on thin ideally conductive screens is reduced to vector hypersingular integral equation with integral treated in the sense of finite Hadamard value. An numerical scheme to solve the equation is introduced. The scheme is based on piecewise approximation of unknown function. The advantage of the scheme is that integral of singular part is reduced to contour integral which can be analytically calculated so numerical calculation are significantly accelerated. Several examples of resulting numerical experiments are given in comparison with known theoretical and experimental data.

  3. Pollutant transport by shallow water equations on unstructured meshes: Hyperbolization of the model and numerical solution via a novel flux splitting scheme

    NASA Astrophysics Data System (ADS)

    Vanzo, Davide; Siviglia, Annunziato; Toro, Eleuterio F.

    2016-09-01

    The purpose of this paper is twofold. First, using the Cattaneo's relaxation approach, we reformulate the system of governing equations for the pollutant transport by shallow water flows over non-flat topography and anisotropic diffusion as hyperbolic balance laws with stiff source terms. The proposed relaxation system circumvents the infinite wave speed paradox which is inherent in standard advection-diffusion models. This turns out to give a larger stability range for the choice of the time step. Second, following a flux splitting approach, we derive a novel numerical method to discretise the resulting problem. In particular, we propose a new flux splitting and study the associated two systems of differential equations, called the "hydrodynamic" and the "relaxed diffusive" system, respectively. For the presented splitting we analyse the resulting two systems of differential equations and propose two discretisation schemes of the Godunov-type. These schemes are simple to implement, robust, accurate and fast when compared with existing methods. The resulting method is implemented on unstructured meshes and is systematically assessed for accuracy, robustness and efficiency on a carefully selected suite of test problems including non-flat topography and wetting and drying problems. Formal second order accuracy is assessed through convergence rates studies.

  4. Comparison of Numerical Schemes for a Realistic Computational Aeroacoustics Benchmark Problem

    NASA Technical Reports Server (NTRS)

    Hixon, R.; Wu, J.; Nallasamy, M.; Sawyer, S.; Dyson, R.

    2004-01-01

    In this work, a nonlinear structured-multiblock CAA solver, the NASA GRC BASS code, will be tested on a realistic CAA benchmark problem. The purpose of this test is to ascertain what effect the high-accuracy solution methods used in CAA have on a realistic test problem, where both the mean flow and the unsteady waves are simultaneously computed on a fully curvilinear grid from a commercial grid generator. The proposed test will compare the solutions obtained using several finite-difference methods on identical grids to determine whether high-accuracy schemes have advantages for this benchmark problem.

  5. Numerical study of unsteady shockwave reflections using an upwind TVD scheme

    NASA Technical Reports Server (NTRS)

    Hsu, Andrew T.; Liou, Meng-Sing

    1990-01-01

    An unsteady TVD Navier-Stokes solver was developed and applied to the problem of shock reflection on a circular cylinder. The obtained numerical results were compared with the Schlieren photos from an experimental study. These results show that the present computer code has the ability of capturing moving shocks.

  6. Numerical and experimental investigation into passive hydrogen recovery scheme using vacuum ejector

    NASA Astrophysics Data System (ADS)

    Hwang, Jenn-Jiang; Cho, Ching-Chang; Wu, Wei; Chiu, Ching-Huang; Chiu, Kuo-Ching; Lin, Chih-Hong

    2015-02-01

    The current work presents a numerical and experimental investigation into a passive ejector for recovering the anode off-gas in a proton exchange membrane fuel cell (PEMFC) system. The proposed ejector is consisted of a convergent-divergent channel and a suction channel, and it is connected with the anode outlet of PEMFC system for recovery the anode off-gas into the main gas supply. Numerical simulations based on a three-dimensional compressible steady-state k-ɛ turbulent model are performed to examine the effects of the inlet mass flow rate and nozzle throat diameter on the pressure, Mach number, temperature, suction channel mass flow rate, outlet channel mass flow rate, and suction channel entrainment ratio, respectively. The numerical results are confirmed by means of an experimental investigation. It is shown that supersonic flow conditions are induced in the ejector; resulting in the induction of a vacuum pressure in the suction channel and the subsequent recovery of the anode off-gas at the outlet of the main channel. In addition, it is shown that the mass flow rate in the suction channel increases with an increasing mass flow rate at the primary channel inlet. Finally, the results show that a higher entrainment ratio is obtained as the throat diameter of the nozzle in the ejector is reduced. Overall, the results presented in this study provide a useful source of reference for developing the ejector devices applied to fuel cell systems while simultaneously avoiding extra energy consumption.

  7. 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

    The work in this report was conducted at NASA Ames Research Center during the period from August 1993 to January 1995 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 numerical method used here can be applied to complex geometries in a straightforward manner.

  8. 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.

  9. Effect of spatial configuration of an extended nonlinear Kierstead-Slobodkin reaction-transport model with adaptive numerical scheme.

    PubMed

    Owolabi, Kolade M; Patidar, Kailash C

    2016-01-01

    In this paper, we consider the numerical simulations of an extended nonlinear form of Kierstead-Slobodkin reaction-transport system in one and two dimensions. We employ the popular fourth-order exponential time differencing Runge-Kutta (ETDRK4) schemes proposed by Cox and Matthew (J Comput Phys 176:430-455, 2002), that was modified by Kassam and Trefethen (SIAM J Sci Comput 26:1214-1233, 2005), for the time integration of spatially discretized partial differential equations. We demonstrate the supremacy of ETDRK4 over the existing exponential time differencing integrators that are of standard approaches and provide timings and error comparison. Numerical results obtained in this paper have granted further insight to the question 'What is the minimal size of the spatial domain so that the population persists?' posed by Kierstead and Slobodkin (J Mar Res 12:141-147, 1953), with a conclusive remark that the population size increases with the size of the domain. In attempt to examine the biological wave phenomena of the solutions, we present the numerical results in both one- and two-dimensional space, which have interesting ecological implications. Initial data and parameter values were chosen to mimic some existing patterns.

  10. A Numerical Scheme for Special Relativistic Radiation Magnetohydrodynamics Based on Solving the Time-dependent Radiative Transfer Equation

    NASA Astrophysics Data System (ADS)

    Ohsuga, Ken; Takahashi, Hiroyuki R.

    2016-02-01

    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 explicitly 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.

  11. On a class of TVD schemes for gas dynamic calculations. [Total Variation Diminishing

    NASA Technical Reports Server (NTRS)

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

    1985-01-01

    The purpose of this paper is to review a class of explicit and implicit second-order accurate Total Variation Diminishing (TVD) schemes and to show by numerical experiments, the performance of these schemes to the Euler equations of gas dynamics. The method of constructing these second-order accurate TVD schemes is sometimes known as the modified flux approach.

  12. PROBABILISTIC SIMULATION OF SUBSURFACE FLUID FLOW: A STUDY USING A NUMERICAL SCHEME

    SciTech Connect

    Buscheck, Timothy Eric

    1980-03-01

    There has been an increasing interest in probabilistic modeling of hydrogeologic systems. The classical approach to groundwater modeling has been deterministic in nature, where individual layers and formations are assumed to be uniformly homogeneous. Even in the case of complex heterogeneous systems, the heterogeneities describe the differences in parameter values between various layers, but not within any individual layer. In a deterministic model a single-number is assigned to each hydrogeologic parameter, given a particular scale of interest. However, physically there is no such entity as a truly uniform and homogeneous unit. Single-number representations or deterministic predictions are subject to uncertainties. The approach used in this work models such uncertainties with probabilistic parameters. The resulting statistical distributions of output variables are analyzed. A numerical algorithm, based on axiomatic principles of probability theory, performs arithmetic operations between probability distributions. Two subroutines are developed from the algorithm and incorporated into the computer program TERZAGI, which solves groundwater flow problems in saturated, multi-dimensional systems. The probabilistic computer program is given the name, PROGRES. The algorithm has been applied to study the following problems: one-dimensional flow through homogeneous media, steady-state and transient flow conditions, one-dimensional flow through heterogeneous media, steady-state and transient flow conditions, and two-dimensional steady-stte flow through heterogeneous media. The results are compared with those available in the literature.

  13. Immersed boundary Eulerian-Lagrangian 3D simulation of pyroclastic density currents: numerical scheme and experimental validation

    NASA Astrophysics Data System (ADS)

    Doronzo, Domenico Maria; de Tullio, Marco; Pascazio, Giuseppe; Dellino, Pierfrancesco

    2010-05-01

    Pyroclastic density currents are ground hugging, hot, gas-particle flows representing the most hazardous events of explosive volcanism. Their impact on structures is a function of dynamic pressure, which expresses the lateral load that such currents exert over buildings. In this paper we show how analog experiments can be matched with numerical simulations for capturing the essential physics of the multiphase flow. We used an immersed boundary scheme for the mesh generation, which helped in reconstructing the steep velocity and particle concentration gradients near the ground surface. Results show that the calculated values of dynamic pressure agree reasonably with the experimental measurements. These outcomes encourage future application of our method for the assessment of the impact of pyroclastic density currents at the natural scale.

  14. 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.

  15. Investigation of magnetic field generation by non-Gaussian, non-Markovian velocity fluctuations using meshless, Lagrangian numerical schemes

    NASA Astrophysics Data System (ADS)

    Sanchez, Raul; Newman, David

    2014-10-01

    Turbulent velocity fields can generate perturbations of the electric current and magnetic field that, under certain conditions, may generate an average, large-scale magnetic field. Such generation is important to understand the behavior of stars, planetary and laboratory plasmas. This generation is traditionally studied by assuming near-Gaussian, random velocity fluctuations. This simplification allows to exprese the effective electromotive force in Faraday's law in terms of a piece proportional to the large-scale magnetic field itself (the α-term) and another proportional to its curl (the β term) assuming certain symmetry conditions are met. Physically, the α-term is a measure of the mean helicity of the flow and drives the dynamo process. In a previous contribution, we examined theoretically what consequences would follow from assuming instead Levy-distributed, Lagrangianly-correlated velocity fields, that have been recently identified as of relevance in regimes of near-marginal turbulence or in the presence of a strong, stable sheared flow. Here, we will discuss and extend these results numerically by implementing the kinematic dynamo equation using a Lagrangian, meshless numerical method inspired by the SPH schemes frequently used in hydrodynamics.

  16. BlueDetect: An iBeacon-Enabled Scheme for Accurate and Energy-Efficient Indoor-Outdoor Detection and Seamless Location-Based Service.

    PubMed

    Zou, Han; Jiang, Hao; Luo, Yiwen; Zhu, Jianjie; Lu, Xiaoxuan; Xie, Lihua

    2016-01-01

    The location and contextual status (indoor or outdoor) is fundamental and critical information for upper-layer applications, such as activity recognition and location-based services (LBS) for individuals. In addition, optimizations of building management systems (BMS), such as the pre-cooling or heating process of the air-conditioning system according to the human traffic entering or exiting a building, can utilize the information, as well. The emerging mobile devices, which are equipped with various sensors, become a feasible and flexible platform to perform indoor-outdoor (IO) detection. However, power-hungry sensors, such as GPS and WiFi, should be used with caution due to the constrained battery storage on mobile device. We propose BlueDetect: an accurate, fast response and energy-efficient scheme for IO detection and seamless LBS running on the mobile device based on the emerging low-power iBeacon technology. By leveraging the on-broad Bluetooth module and our proposed algorithms, BlueDetect provides a precise IO detection service that can turn on/off on-board power-hungry sensors smartly and automatically, optimize their performances and reduce the power consumption of mobile devices simultaneously. Moreover, seamless positioning and navigation services can be realized by it, especially in a semi-outdoor environment, which cannot be achieved by GPS or an indoor positioning system (IPS) easily. We prototype BlueDetect on Android mobile devices and evaluate its performance comprehensively. The experimental results have validated the superiority of BlueDetect in terms of IO detection accuracy, localization accuracy and energy consumption. PMID:26907295

  17. BlueDetect: An iBeacon-Enabled Scheme for Accurate and Energy-Efficient Indoor-Outdoor Detection and Seamless Location-Based Service

    PubMed Central

    Zou, Han; Jiang, Hao; Luo, Yiwen; Zhu, Jianjie; Lu, Xiaoxuan; Xie, Lihua

    2016-01-01

    The location and contextual status (indoor or outdoor) is fundamental and critical information for upper-layer applications, such as activity recognition and location-based services (LBS) for individuals. In addition, optimizations of building management systems (BMS), such as the pre-cooling or heating process of the air-conditioning system according to the human traffic entering or exiting a building, can utilize the information, as well. The emerging mobile devices, which are equipped with various sensors, become a feasible and flexible platform to perform indoor-outdoor (IO) detection. However, power-hungry sensors, such as GPS and WiFi, should be used with caution due to the constrained battery storage on mobile device. We propose BlueDetect: an accurate, fast response and energy-efficient scheme for IO detection and seamless LBS running on the mobile device based on the emerging low-power iBeacon technology. By leveraging the on-broad Bluetooth module and our proposed algorithms, BlueDetect provides a precise IO detection service that can turn on/off on-board power-hungry sensors smartly and automatically, optimize their performances and reduce the power consumption of mobile devices simultaneously. Moreover, seamless positioning and navigation services can be realized by it, especially in a semi-outdoor environment, which cannot be achieved by GPS or an indoor positioning system (IPS) easily. We prototype BlueDetect on Android mobile devices and evaluate its performance comprehensively. The experimental results have validated the superiority of BlueDetect in terms of IO detection accuracy, localization accuracy and energy consumption. PMID:26907295

  18. BlueDetect: An iBeacon-Enabled Scheme for Accurate and Energy-Efficient Indoor-Outdoor Detection and Seamless Location-Based Service.

    PubMed

    Zou, Han; Jiang, Hao; Luo, Yiwen; Zhu, Jianjie; Lu, Xiaoxuan; Xie, Lihua

    2016-02-22

    The location and contextual status (indoor or outdoor) is fundamental and critical information for upper-layer applications, such as activity recognition and location-based services (LBS) for individuals. In addition, optimizations of building management systems (BMS), such as the pre-cooling or heating process of the air-conditioning system according to the human traffic entering or exiting a building, can utilize the information, as well. The emerging mobile devices, which are equipped with various sensors, become a feasible and flexible platform to perform indoor-outdoor (IO) detection. However, power-hungry sensors, such as GPS and WiFi, should be used with caution due to the constrained battery storage on mobile device. We propose BlueDetect: an accurate, fast response and energy-efficient scheme for IO detection and seamless LBS running on the mobile device based on the emerging low-power iBeacon technology. By leveraging the on-broad Bluetooth module and our proposed algorithms, BlueDetect provides a precise IO detection service that can turn on/off on-board power-hungry sensors smartly and automatically, optimize their performances and reduce the power consumption of mobile devices simultaneously. Moreover, seamless positioning and navigation services can be realized by it, especially in a semi-outdoor environment, which cannot be achieved by GPS or an indoor positioning system (IPS) easily. We prototype BlueDetect on Android mobile devices and evaluate its performance comprehensively. The experimental results have validated the superiority of BlueDetect in terms of IO detection accuracy, localization accuracy and energy consumption.

  19. Numerical Simulation of the Slider Air Bearing Problem of Hard Disk Drives by Two Multidimensional Upwind Residual Distribution Schemes over Unstructured Triangular Meshes

    NASA Astrophysics Data System (ADS)

    Wu, Lin; Bogy, D. B.

    2001-09-01

    In this paper we present two multigrid numerical schemes over unstructured triangular meshes that solve the slider air bearing problem of hard disk drives. For each fixed slider attitude, the air bearing pressure is obtained by solving the generalized Reynolds equation. The convection part of the equation is modeled in one scheme by the PSI multidimensional upwind residual distribution approach and in the other scheme by the SUPG finite element approach cast in residual distribution form. In both schemes, a linear Galerkin method is used to discretize the diffusion terms. In addition, a non-nested multigrid iteration technique is used to speed up the convergence rate. Finally, the balanced steady state flying attitude of the slider subject to pre-applied suspension force and torques is obtained by a Quasi-Newton iteration method (Broyden's method), and the results of the numerical solutions are compared to each other and to experimental data.

  20. Evaluation of Injection Efficiency of Carbon Dioxide Using an Integrated Injection Well and Geologic Formation Numerical Simulation Scheme

    NASA Astrophysics Data System (ADS)

    Kihm, J.; Park, S.; Kim, J.; SNU CO2 GEO-SEQ TEAM

    2011-12-01

    A series of integrated injection well and geologic formation numerical simulations was performed to evaluate the injection efficiency of carbon dioxide using a multiphase thermo-hydrological numerical model. The numerical simulation results show that groundwater flow, carbon dioxide flow, and heat transport in both injection well and sandstone formation can be simultaneously analyzed, and thus the injection efficiency (i.e., injection rate and injectivity) of carbon dioxide can be quantitatively evaluated using the integrated injection well and geologic formation numerical simulation scheme. The injection rate and injectivity of carbon dioxide increase rapidly during the early period of time (about 10 days) and then increase slightly up to about 2.07 kg/s (equivalent to 0.065 Mton/year) and about 2.84 × 10-7 kg/s/Pa, respectively, until 10 years for the base case. The sensitivity test results show that the injection pressure and temperature of carbon dioxide at the wellhead have significant impacts on its injection rate and injectivity. The vertical profile of the fluid pressure in the injection well becomes almost a hydrostatical equilibrium state within 1 month for all the cases. The vertical profile of the fluid temperature in the injection well becomes a monotonously increasing profile with the depth due to isenthalpic or adiabatic compression within 6 months for all the cases. The injection rate of carbon dioxide increases linearly with the fluid pressure difference between the well bottom and the sandstone formation far from the injection well. In contrast, the injectivity of carbon dioxide varies unsystematically with the fluid pressure difference. On the other hand, the reciprocal of the kinematic viscosity of carbon dioxide at the well bottom has an excellent linear relationship with the injectivity of carbon dioxide. It indicates that the above-mentioned variation of the injectivity of carbon dioxide can be corrected using this linear relationship. The

  1. Analytical and numerical schemes for a derivative with filtering property and no singular kernel with applications to diffusion

    NASA Astrophysics Data System (ADS)

    Doungmo Goufo, Emile Franc; Atangana, Abdon

    2016-08-01

    There have been numbers of conflicting and confusing situations, but also uniformity, in the application of the two most popular fractional derivatives, namely the classic Riemann-Liouville and Caputo fractional derivatives. The range of these issues is wide, including the initialization with the Caputo derivative and its observed difficulties compared to the Riemann-Liouville initialization conditions. In this paper, being aware of these issues and reacting to the newly introduced Caputo-Fabrizio fractional derivative (CFFD) without singular kernel, we introduce a new definition of fractional derivative called the new Riemann-Liouville fractional derivative (NRLFD) without singular kernel. The filtering property of the NRLFD is pointed out by showing it as the derivative of a convolution and contrary to the CFFD, it matches with the function when the order is zero. We also explore various scientific situations that may be conflicting and confusing in the applicability of both new derivatives. In particular, we show that both definitions still have some basic similarities, like not obeying the traditional chain rule. Furthermore, we provide the explicit formula for the Laplace transform of the NRLFD and we prove that, contrary to the CFFD, the NRLFD requires non-constant initial conditions and does not require the function f to be continuous or differentiable. Some simulations for the NRLFD are presented for different values of the derivative order. In the second part of this work, numerical approximations for the first- and second-order NRLFD are developped followed by a concrete application to diffusion. The stability of the numerical scheme is proved and numerical simulations are performed for different values of the derivative order α. They exhibit similar behavior for closed values of α.

  2. Self-consistent field theory and numerical scheme for calculating the phase diagram of wormlike diblock copolymers.

    PubMed

    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. PMID:24229202

  3. 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.

  4. Numerical parameter constraints for accurate PIC-DSMC simulation of breakdown from arc initiation to stable arcs

    NASA Astrophysics Data System (ADS)

    Moore, Christopher; Hopkins, Matthew; Moore, Stan; Boerner, Jeremiah; Cartwright, Keith

    2015-09-01

    Simulation of breakdown is important for understanding and designing a variety of applications such as mitigating undesirable discharge events. Such simulations need to be accurate through early time arc initiation to late time stable arc behavior. Here we examine constraints on the timestep and mesh size required for arc simulations using the particle-in-cell (PIC) method with direct simulation Monte Carlo (DMSC) collisions. Accurate simulation of electron avalanche across a fixed voltage drop and constant neutral density (reduced field of 1000 Td) was found to require a timestep ~ 1/100 of the mean time between collisions and a mesh size ~ 1/25 the mean free path. These constraints are much smaller than the typical PIC-DSMC requirements for timestep and mesh size. Both constraints are related to the fact that charged particles are accelerated by the external field. Thus gradients in the electron energy distribution function can exist at scales smaller than the mean free path and these must be resolved by the mesh size for accurate collision rates. Additionally, the timestep must be small enough that the particle energy change due to the fields be small in order to capture gradients in the cross sections versus energy. Sandia National Laboratories is a multi-program laboratory managed and operated by Sandia Corporation, a wholly owned subsidiary of Lockheed Martin Corporation, for the U.S. DOE's National Nuclear Security Administration under Contract DE-AC04-94AL85000.

  5. Simulation of ammonium and chromium transport in porous media using coupling scheme of a numerical algorithm and a stochastic algorithm.

    PubMed

    Palanichamy, Jegathambal; Schüttrumpf, Holger; Köngeter, Jürgen; Becker, Torsten; Palani, Sundarambal

    2009-01-01

    The migration of the species of chromium and ammonium in groundwater and their effective remediation depend on the various hydro-geological characteristics of the system. The computational modeling of the reactive transport problems is one of the most preferred tools for field engineers in groundwater studies to make decision in pollution abatement. The analytical models are less modular in nature with low computational demand where the modification is difficult during the formulation of different reactive systems. Numerical models provide more detailed information with high computational demand. Coupling of linear partial differential Equations (PDE) for the transport step with a non-linear system of ordinary differential equations (ODE) for the reactive step is the usual mode of solving a kinetically controlled reactive transport equation. This assumption is not appropriate for a system with low concentration of species such as chromium. Such reaction systems can be simulated using a stochastic algorithm. In this paper, a finite difference scheme coupled with a stochastic algorithm for the simulation of the transport of ammonium and chromium in subsurface media has been detailed.

  6. Numerical simulation of pharyngeal airflow applied to obstructive sleep apnea: effect of the nasal cavity in anatomically accurate airway models.

    PubMed

    Cisonni, Julien; Lucey, Anthony D; King, Andrew J C; Islam, Syed Mohammed Shamsul; Lewis, Richard; Goonewardene, Mithran S

    2015-11-01

    Repetitive brief episodes of soft-tissue collapse within the upper airway during sleep characterize obstructive sleep apnea (OSA), an extremely common and disabling disorder. Failure to maintain the patency of the upper airway is caused by the combination of sleep-related loss of compensatory dilator muscle activity and aerodynamic forces promoting closure. The prediction of soft-tissue movement in patient-specific airway 3D mechanical models is emerging as a useful contribution to clinical understanding and decision making. Such modeling requires reliable estimations of the pharyngeal wall pressure forces. While nasal obstruction has been recognized as a risk factor for OSA, the need to include the nasal cavity in upper-airway models for OSA studies requires consideration, as it is most often omitted because of its complex shape. A quantitative analysis of the flow conditions generated by the nasal cavity and the sinuses during inspiration upstream of the pharynx is presented. Results show that adequate velocity boundary conditions and simple artificial extensions of the flow domain can reproduce the essential effects of the nasal cavity on the pharyngeal flow field. Therefore, the overall complexity and computational cost of accurate flow predictions can be reduced.

  7. Simplification of the unified gas kinetic scheme.

    PubMed

    Chen, Songze; Guo, Zhaoli; Xu, Kun

    2016-08-01

    The unified gas kinetic scheme (UGKS) is an asymptotic preserving (AP) scheme for kinetic equations. It is superior for transition flow simulation and has been validated in the past years. However, compared to the well-known discrete ordinate method (DOM), which is a classical numerical method solving the kinetic equations, the UGKS needs more computational resources. In this study, we propose a simplification of the unified gas kinetic scheme. It allows almost identical numerical cost as the DOM, but predicts numerical results as accurate as the UGKS. In the simplified scheme, the numerical flux for the velocity distribution function and the numerical flux for the macroscopic conservative quantities are evaluated separately. The equilibrium part of the UGKS flux is calculated by analytical solution instead of the numerical quadrature in velocity space. The simplification is equivalent to a flux hybridization of the gas kinetic scheme for the Navier-Stokes (NS) equations and the conventional discrete ordinate method. Several simplification strategies are tested, through which we can identify the key ingredient of the Navier-Stokes asymptotic preserving property. Numerical tests show that, as long as the collision effect is built into the macroscopic numerical flux, the numerical scheme is Navier-Stokes asymptotic preserving, regardless the accuracy of the microscopic numerical flux for the velocity distribution function. PMID:27627418

  8. Simplification of the unified gas kinetic scheme

    NASA Astrophysics Data System (ADS)

    Chen, Songze; Guo, Zhaoli; Xu, Kun

    2016-08-01

    The unified gas kinetic scheme (UGKS) is an asymptotic preserving (AP) scheme for kinetic equations. It is superior for transition flow simulation and has been validated in the past years. However, compared to the well-known discrete ordinate method (DOM), which is a classical numerical method solving the kinetic equations, the UGKS needs more computational resources. In this study, we propose a simplification of the unified gas kinetic scheme. It allows almost identical numerical cost as the DOM, but predicts numerical results as accurate as the UGKS. In the simplified scheme, the numerical flux for the velocity distribution function and the numerical flux for the macroscopic conservative quantities are evaluated separately. The equilibrium part of the UGKS flux is calculated by analytical solution instead of the numerical quadrature in velocity space. The simplification is equivalent to a flux hybridization of the gas kinetic scheme for the Navier-Stokes (NS) equations and the conventional discrete ordinate method. Several simplification strategies are tested, through which we can identify the key ingredient of the Navier-Stokes asymptotic preserving property. Numerical tests show that, as long as the collision effect is built into the macroscopic numerical flux, the numerical scheme is Navier-Stokes asymptotic preserving, regardless the accuracy of the microscopic numerical flux for the velocity distribution function.

  9. Numerical framework and performance of the new multiple-phase cloud microphysics scheme in RegCM4.5: precipitation, cloud microphysics, and cloud radiative effects

    NASA Astrophysics Data System (ADS)

    Nogherotto, Rita; Tompkins, Adrian Mark; Giuliani, Graziano; Coppola, Erika; Giorgi, Filippo

    2016-07-01

    We implement and evaluate a new parameterization scheme for stratiform cloud microphysics and precipitation within regional climate model RegCM4. This new parameterization is based on a multiple-phase one-moment cloud microphysics scheme built upon the implicit numerical framework recently developed and implemented in the ECMWF operational forecasting model. The parameterization solves five prognostic equations for water vapour, cloud liquid water, rain, cloud ice, and snow mixing ratios. Compared to the pre-existing scheme, it allows a proper treatment of mixed-phase clouds and a more physically realistic representation of cloud microphysics and precipitation. Various fields from a 10-year long integration of RegCM4 run in tropical band mode with the new scheme are compared with their counterparts using the previous cloud scheme and are evaluated against satellite observations. In addition, an assessment using the Cloud Feedback Model Intercomparison Project (CFMIP) Observational Simulator Package (COSP) for a 1-year sub-period provides additional information for evaluating the cloud optical properties against satellite data. The new microphysics parameterization yields an improved simulation of cloud fields, and in particular it removes the overestimation of upper level cloud characteristics of the previous scheme, increasing the agreement with observations and leading to an amelioration of a long-standing problem in the RegCM system. The vertical cloud profile produced by the new scheme leads to a considerably improvement of the representation of the longwave and shortwave components of the cloud radiative forcing.

  10. Numerical simulation of precipitation formation in the case orographically induced convective cloud: Comparison of the results of bin and bulk microphysical schemes

    NASA Astrophysics Data System (ADS)

    Sarkadi, N.; Geresdi, I.; Thompson, G.

    2016-11-01

    In this study, results of bulk and bin microphysical schemes are compared in the case of idealized simulations of pre-frontal orographic clouds with enhanced embedded convection. The description graupel formation by intensive riming of snowflakes was improved compared to prior versions of each scheme. Two methods of graupel melting coincident with collisions with water drops were considered: (1) all simulated melting and collected water drops increase the amount of melted water on the surface of graupel particles with no shedding permitted; (2) also no shedding permitted due to melting, but the collision with the water drops can induce shedding from the surface of the graupel particles. The results of the numerical experiments show: (i) The bin schemes generate graupel particles more efficiently by riming than the bulk scheme does; the intense riming of snowflakes was the most dominant process for the graupel formation. (ii) The collision-induced shedding significantly affects the evolution of the size distribution of graupel particles and water drops below the melting level. (iii) The three microphysical schemes gave similar values for the domain integrated surface precipitation, but the patterns reveal meaningful differences. (iv) Sensitivity tests using the bulk scheme show that the depth of the melting layer is sensitive to the description of the terminal velocity of the melting snow. (v) Comparisons against Convair-580 flight measurements suggest that the bin schemes simulate well the evolution of the pristine ice particles and liquid drops, while some inaccuracy can occur in the description of snowflakes riming. (vi) The bin scheme with collision-induced shedding reproduced well the quantitative characteristics of the observed bright band.

  11. Well-balanced schemes for the Euler equations with gravitation

    NASA Astrophysics Data System (ADS)

    Käppeli, R.; Mishra, S.

    2014-02-01

    Well-balanced high-order finite volume schemes are designed to approximate the Euler equations with gravitation. The schemes preserve discrete equilibria, corresponding to a large class of physically stable hydrostatic steady states. Based on a novel local hydrostatic reconstruction, the derived schemes are well-balanced for any consistent numerical flux for the Euler equations. The form of the hydrostatic reconstruction is both very simple and computationally efficient as it requires no analytical or numerical integration. Moreover, as required by many interesting astrophysical scenarios, the schemes are applicable beyond the ideal gas law. Both first- and second-order accurate versions of the schemes and their extension to multi-dimensional equilibria are presented. Several numerical experiments demonstrating the superior performance of the well-balanced schemes, as compared to standard finite volume schemes, are also presented.

  12. Application of TVD schemes for the Euler equations of gas dynamics. [method of Total Variation Diminishing for shock wave computation

    NASA Technical Reports Server (NTRS)

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

    1985-01-01

    Highly accurate and yet stable shock-capturing finite difference schemes have been designed for the computation of the Euler equations of gas dynamics. Four different principles for the construction of high resolution total variation diminishing (TVD) schemes are available, including hybrid schemes, a second-order extension of Godunov's scheme by van Leer (1979), the modified flux approach of Harten (1983, 1984), and the numerical fluctuation approach of Roe (1985). The present paper has the objective to review the class of second-order TVD schemes via the modified flux approach. Attention is given to first-order TVD schemes, a second-order accurate explicit TVD scheme, the global order of accuracy of the second-order TVD scheme, extensions to systems and two-dimensional conservation laws, numerical experiments with a second-order explicit TVD scheme, implicit TVD schemes, and second-order implicit TVD schemes.

  13. 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.

  14. Numerical simulation of a dust event in northeastern Germany with a new dust emission scheme in COSMO-ART

    Technology Transfer Automated Retrieval System (TEKTRAN)

    The dust emission scheme of Shao (2004) has been implemented into the regional atmospheric model COSMO-ART and has been applied to a severe dust event in northeastern Germany on 8th April 2011. The model sensitivity to soil moisture and vegetation cover has been studied. Soil moisture has been found...

  15. Accurate calculation of chemical shifts in highly dynamic H2@C60 through an integrated quantum mechanics/molecular dynamics scheme.

    PubMed

    Jiménez-Osés, Gonzalo; García, José I; Corzana, Francisco; Elguero, José

    2011-05-20

    A new protocol combining classical MD simulations and DFT calculations is presented to accurately estimate the (1)H NMR chemical shifts of highly mobile guest-host systems and their thermal dependence. This strategy has been successfully applied for the hydrogen molecule trapped into C(60) fullerene, an unresolved and challenging prototypical case for which experimental values have never been reproduced. The dependence of the final values on the theoretical method and their implications to avoid over interpretation of the obtained results are carefully described.

  16. An energy and potential enstrophy conserving numerical scheme for the multi-layer shallow water equations with complete Coriolis force

    NASA Astrophysics Data System (ADS)

    Stewart, Andrew L.; Dellar, Paul J.

    2016-05-01

    We present an energy- and potential enstrophy-conserving scheme for the non-traditional shallow water equations that include the complete Coriolis force and topography. These integral conservation properties follow from material conservation of potential vorticity in the continuous shallow water equations. The latter property cannot be preserved by a discretisation on a fixed Eulerian grid, but exact conservation of a discrete energy and a discrete potential enstrophy seems to be an effective substitute that prevents any distortion of the forward and inverse cascades in quasi-two dimensional turbulence through spurious sources and sinks of energy and potential enstrophy, and also increases the robustness of the scheme against nonlinear instabilities. We exploit the existing Arakawa-Lamb scheme for the traditional shallow water equations, reformulated by Salmon as a discretisation of the Hamiltonian and Poisson bracket for this system. The non-rotating, traditional, and our non-traditional shallow water equations all share the same continuous Hamiltonian structure and Poisson bracket, provided one distinguishes between the particle velocity and the canonical momentum per unit mass. We have determined a suitable discretisation of the non-traditional canonical momentum, which includes additional coupling between the layer thickness and velocity fields, and modified the discrete kinetic energy to suppress an internal symmetric computational instability that otherwise arises for multiple layers. The resulting scheme exhibits the expected second-order convergence under spatial grid refinement. We also show that the drifts in the discrete total energy and potential enstrophy due to temporal truncation error may be reduced to machine precision under suitable refinement of the timestep using the third-order Adams-Bashforth or fourth-order Runge-Kutta integration schemes.

  17. An optimal scheme for numerical evaluation of Eshelby tensors and its implementation in a MATLAB package for simulating the motion of viscous ellipsoids in slow flows

    NASA Astrophysics Data System (ADS)

    Qu, Mengmeng; Jiang, Dazhi; Lu, Lucy X.

    2016-11-01

    To address the multiscale deformation and fabric development in Earth's ductile lithosphere, micromechanics-based self-consistent homogenization is commonly used to obtain macroscale rheological properties from properties of constituent elements. The homogenization is heavily based on the solution of an Eshelby viscous inclusion in a linear viscous medium and the extension of the solution to nonlinear viscous materials. The homogenization requires repeated numerical evaluation of Eshelby tensors for constituent elements and becomes ever more computationally challenging as the elements are deformed to more elongate or flattened shapes. In this paper, we develop an optimal scheme for evaluating Eshelby tensors, using a combination of a product Gaussian quadrature and the Lebedev quadrature. We first establish, through numerical experiments, an empirical relationship between the inclusion shape and the computational time it takes to evaluate its Eshelby tensors. We then use the relationship to develop an optimal scheme for selecting the most efficient quadrature to obtain the Eshelby tensors. The optimal scheme is applicable to general homogenizations. In this paper, it is implemented in a MATLAB package for investigating the evolution of solitary rigid or deformable inclusions and the development of shape preferred orientations in multi-inclusion systems during deformation. The MATLAB package, upgrading an earlier effort written in MathCad, can be downloaded online.

  18. Towards an "All Speed" Unstructured Upwind Scheme

    NASA Technical Reports Server (NTRS)

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

    2009-01-01

    In the authors previous studies [1], a time-accurate, upwind finite volume method (ETAU scheme) for computing compressible flows on unstructured grids was proposed. The scheme is second order accurate in space and time and yields high resolution in the presence of discontinuities. The scheme features a multidimensional limiter and multidimensional numerical dissipation. These help to stabilize the numerical process and to overcome the annoying pathological behaviors of upwind schemes. In the present paper, it will be further shown that such multidimensional treatments also lead to a nearly all-speed or Mach number insensitive upwind scheme. For flows at very high Mach number, e.g., 10, local numerical instabilities or the pathological behaviors are suppressed, while for flows at very low Mach number, e.g., 0.02, computation can be directly carried out without invoking preconditioning. For flows in different Mach number regimes, i.e., low, medium, and high Mach numbers, one only needs to adjust one or two parameters in the scheme. Several examples with low and high Mach numbers are demonstrated in this paper. Thus, the ETAU scheme is applicable to a broad spectrum of flow regimes ranging from high supersonic to low subsonic, appropriate for both CFD (computational fluid dynamics) and CAA (computational aeroacoustics).

  19. Investigation of numerical viscosities and dissipation rates of second-order TVD-MUSCL schemes for implicit large-eddy simulation

    NASA Astrophysics Data System (ADS)

    Bidadi, Shreyas; Rani, Sarma L.

    2015-01-01

    Monotonically integrated large-eddy simulation (MILES) approach utilizes the dissipation inherent to shock-capturing schemes to emulate the role played by explicit subgrid-scale eddy diffusivity at the high-wavenumber end of the turbulent energy spectrum. In the current study, a novel formulation is presented for quantifying the numerical viscosity inherent to Roe-based second-order TVD-MUSCL schemes for the Euler equations. Using this formulation, the effects of numerical viscosity and dissipation rate on implicit large-eddy simulations of turbulent flows are investigated. At first, the three-dimensional (3-D) finite-volume extension of the original Roe's flux, including Roe's Jacobian matrix, is presented. The fluxes are then extended to second-order using van Leer's MUSCL extrapolation technique. Starting from the 3-D Roe-MUSCL flux, an expression is derived for the numerical viscosity as a function of flux limiter and characteristic speed for each conserved variable, distance between adjacent cell centers, and a scaling parameter. Motivated by Thornber et al. [16] study, the high numerical viscosity inherent to TVD-MUSCL schemes is mitigated using a z-factor that depends on local Mach number. The TVD limiters, along with the z-factor, were initially applied to the 1-D shock-tube and 2-D inviscid supersonic wedge flows. Spatial profiles of numerical viscosities are plotted, which provide insights into the role of these limiters in controlling the dissipative nature of Roe's flux while maintaining monotonicity and stability in regions of high gradients. Subsequently, a detailed investigation was performed of decaying homogeneous isotropic turbulence with varying degrees of compressibility. Spectra of numerical viscosity and dissipation rate are presented, which clearly demonstrate the effectiveness of the z-factor both in narrowing the wavenumber range in which dissipation occurs, and in shifting the location of dissipation peak closer to the cut-off wavenumber

  20. Using the PPML approach for constructing a low-dissipation, operator-splitting scheme for numerical simulations of hydrodynamic flows

    NASA Astrophysics Data System (ADS)

    Kulikov, Igor; Vorobyov, Eduard

    2016-07-01

    An approach for constructing a low-dissipation numerical method is described. The method is based on a combination of the operator-splitting method, Godunov method, and piecewise-parabolic method on the local stencil. Numerical method was tested on a standard suite of hydrodynamic test problems. In addition, the performance of the method is demonstrated on a global test problem showing the development of a spiral structure in a gravitationally unstable gaseous galactic disk.

  1. A novel stress-accurate FE technology for highly non-linear analysis with incompressibility constraint. Application to the numerical simulation of the FSW process

    NASA Astrophysics Data System (ADS)

    Chiumenti, M.; Cervera, M.; Agelet de Saracibar, C.; Dialami, N.

    2013-05-01

    In this work a novel finite element technology based on a three-field mixed formulation is presented. The Variational Multi Scale (VMS) method is used to circumvent the LBB stability condition allowing the use of linear piece-wise interpolations for displacement, stress and pressure fields, respectively. The result is an enhanced stress field approximation which enables for stress-accurate results in nonlinear computational mechanics. The use of an independent nodal variable for the pressure field allows for an adhoc treatment of the incompressibility constraint. This is a mandatory requirement due to the isochoric nature of the plastic strain in metal forming processes. The highly non-linear stress field typically encountered in the Friction Stir Welding (FSW) process is used as an example to show the performance of this new FE technology. The numerical simulation of the FSW process is tackled by means of an Arbitrary-Lagrangian-Eulerian (ALE) formulation. The computational domain is split into three different zones: the work.piece (defined by a rigid visco-plastic behaviour in the Eulerian framework), the pin (within the Lagrangian framework) and finally the stirzone (ALE formulation). A fully coupled thermo-mechanical analysis is introduced showing the heat fluxes generated by the plastic dissipation in the stir-zone (Sheppard rigid-viscoplastic constitutive model) as well as the frictional dissipation at the contact interface (Norton frictional contact model). Finally, tracers have been implemented to show the material flow around the pin allowing a better understanding of the welding mechanism. Numerical results are compared with experimental evidence.

  2. Explicit robust schemes for implementation of a class of principal value-based constitutive models: Symbolic and numeric implementation

    NASA Technical Reports Server (NTRS)

    Arnold, S. M.; Saleeb, A. F.; Tan, H. Q.; Zhang, Y.

    1993-01-01

    The issue of developing effective and robust schemes to implement a class of the Ogden-type hyperelastic constitutive models is addressed. To this end, special purpose functions (running under MACSYMA) are developed for the symbolic derivation, evaluation, and automatic FORTRAN code generation of explicit expressions for the corresponding stress function and material tangent stiffness tensors. These explicit forms are valid over the entire deformation range, since the singularities resulting from repeated principal-stretch values have been theoretically removed. The required computational algorithms are outlined, and the resulting FORTRAN computer code is presented.

  3. Improved scheme for parametrization of convection in the Met Office's Numerical Atmospheric-dispersion Modelling Environment (NAME)

    NASA Astrophysics Data System (ADS)

    Meneguz, Elena; Thomson, David; Witham, Claire; Kusmierczyk-Michulec, Jolanta

    2015-04-01

    NAME is a Lagrangian atmospheric dispersion model used by the Met Office to predict the dispersion of both natural and man-made contaminants in the atmosphere, e.g. volcanic ash, radioactive particles and chemical species. Atmospheric convection is responsible for transport and mixing of air resulting in a large exchange of heat and energy above the boundary layer. Although convection can transport material through the whole troposphere, convective clouds have a small horizontal length scale (of the order of few kilometres). Therefore, for large-scale transport the horizontal scale on which the convection exists is below the global NWP resolution used as input to NAME and convection must be parametrized. Prior to the work presented here, the enhanced vertical mixing generated by non-resolved convection was reproduced by randomly redistributing Lagrangian particles between the cloud base and cloud top with probability equal to 1/25th of the NWP predicted convective cloud fraction. Such a scheme is essentially diffusive and it does not make optimal use of all the information provided by the driving meteorological model. To make up for these shortcomings and make the parametrization more physically based, the convection scheme has been recently revised. The resulting version, presented in this paper, is now based on the balance equation between upward, entrainment and detrainment fluxes. In particular, upward mass fluxes are calculated with empirical formulas derived from Cloud Resolving Models and using the NWP convective precipitation diagnostic as closure. The fluxes are used to estimate how many particles entrain, move upward and detrain. Lastly, the scheme is completed by applying a compensating subsidence flux. The performance of the updated convection scheme is benchmarked against available observational data of passive tracers. In particular, radioxenon is a noble gas that can undergo significant long range transport: this study makes use of observations of

  4. Numerical simulation of electrospray in the cone-jet mode.

    PubMed

    Herrada, M A; López-Herrera, J M; Gañán-Calvo, A M; Vega, E J; Montanero, J M; Popinet, S

    2012-08-01

    We present a robust and computationally efficient numerical scheme for simulating steady electrohydrodynamic atomization processes (electrospray). The main simplification assumed in this scheme is that all the free electrical charges are distributed over the interface. A comparison of the results with those calculated with a volume-of-fluid method showed that the numerical scheme presented here accurately describes the flow pattern within the entire liquid domain. Experiments were performed to partially validate the numerical predictions. The simulations reproduced accurately the experimental shape of the liquid cone jet, providing correct values of the emitted electric current even for configurations very close to the cone-jet stability limit. PMID:23005852

  5. Numerical simulation of electrospray in the cone-jet mode.

    PubMed

    Herrada, M A; López-Herrera, J M; Gañán-Calvo, A M; Vega, E J; Montanero, J M; Popinet, S

    2012-08-01

    We present a robust and computationally efficient numerical scheme for simulating steady electrohydrodynamic atomization processes (electrospray). The main simplification assumed in this scheme is that all the free electrical charges are distributed over the interface. A comparison of the results with those calculated with a volume-of-fluid method showed that the numerical scheme presented here accurately describes the flow pattern within the entire liquid domain. Experiments were performed to partially validate the numerical predictions. The simulations reproduced accurately the experimental shape of the liquid cone jet, providing correct values of the emitted electric current even for configurations very close to the cone-jet stability limit.

  6. Melt-rock reaction in the asthenospheric mantle: Perspectives from high-order accurate numerical simulations in 2D and 3D

    NASA Astrophysics Data System (ADS)

    Tirupathi, S.; Schiemenz, A. R.; Liang, Y.; Parmentier, E.; Hesthaven, J.

    2013-12-01

    The style and mode of melt migration in the mantle are important to the interpretation of basalts erupted on the surface. Both grain-scale diffuse porous flow and channelized melt migration have been proposed. To better understand the mechanisms and consequences of melt migration in a heterogeneous mantle, we have undertaken a numerical study of reactive dissolution in an upwelling and viscously deformable mantle where solubility of pyroxene increases upwards. Our setup is similar to that described in [1], except we use a larger domain size in 2D and 3D and a new numerical method. To enable efficient simulations in 3D through parallel computing, we developed a high-order accurate numerical method for the magma dynamics problem using discontinuous Galerkin methods and constructed the problem using the numerical library deal.II [2]. Linear stability analyses of the reactive dissolution problem reveal three dynamically distinct regimes [3] and the simulations reported in this study were run in the stable regime and the unstable wave regime where small perturbations in porosity grows periodically. The wave regime is more relevant to melt migration beneath the mid-ocean ridges but computationally more challenging. Extending the 2D simulations in the stable regime in [1] to 3D using various combinations of sustained perturbations in porosity at the base of the upwelling column (which may result from a viened mantle), we show the geometry and distribution of dunite channel and high-porosity melt channels are highly correlated with inflow perturbation through superposition. Strong nonlinear interactions among compaction, dissolution, and upwelling give rise to porosity waves and high-porosity melt channels in the wave regime. These compaction-dissolution waves have well organized but time-dependent structures in the lower part of the simulation domain. High-porosity melt channels nucleate along nodal lines of the porosity waves, growing downwards. The wavelength scales

  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. 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

    SciTech Connect

    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{sup −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

  9. Development of comprehensive numerical schemes for predicting evaporating gas-droplets flow processes of a liquid-fueled combustor

    NASA Technical Reports Server (NTRS)

    Chen, C. P.

    1990-01-01

    An existing Computational Fluid Dynamics code for simulating complex turbulent flows inside a liquid rocket combustion chamber was validated and further developed. The Advanced Rocket Injector/Combustor Code (ARICC) is simplified and validated against benchmark flow situations for laminar and turbulent flows. The numerical method used in ARICC Code is re-examined for incompressible flow calculations. For turbulent flows, both the subgrid and the two equation k-epsilon turbulence models are studied. Cases tested include idealized Burger's equation in complex geometries and boundaries, a laminar pipe flow, a high Reynolds number turbulent flow, and a confined coaxial jet with recirculations. The accuracy of the algorithm is examined by comparing the numerical results with the analytical solutions as well as experimented data with different grid sizes.

  10. The numerical investigation of spreading process of two viscoelastic droplets impact problem by using an improved SPH scheme

    NASA Astrophysics Data System (ADS)

    Jiang, Tao; Lu, Lin-Guang; Lu, Wei-Gang

    2014-05-01

    In this paper, the spreading process of two XPP model droplets impacting on a plate in sequence at low Reynolds number is numerically simulated by using an improved smoothed particle hydrodynamics (I-SPH) method. The I-SPH method is a coupled approach which uses the traditional SPH (TSPH) method near the boundary domain and uses a kernel-gradient-corrected SPH method in the interior of fluid flow for the reason of remedying the accuracy and stability of TSPH. Meanwhile, an artificial stress term and a periodic density re-initialization technique are presented to eliminate the tensile instability and restrain pressure oscillation, respectively. A new boundary treatment is also adopted. The ability and merit of proposed I-SPH method combined with other techniques are first illustrated by simulating three typical examples. Subsequently, the deformation phenomena of two viscoelastic droplets impacting and spreading on a plate in sequence are numerically investigated. Particularly, the influences of the falling time interval, Weissenberg number and other rheological parameters on the deformation process are studied respectively. All numerical results agree well with the available data.

  11. A new design of the LAPS land surface scheme for use over and through heterogeneous and non-heterogeneous surfaces: Numerical simulations and tests

    NASA Astrophysics Data System (ADS)

    Mihailovic, Dragutin T.; Lazic, Jelena; Leśny, Jacek; Olejnik, Janusz; Lalic, Branislava; Kapor, Darko; Cirisan, Ana

    2010-05-01

    Numerical simulations and tests with the recently redesigned land-air parameterization scheme (LAPS) are presented. In all experiments, supported either by one-point micrometeorological, 1D or 3D simulations, the attention has been directed to: (1) comparison of simulation outputs, expressing the energy transfer over and through heterogeneous and non-heterogeneous surfaces, versus observations and (2) analysis of uncertainties occurring in the solution of the energy balance equation at the land-air interface. To check the proposed method for aggregation of albedo, "propagating hole" sensitivity tests with LAPS over a sandstone rock grid cell have been performed with the forcing meteorological data for July 17, 1999 in Baxter site, Philadelphia (USA). Micrometeorological and biophysical measurements from the surface experiments conducted over crops and apple orchard in Serbia, Poland, Austria and France were used to test the operation of LAPS in calculating surface fluxes and canopy environment temperatures within and above plant covers of different densities. In addition, sensitivity tests with single canopy covers over the Central Europe region and comparison against the observations taken from SYNOP data using 3D simulations were made. Validation of LAPS performances over a solid surface has been done by comparison of 2 m air temperature observations against 5-day simulations over the Sahara Desert rocky ground using 3D model. To examine how realistically the LAPS simulates surface processes over a heterogeneous surface, we compared the air temperature measured at 2 m and that predicted by the 1D model with the LAPS as the surface scheme. Finally, the scheme behaviour over urban surface was tested by runs over different parts of a hypothetical urban area. The corresponding 1D simulations were carried out with an imposed meteorological dataset collected during HAPEX-MOBILHY experiment at Caumont (France). The quantities predicted by the LAPS compare well with the

  12. 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.

  13. Coarse- and fine-grid numerical behavior of MRT/TRT lattice-Boltzmann schemes in regular and random sphere packings

    NASA Astrophysics Data System (ADS)

    Khirevich, Siarhei; Ginzburg, Irina; Tallarek, Ulrich

    2015-01-01

    We analyze the intrinsic impact of free-tunable combinations of the relaxation rates controlling viscosity-independent accuracy of the multiple-relaxation-times (MRT) lattice-Boltzmann models. Preserving all MRT degrees of freedom, we formulate the parametrization conditions which enable the MRT schemes to provide viscosity-independent truncation errors for steady state solutions, and support them with the second- and third-order accurate ("linear" and "parabolic", respectively) boundary schemes. The parabolic schemes demonstrate the advanced accuracy with weak dependency on the relaxation rates, as confirmed by the simulations with the D3Q15 model in three regular arrays (SC, BCC, FCC) of touching spheres. Yet, the low-order, bounce-back boundary rule remains appealing for pore-scale simulations where the precise distance to the boundaries is undetermined. However, the effective accuracy of the bounce-back crucially depends on the free-tunable combinations of the relaxation rates. We find that the combinations of the kinematic viscosity rate with the available "ghost" antisymmetric collision mode rates mainly impact the accuracy of the bounce-back scheme. As the first step, we reduce them to the one combination (presented by so-called "magic" parameter Λ in the frame of the two-relaxation-times (TRT) model), and study its impact on the accuracy of the drag force/permeability computations with the D3Q19 velocity set in two different, dense, random packings of 8000 spheres each. We also run the simulations in the regular (BCC and FCC) packings of the same porosity for the broad range of the discretization resolutions, ranging from 5 to 750 lattice nodes per sphere diameter. A special attention is given to the discretization procedure resulting in significantly reduced scatter of the data obtained at low resolutions. The results reveal the identical Λ-dependency versus the discretization resolution in all four packings, regular and random. While very small

  14. Blood flow velocity estimation from x-ray densitometric data: an efficient numerical scheme for the inverse advection problem

    NASA Astrophysics Data System (ADS)

    Sarry, L.; Peng, Y. J.; Boire, J. Y.

    2002-01-01

    In previously published studies, blood flow velocity from x-ray biplane angiography was measured by solving an inverse advection problem, relating velocity to bolus densities summed across sections. Both spatial and temporal velocity variations were recovered through a computationally expensive parameter estimation algorithm. Here we prove the existence and uniqueness of the solution on three sub-domains of the plane defined by the axial position along the vessel and the time of the angiographic sequence. A fast direct scheme was designed in conjunction with a regularization step stemming from the volume flow conservation law applied on consecutive segments. Its accuracy and immunity towards noise were tested on both simulated and real densitometric data. The relative error between the estimated and expected velocities was less than 5% for more than 90% of the points of the spatiotemporal plane with simulated densities normalized to 1.0 and a Gaussian additive noise of standard deviation 0.01. For densities reconstructed from a biplane angiographic sequence, increase in velocity is used as a functional index for the stenosis ratio and to characterize the sharing of flow at bifurcation.

  15. Numerical simulations of bubble-induced star formation in dwarf irregular galaxies with a novel stellar feedback scheme

    NASA Astrophysics Data System (ADS)

    Kawata, Daisuke; Gibson, Brad K.; Barnes, David J.; Grand, Robert J. J.; Rahimi, Awat

    2014-02-01

    To study the star formation and feedback mechanism, we simulate the evolution of an isolated dwarf irregular galaxy (dIrr) in a fixed dark matter halo, similar in size to Wolf-Lundmark-Melotte, using a new stellar feedback scheme. We use the new version of our original N-body/smoothed particle chemodynamics code, GCD+, which adopts improved hydrodynamics, metal diffusion between the gas particles and new modelling of star formation and stellar wind and supernovae feedback. Comparing the simulations with and without stellar feedback effects, we demonstrate that the collisions of bubbles produced by strong feedback can induce star formation in a more widely spread area. We also demonstrate that the metallicity in star-forming regions is kept low due to the mixing of the metal-rich bubbles and the metal-poor interstellar medium. Our simulations also suggest that the bubble-induced star formation leads to many counter-rotating stars. The bubble-induced star formation could be a dominant mechanism to maintain star formation in dIrrs, which is different from larger spiral galaxies where the non-axisymmetric structures, such as spiral arms, are a main driver of star formation.

  16. Numerical simulation of small perturbation transonic flows

    NASA Technical Reports Server (NTRS)

    Seebass, A. R.; Yu, N. J.

    1976-01-01

    The results of a systematic study of small perturbation transonic flows are presented. Both the flow over thin airfoils and the flow over wedges were investigated. Various numerical schemes were employed in the study. The prime goal of the research was to determine the efficiency of various numerical procedures by accurately evaluating the wave drag, both by computing the pressure integral around the body and by integrating the momentum loss across the shock. Numerical errors involved in the computations that affect the accuracy of drag evaluations were analyzed. The factors that effect numerical stability and the rate of convergence of the iterative schemes were also systematically studied.

  17. A finite-difference, frequency-domain numerical scheme for the solution of the linearized unsteady Euler equations

    NASA Technical Reports Server (NTRS)

    Scott, James R.; Atassi, Hafiz M.

    1991-01-01

    A numerical method is developed for solving periodic, three-dimensional, vortical flows around lifting airfoils in subsonic flow. The first-order method, that is presented, fully accounts for the distortion effects of the nonuniform mean flow on the convected upstream vortical disturbances. The unsteady velocity is split into a vortical component which is a known function of the upstream flow conditions and the Lagrangian coordinates of the mean flow, and an irrotational field whose potential satisfies a nonconstant-coefficient, inhomogeneous, convective wave equation. Using an elliptic coordinate transformation, the unsteady boundary value problem is solved in the frequency domain on grids which are determined as a function of the Mach number and reduced frequency. Extensive comparisons are made with known solutions to unsteady vortical flow problems, and it is seen that the agreement is generally very good for reduced frequencies ranging from 0 up to 4.

  18. Implementation of Black Sea numerical model based on NEMO and 3DVAR data assimilation scheme for operational forecasting

    NASA Astrophysics Data System (ADS)

    Ciliberti, Stefania Angela; Peneva, Elisaveta; Storto, Andrea; Rostislav, Kandilarov; Lecci, Rita; Yang, Chunxue; Coppini, Giovanni; Masina, Simona; Pinardi, Nadia

    2016-04-01

    This study describes a new model implementation for the Black Sea, which uses data assimilation, towards operational forecasting, based on NEMO (Nucleus for European Modelling of the Ocean, Madec et al., 2012). The Black Sea domain is resolved with 1/27°×1/36° horizontal resolution (~3 km) and 31 z-levels with partial steps based on the GEBCO bathymetry data (Grayek et al., 2010). The model is forced by momentum, water and heat fluxes interactively computed by bulk formulae using high resolution atmospheric forcing provided by the European Centre for Medium-Range Forecast (ECMWF). The initial condition is calculated from long-term climatological temperature and salinity 3D fields. Precipitation field over the basin has been computed from the climatological GPCP rainfall monthly data (Adler et al., 2003; Huffman et al., 2009), while the evaporation is derived from the latent heat flux. The climatological monthly mean runoff of the major rivers in the Black Sea is computed using the hydrological dataset provided by SESAME project (Ludvig et al., 2009). The exchange with Mediterranean Sea through the Bosporus Straits is represented by a surface boundary condition taking into account the barotropic transport calculated to balance the fresh water fluxes on monthly bases (Stanev and Beckers, 1999, Peneva et al., 2001). A multi-annual run 2011-2015 has been completed in order to describe the main characteristics of the Black Sea circulation dynamics and thermohaline structure and the numerical results have been validated using in-situ (ARGO) and satellite (SST, SLA) data. The Black Sea model represents also the core of the new Black Sea Forecasting System, implemented at CMCC operationally since January 2016, which produces at daily frequency 10-day forecasts, 3-days analyses and 1-day simulation. Once a week, the system is run 15-day in the past in analysis mode to compute the new optimal initial condition for the forecast cycle. The assimilation is performed by a

  19. 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.

  20. Numerical study of the two-species Vlasov-Ampère system: Energy-conserving schemes and the current-driven ion-acoustic instability

    NASA Astrophysics Data System (ADS)

    Cheng, Yingda; Christlieb, Andrew J.; Zhong, Xinghui

    2015-05-01

    In this paper, we propose energy-conserving Eulerian solvers for the two-species Vlasov-Ampère (VA) system and apply the methods to simulate current-driven ion-acoustic instability. The two-species VA systems are of practical importance in applications, and they conserve many physical quantities including the particle number of each species and the total energy that is comprised of kinetic energy for both species and the electric energy. The main goal of this paper is to generalize our previous work for the single-species VA system [9] and Vlasov-Maxwell (VM) system [8] to the two-species case. The methodologies proposed involve careful design of temporal discretization and the use of the discontinuous Galerkin (DG) spatial discretizations. We show that the energy-conserving time discretizations for single-species equations [9,8] can also work for the two-species case if extended properly. Compared to other high order schemes, we emphasize that our schemes can preserve the total particle number and total energy on the fully discrete level regardless of mesh size, making them very attractive for long time simulations. We benchmark our algorithms on a test example to check the one-species limit, and the current-driven ion-acoustic instability. To simulate the current-driven ion-acoustic instability, a slight modification for the implicit method is necessary to fully decouple the split equations. This is achieved by a Gauss-Seidel type iteration technique. Numerical results verified the conservation and performance of our methods. Finally, we remark that the schemes in this paper can be readily extended to applications when the models take more general form, such as the multi-species VM equations.

  1. 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.

  2. Progress in the study of magnetic dynamo generation processes by non-Gaussian, non-Markovian velocity fluctuations using meshless, Lagrangian numerical schemes

    NASA Astrophysics Data System (ADS)

    Sanchez, Raul; Reynolds-Barredo, J. Miguel; Newman, David E.

    2015-11-01

    The generation of magnetic dynamos by turbulent velocity fields is traditionally studied, at the simplest level, by assuming near-Gaussian, random velocity fluctuations. This allows to express the effective electromotive force in terms of a piece proportional to the large-scale magnetic field (the α-term) and another proportional to its curl (the β term), once certain symmetry conditions are assumed. Physically, the α-term is a measure of the mean helicity of the flow and drives the dynamo. Previously, we examined theoretically the consequences of assuming instead Levy-distributed, Lagrangianly-correlated velocity fields, which have been recently identified as relevant in regimes of near-marginal turbulence (superdiffusion) or in the presence of strong, stable sheared flows (subdiffusion). Here, we report on recent numerical progress on the study of these processes by implementing the kinematic dynamo equation using a meshless numerical method inspired by the SPH schemes frequently used in hydrodynamics. The results suggest that subdiffusive flows may importantly enhance the dynamo generation, even in the absence of mean helicity, which might be meaningful for the understanding of dynamo generation in situations where sheared, zonal flows are present.

  3. A new class of high accuracy TVD schemes for hyperbolic conservation laws. [Total Variation Diminishing

    NASA Technical Reports Server (NTRS)

    Chakravarthy, S. R.; Osher, S.

    1985-01-01

    A new family of high accuracy Total Variation Diminishing (TVD) schemes has been developed. Members of the family include the conventional second-order TVD upwind scheme, various other second-order accurate TVD schemes with lower truncation error, and even a third-order accurate TVD approximation. All the schemes are defined with a five-point grid bandwidth. In this paper, the new algorithms are described for scalar equations, systems, and arbitrary coordinates. Selected numerical results are provided to illustrate the new algorithms and their properties.

  4. On Approximate Factorization Schemes for Solving the Full Potential Equation

    NASA Technical Reports Server (NTRS)

    Holst, Terry L.

    1997-01-01

    An approximate factorization scheme based on the AF2 algorithm is presented for solving the three-dimensional full potential equation for the transonic flow about isolated wings. Two spatial discretization variations are presented, one using a hybrid first-order/second-order-accurate scheme and the second using a fully second-order-accurate scheme. The present algorithm utilizes a C-H grid topology to map the flow field about the wing. One version of the AF2 iteration scheme is used on the upper wing surface and another slightly modified version is used on the lower surface. These two algorithm variations are then connected at the wing leading edge using a local iteration technique. The resulting scheme has improved linear stability characteristics and improved time-like damping characteristics relative to previous implementations of the AF2 algorithm. The presentation is highlighted with a grid refinement study and a number of numerical results.

  5. The Implicit and Explicit alpha-mu Schemes

    NASA Technical Reports Server (NTRS)

    Chang, Sin-Chung; Himansu, Ananda

    1997-01-01

    Artificial numerical dissipation is an 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 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 method of space-time conservation element and solution element, currently under development, is a nontraditional numerical method for solving conservation laws. The method is developed on the basis of local and global flux conservation in a space-time domain, in which space and time are treated in a unified manner. Explicit solvers for model and fluid dynamic conservation laws have previously been investigated. In this paper, we introduce a new concept in the design of implicit schemes, and use it to construct two highly accurate 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 purely inviscid (convective) equations. The stability and consistency of the schemes are analyzed, 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. We also construct an explicit solver

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

    NASA Astrophysics Data System (ADS)

    Liu, Fang; Lin, Lin; Vigil-Fowler, Derek; Lischner, Johannes; Kemper, Alexander F.; Sharifzadeh, Sahar; da Jornada, Felipe H.; Deslippe, Jack; Yang, Chao; Neaton, Jeffrey B.; Louie, Steven G.

    2015-04-01

    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 of using different self energy expressions to perform the numerical convolution at different frequencies.

  7. 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.

  8. Development of a numerical scheme to predict geomagnetic storms after intense solar events and geomagnetic activity 27 days in advance. Final report, 6 Aug 86-16 Nov 90

    SciTech Connect

    Akasofu, S.I.; Lee, L.H.

    1991-02-01

    The modern geomagnetic storm prediction scheme should be based on a numerical simulation method, rather than on a statistical result. Furthermore, the scheme should be able to predict the geomagnetic storm indices, such as the Dst and AE indices, as a function of time. By recognizing that geomagnetic storms are powered by the solar wind-magnetosphere generator and that its power is given in terms of the solar wind speed, the interplanetary magnetic field (IMF) magnitude and polar angle, the authors have made a major advance in predicting both flare-induced storms and recurrent storms. Furthermore, it is demonstrated that the prediction scheme can be calibrated using the interplanetary scintillation (IPS) observation, when the solar disturbance advances about half-way to the earth. It is shown, however, that we are still far from a reliable prediction scheme. The prediction of the IMF polar angle requires future advance in understanding characteristics of magnetic clouds.

  9. Numerous Numerals.

    ERIC Educational Resources Information Center

    Henle, James M.

    This pamphlet consists of 17 brief chapters, each containing a discussion of a numeration system and a set of problems on the use of that system. The numeration systems used include Egyptian fractions, ordinary continued fractions and variants of that method, and systems using positive and negative bases. The book is informal and addressed to…

  10. Evidence that bisphenol A (BPA) can be accurately measured without contamination in human serum and urine, and that BPA causes numerous hazards from multiple routes of exposure.

    PubMed

    vom Saal, Frederick S; Welshons, Wade V

    2014-12-01

    There is extensive evidence that bisphenol A (BPA) is related to a wide range of adverse health effects based on both human and experimental animal studies. However, a number of regulatory agencies have ignored all hazard findings. Reports of high levels of unconjugated (bioactive) serum BPA in dozens of human biomonitoring studies have also been rejected based on the prediction that the findings are due to assay contamination and that virtually all ingested BPA is rapidly converted to inactive metabolites. NIH and industry-sponsored round robin studies have demonstrated that serum BPA can be accurately assayed without contamination, while the FDA lab has acknowledged uncontrolled assay contamination. In reviewing the published BPA biomonitoring data, we find that assay contamination is, in fact, well controlled in most labs, and cannot be used as the basis for discounting evidence that significant and virtually continuous exposure to BPA must be occurring from multiple sources.

  11. Evidence that bisphenol A (BPA) can be accurately measured without contamination in human serum and urine, and that BPA causes numerous hazards from multiple routes of exposure

    PubMed Central

    vom Saal, Frederick S.; Welshons, Wade V.

    2016-01-01

    There is extensive evidence that bisphenol A (BPA) is related to a wide range of adverse health effects based on both human and experimental animal studies. However, a number of regulatory agencies have ignored all hazard findings. Reports of high levels of unconjugated (bioactive) serum BPA in dozens of human biomonitoring studies have also been rejected based on the prediction that the findings are due to assay contamination and that virtually all ingested BPA is rapidly converted to inactive metabolites. NIH and industry-sponsored round robin studies have demonstrated that serum BPA can be accurately assayed without contamination, while the FDA lab has acknowledged uncontrolled assay contamination. In reviewing the published BPA biomonitoring data, we find that assay contamination is, in fact, well controlled in most labs, and cannot be used as the basis for discounting evidence that significant and virtually continuous exposure to BPA must be occurring from multiple sources. PMID:25304273

  12. Implicit TVD schemes for hyperbolic conservation laws in curvilinear coordinates

    NASA Technical Reports Server (NTRS)

    Yee, H. C.; Harten, A.

    1985-01-01

    The Harten (1983, 1984) total variation-diminishing (TVD) schemes, constituting a one-parameter explicit and implicit, second-order-accurate family, have the property of not generating spurious oscillations when applied to one-dimensional, nonlinear scalar hyperbolic conservation laws and constant coefficient hyperbolic systems. These methods are presently extended to the multidimensional hyperbolic conservation laws in curvilinear coordinates. Means by which to linearize the implicit operator and solution strategies, in order to improve the computation efficiency of the implicit algorithm, are discussed. Numerical experiments with steady state airfoil calculations indicate that the proposed linearized implicit TVD schemes are accurate and robust.

  13. Practical aspects of spatially high accurate methods

    NASA Technical Reports Server (NTRS)

    Godfrey, Andrew G.; Mitchell, Curtis R.; Walters, Robert W.

    1992-01-01

    The computational qualities of high order spatially accurate methods for the finite volume solution of the Euler equations are presented. Two dimensional essentially non-oscillatory (ENO), k-exact, and 'dimension by dimension' ENO reconstruction operators are discussed and compared in terms of reconstruction and solution accuracy, computational cost and oscillatory behavior in supersonic flows with shocks. Inherent steady state convergence difficulties are demonstrated for adaptive stencil algorithms. An exact solution to the heat equation is used to determine reconstruction error, and the computational intensity is reflected in operation counts. Standard MUSCL differencing is included for comparison. Numerical experiments presented include the Ringleb flow for numerical accuracy and a shock reflection problem. A vortex-shock interaction demonstrates the ability of the ENO scheme to excel in simulating unsteady high-frequency flow physics.

  14. Numerical Simulation of Natural Convection of a Nanofluid in an Inclined Heated Enclosure Using Two-Phase Lattice Boltzmann Method: Accurate Effects of Thermophoresis and Brownian Forces.

    PubMed

    Ahmed, Mahmoud; Eslamian, Morteza

    2015-12-01

    Laminar natural convection in differentially heated (β = 0°, where β is the inclination angle), inclined (β = 30° and 60°), and bottom-heated (β = 90°) square enclosures filled with a nanofluid is investigated, using a two-phase lattice Boltzmann simulation approach. The effects of the inclination angle on Nu number and convection heat transfer coefficient are studied. The effects of thermophoresis and Brownian forces which create a relative drift or slip velocity between the particles and the base fluid are included in the simulation. The effect of thermophoresis is considered using an accurate and quantitative formula proposed by the authors. Some of the existing results on natural convection are erroneous due to using wrong thermophoresis models or simply ignoring the effect. Here we show that thermophoresis has a considerable effect on heat transfer augmentation in laminar natural convection. Our non-homogenous modeling approach shows that heat transfer in nanofluids is a function of the inclination angle and Ra number. It also reveals some details of flow behavior which cannot be captured by single-phase models. The minimum heat transfer rate is associated with β = 90° (bottom-heated) and the maximum heat transfer rate occurs in an inclination angle which varies with the Ra number.

  15. Numerical Simulation of Natural Convection of a Nanofluid in an Inclined Heated Enclosure Using Two-Phase Lattice Boltzmann Method: Accurate Effects of Thermophoresis and Brownian Forces.

    PubMed

    Ahmed, Mahmoud; Eslamian, Morteza

    2015-12-01

    Laminar natural convection in differentially heated (β = 0°, where β is the inclination angle), inclined (β = 30° and 60°), and bottom-heated (β = 90°) square enclosures filled with a nanofluid is investigated, using a two-phase lattice Boltzmann simulation approach. The effects of the inclination angle on Nu number and convection heat transfer coefficient are studied. The effects of thermophoresis and Brownian forces which create a relative drift or slip velocity between the particles and the base fluid are included in the simulation. The effect of thermophoresis is considered using an accurate and quantitative formula proposed by the authors. Some of the existing results on natural convection are erroneous due to using wrong thermophoresis models or simply ignoring the effect. Here we show that thermophoresis has a considerable effect on heat transfer augmentation in laminar natural convection. Our non-homogenous modeling approach shows that heat transfer in nanofluids is a function of the inclination angle and Ra number. It also reveals some details of flow behavior which cannot be captured by single-phase models. The minimum heat transfer rate is associated with β = 90° (bottom-heated) and the maximum heat transfer rate occurs in an inclination angle which varies with the Ra number. PMID:26183389

  16. Interpolated Differential Operator (IDO) scheme for solving partial differential equations

    NASA Astrophysics Data System (ADS)

    Aoki, Takayuki

    1997-05-01

    We present a numerical scheme applicable to a wide variety of partial differential equations (PDEs) in space and time. The scheme is based on a high accurate interpolation of the profile for the independent variables over a local area and repetitive differential operations regarding PDEs as differential operators. We demonstrate that the scheme is uniformly applicable to hyperbolic, ellipsoidal and parabolic equations. The equations are solved in terms of the primitive independent variables, so that the scheme has flexibility for various types of equations including source terms. We find out that the conservation holds accurate when a Hermite interpolation is used. For compressible fluid problems, the shock interface is found to be sharply described by adding an artificial viscosity term.

  17. 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.

  18. Adaptive Numerical Dissipation Controls for High Order Methods

    NASA Technical Reports Server (NTRS)

    Yee, Helen C.; Sjogreen, B.; Sandham, N. D.; Mansour, Nagi (Technical Monitor)

    2001-01-01

    A numerical scheme for direct numerical simulation of shock-turbulence interactions of high speed compressible flows would ideally not be significantly more expensive than the standard fourth or sixth-order compact or non-compact central differencing scheme. It should be possible to resolve all scales down to scales of order of the Kolmogorov scales of turbulence accurately and efficiently, while at the same time being able to capture steep gradients occurring at much smaller scales efficiently. The goal of this lecture is to review the progress and new development of the low dissipative high order shock-capturing schemes proposed by Yee et al. Comparison on the efficiency and accuracy of this class of schemes with spectral and the fifth-order WENO (weighted essentially nonoscillatory) scheme will be presented. A new approach to dynamically sense the appropriate amount of numerical dissipation to be added at each grid point using non-orthogonal wavelets will be discussed.

  19. WENO schemes on arbitrary unstructured meshes for laminar, transitional and turbulent flows

    SciTech Connect

    Tsoutsanis, Panagiotis Antoniadis, Antonios Foivos Drikakis, Dimitris

    2014-01-01

    This paper presents the development and implementation of weighted-essentially-non-oscillatory (WENO) schemes for viscous flows on arbitrary unstructured grids. WENO schemes up to fifth-order accurate have been implemented in conjunction with hybrid and non-hybrid unstructured grids. The schemes are investigated with reference to numerical and experimental results for the Taylor–Green vortex, as well as for laminar and turbulent flows around a sphere, and the turbulent shock-wave boundary layer interaction flow problem. The results show that the accuracy of the schemes depends on the arbitrariness of shape and orientation of the unstructured mesh elements, as well as the compactness of directional stencils. The WENO schemes provide a more accurate numerical framework compared to second-order and third-order total variation diminishing (TVD) methods, however, the fifth-order version of the schemes is computationally too expensive to make the schemes practically usable. On the other hand, the third-order variant offers an excellent numerical framework in terms of accuracy and computational cost compared to the fifth-order WENO and second-order TVD schemes. Parallelisation of the CFD code (henceforth labelled as UCNS3D), where the schemes have been implemented, shows that the present methods offer very good scalable performance.

  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. 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. Previously announced in STAR as N83-23085

  2. 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.

  3. Numerical simulation and intercomparison of boundary layer structure with different PBL schemes in WRF using experimental observations at a tropical site

    NASA Astrophysics Data System (ADS)

    Hariprasad, K. B. R. R.; Srinivas, C. V.; Singh, A. Bagavath; Vijaya Bhaskara Rao, S.; Baskaran, R.; Venkatraman, B.

    2014-08-01

    In this study the performance of seven PBL parameterizations in the Weather Research and Forecast (WRF-ARW) mesoscale model was tested at the tropical site Kalpakkam. Meteorological observations collected during an intense observation campaign for wind field modeling called Round Robin Exercise (RRE) were used for comparison. High resolution simulations were conducted for a warm summer condition on 22-24 September 2010. The observations included GPS Sonde vertical profiles, surface level data from meteorological towers and turbulent fluxes from sonic anemometers. Sensitivity experiments with seven PBL schemes [Mellor-Yamada-Janjic (MYJ), Mellor-Yamada-Nakanishi-Niino (MYNN), Quasi Normal Scale Elimination (QNSE), Yonsei University (YSU), Asymmetric Convective Model (ACM2), Bougeault-Lacarrére (BL), Bretherton-Park (UW)] indicated that while all the schemes similarly produced the stable boundary layer characteristics there were large differences in the convective daytime PBL. It has been found that while ACM2 and QNSE produced highly unstable and deep convective layers, the UW produced relatively shallow mixed layer and all other schemes (YSU, MYNN, MYJ, BL) produced intermediately deep convective layers. All the schemes well produced the vertical wind directional shear within the PBL. A wide variation in the eddy diffusivities was simulated by different PBL schemes in convective daytime condition. ACM2 and UW produced excessive diffusivities which led to relatively weaker winds, warmer and dryer mixed layers with these schemes. Overall the schemes MYNN and YSU simulated the various PBL quantities in better agreement with observations. The differences in the simulated PBL structures could be partly due to various surface layer formulations that produced variation in friction velocity and heat fluxes in each case.

  4. 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.

  5. TE/TM alternating direction scheme for wake field calculation in 3D

    NASA Astrophysics Data System (ADS)

    Zagorodnov, Igor; Weiland, Thomas

    2006-03-01

    In the future, accelerators with very short bunches will be used. It demands developing new numerical approaches for long-time calculation of electromagnetic fields in the vicinity of relativistic bunches. The conventional FDTD scheme, used in MAFIA, ABCI and other wake and PIC codes, suffers from numerical grid dispersion and staircase approximation problem. As an effective cure of the dispersion problem, a numerical scheme without dispersion in longitudinal direction can be used as it was shown by Novokhatski et al. [Transition dynamics of the wake fields of ultrashort bunches, TESLA Report 2000-03, DESY, 2000] and Zagorodnov et al. [J. Comput. Phys. 191 (2003) 525]. In this paper, a new economical conservative scheme for short-range wake field calculation in 3D is presented. As numerical examples show, the new scheme is much more accurate on long-time scale than the conventional FDTD approach.

  6. Relaxation schemes for Chebyshev spectral multigrid methods

    NASA Technical Reports Server (NTRS)

    Kang, Yimin; Fulton, Scott R.

    1993-01-01

    Two relaxation schemes for Chebyshev spectral multigrid methods are presented for elliptic equations with Dirichlet boundary conditions. The first scheme is a pointwise-preconditioned Richardson relaxation scheme and the second is a line relaxation scheme. The line relaxation scheme provides an efficient and relatively simple approach for solving two-dimensional spectral equations. Numerical examples and comparisons with other methods are given.

  7. A Correction Scheme for Thermal Conductivity Measurement Using the Comparative Cut-bar Technique Based on a 3D Numerical Simulation

    SciTech Connect

    Douglas W. Marshall; Changhu Xing; Charles Folsom; Colby Jensen; Heng Ban

    2014-05-01

    As an important factor affecting the accuracy of the thermal conductivity measurement, systematic (bias) error in the guarded comparative axial heat flow (cut-bar) method was mostly neglected by previous researches. This bias is due primarily to the thermal conductivity mismatch between sample and meter bars (reference), which is common for a sample of unknown thermal conductivity. A correction scheme, based on a finite element simulation of the measurement system, was proposed to reduce the magnitude of the overall measurement uncertainty. This scheme was experimentally validated by applying corrections on four types of sample measurements in which the specimen thermal conductivity is much smaller, slightly smaller, equal and much larger than that of the meter bar. As an alternative to the optimum guarding technique proposed before, the correction scheme can be used to minimize uncertainty contribution from the measurement system with non-optimal guarding conditions. It is especially necessary for large thermal conductivity mismatches between sample and meter bars.

  8. 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.

  9. Numerical Dissipation and Wrong Propagation Speed of Discontinuities for Stiff Source Terms

    NASA Technical Reports Server (NTRS)

    Yee, H. C.; Kotov, D. V.; Sjogreen, B.

    2011-01-01

    In compressible turbulent combustion/nonequilibrium flows, the constructions of numerical schemes for (a) stable and accurate simulation of turbulence with strong shocks, and (b) obtaining correct propagation speed of discontinuities for stiff reacting terms on coarse grids share one important ingredient - minimization of numerical dissipation while maintaining numerical stability. Here coarse grids means standard mesh density requirement for accurate simulation of typical non-reacting flows. This dual requirement to achieve both numerical stability and accuracy with zero or minimal use of numerical dissipation is most often conflicting for existing schemes that were designed for non-reacting flows. The goal of this paper is to relate numerical dissipations that are inherited in a selected set of high order shock-capturing schemes with the onset of wrong propagation speed of discontinuities for two representative stiff detonation wave problems.

  10. Numerical Dissipation and Wrong Propagation Speed of Discontinuities for Stiff Source Terms

    NASA Technical Reports Server (NTRS)

    Yee, H. C.; Kotov, D. V.; Sjoegreen, B.

    2012-01-01

    In compressible turbulent combustion/nonequilibrium flows, the constructions of numerical schemes for (a) stable and accurate simulation of turbulence with strong shocks, and (b) obtaining correct propagation speed of discontinuities for stiff reacting terms on coarse grids share one important ingredient - minimization of numerical dissipation while maintaining numerical stability. Here coarse grids means standard mesh density requirement for accurate simulation of typical non-reacting flows. This dual requirement to achieve both numerical stability and accuracy with zero or minimal use of numerical dissipation is most often conflicting for existing schemes that were designed for non-reacting flows. The goal of this paper is to relate numerical dissipations that are inherited in a selected set of high order shock-capturing schemes with the onset of wrong propagation speed of discontinuities as a function of stiffness of the source term and the grid spacing.

  11. An improvement in the numerical integration procedure used in the NASA Marshall engineering thermosphere model

    NASA Technical Reports Server (NTRS)

    Hickey, Michael Philip

    1988-01-01

    A proposed replacement scheme for the integration of the barometric and diffusion equations in the NASA Marshall Engineering Thermosphere (MET) model is presented. This proposed integration scheme is based on Gaussian Quadrature. Extensive numerical testing reveals it to be faster, more accurate and more reliable than the present integration scheme (a modified form of Simpson's Rule) used in the MET model. Numerous graphical examples are provided, along with a listing of a modified form of the MET model in which subroutine INTEGRATE (using Simpson's Rule) is replaced by subroutine GAUSS (which uses Gaussian Quadrature). It is recommended that the Gaussian Quadrature integration scheme, as used here, be used in the MET model.

  12. Analysis and design of numerical schemes for gas dynamics 1: Artificial diffusion, upwind biasing, limiters and their effect on accuracy and multigrid convergence

    NASA Technical Reports Server (NTRS)

    Jameson, Antony

    1994-01-01

    The theory of non-oscillatory scalar schemes is developed in this paper in terms of the local extremum diminishing (LED) principle that maxima should not increase and minima should not decrease. This principle can be used for multi-dimensional problems on both structured and unstructured meshes, while it is equivalent to the total variation diminishing (TVD) principle for one-dimensional problems. A new formulation of symmetric limited positive (SLIP) schemes is presented, which can be generalized to produce schemes with arbitrary high order of accuracy in regions where the solution contains no extrema, and which can also be implemented on multi-dimensional unstructured meshes. Systems of equations lead to waves traveling with distinct speeds and possibly in opposite directions. Alternative treatments using characteristic splitting and scalar diffusive fluxes are examined, together with modification of the scalar diffusion through the addition of pressure differences to the momentum equations to produce full upwinding in supersonic flow. This convective upwind and split pressure (CUSP) scheme exhibits very rapid convergence in multigrid calculations of transonic flow, and provides excellent shock resolution at very high Mach numbers.

  13. Validating the turbulence parameterization schemes of a numerical model using eddy dissipation rate and turbulent kinetic energy measurements in terrain-disrupted airflow

    NASA Astrophysics Data System (ADS)

    Chan, P. W.

    2010-10-01

    A number of turbulence parameterization schemes are available in the latest version (6.0) of the Regional Atmospheric Modelling System (RAMS). Chan in Meteorol Atmos Phys 103:145-157, (2009), studied the performance of these schemes by simulating the eddy dissipation rate (EDR) distribution in the vicinity of the Hong Kong International Airport (HKIA) and comparing with the EDR measurements of remote-sensing instruments at the airport. For the e-l (turbulent kinetic energy - mixing length) scheme considered in that study, the asymptotic mixing length was assumed to be a constant. This assumption is changed in the present paper, a variable asymptotic mixing length is chosen and simulations of EDR fields are repeated for terrain-disrupted airflow in the vicinity of HKIA. It is found that, with a variable asymptotic mixing length, the performance of the e-l scheme is greatly improved. With suitable choice of the empirical constants in the turbulence closure, the accuracy of the EDR profile (in comparison with LIDAR and wind profiler measurements) is found to be comparable with that predicted by the Deardorff scheme. A study on the sensitivity of the simulation results to these empirical constants has also been performed. Moreover, as a follow-up of the previous study of Chan in Meteorol Atmos Phys 103:145-157, (2009), case studies have been conducted on the following issues of the model simulation of turbulence for aviation application: (a) the effect of vertical gridding on the simulation results, (b) possibility of false alarm (such as over-forecasting of EDR value) in light turbulence cases, and (c) the performance in the simulation of other turbulence intensity metric for aviation purpose, e.g. TKE.

  14. XFEM schemes for level set based structural optimization

    NASA Astrophysics Data System (ADS)

    Li, Li; Wang, Michael Yu; Wei, Peng

    2012-12-01

    In this paper, some elegant extended finite element method (XFEM) schemes for level set method structural optimization are proposed. Firstly, two-dimension (2D) and three-dimension (3D) XFEM schemes with partition integral method are developed and numerical examples are employed to evaluate their accuracy, which indicate that an accurate analysis result can be obtained on the structural boundary. Furthermore, the methods for improving the computational accuracy and efficiency of XFEM are studied, which include the XFEM integral scheme without quadrature sub-cells and higher order element XFEM scheme. Numerical examples show that the XFEM scheme without quadrature sub-cells can yield similar accuracy of structural analysis while prominently reducing the time cost and that higher order XFEM elements can improve the computational accuracy of structural analysis in the boundary elements, but the time cost is increasing. Therefore, the balance of time cost between FE system scale and the order of element needs to be discussed. Finally, the reliability and advantages of the proposed XFEM schemes are illustrated with several 2D and 3D mean compliance minimization examples that are widely used in the recent literature of structural topology optimization. All numerical results demonstrate that the proposed XFEM is a promising structural analysis approach for structural optimization with the level set method.

  15. 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.

  16. A double shooting scheme for certain unstable and singular boundary value problems

    NASA Technical Reports Server (NTRS)

    Bayliss, A.

    1978-01-01

    A scheme is presented to obtain the unique bounded solution for an exponentially unstable linear system. The scheme consists of choosing random data at large initial values and integrating forwards and backwards until accurate regular boundary values are obtained. Proofs of convergence are given for the case that the homogeneous equation has an exponential dichotomy. Applications to other types of problems are discussed and numerical results are presented.

  17. An Improved Lattice Kinetic Scheme for Incompressible Viscous Fluid Flows

    NASA Astrophysics Data System (ADS)

    Suzuki, Kosuke; Inamuro, Takaji

    2014-01-01

    The lattice Boltzmann method (LBM) is an explicit numerical scheme for the incompressible Navier-Stokes equations (INSE) without integrating the Poisson equation for the pressure. In spite of its merit, the LBM has some drawbacks in accuracy. First, we review drawbacks for three numerical methods based on the LBM. The three methods are the LBM with the Bhatnagar-Gross-Krook model (LBGK), the lattice kinetic scheme (LKS) and the link-wise artificial compressibility method (LWACM). Second, in order to remedy the drawbacks, we propose an improved LKS. The present method incorporates (i) the scheme used in the LWACM for determining the kinematic viscosity, (ii) an iterative calculation of the pressure and (iii) a semi-implicit algorithm, while preserving the simplicity of the algorithm of the original LKS. Finally, in simulations of test problems, we find that the improved LKS eliminates the drawbacks and gives more accurate and stable results than LBGK, LKS and LWACM.

  18. Analysis of Finite Difference Discretization Schemes for Diffusion in Spheres with Variable Diffusivity

    PubMed Central

    Versypt, Ashlee N. Ford; Braatz, Richard D.

    2014-01-01

    Two finite difference discretization schemes for approximating the spatial derivatives in the diffusion equation in spherical coordinates with variable diffusivity are presented and analyzed. The numerical solutions obtained by the discretization schemes are compared for five cases of the functional form for the variable diffusivity: (I) constant diffusivity, (II) temporally-dependent diffusivity, (III) spatially-dependent diffusivity, (IV) concentration-dependent diffusivity, and (V) implicitly-defined, temporally- and spatially-dependent diffusivity. Although the schemes have similar agreement to known analytical or semi-analytical solutions in the first four cases, in the fifth case for the variable diffusivity, one scheme produces a stable, physically reasonable solution, while the other diverges. We recommend the adoption of the more accurate and stable of these finite difference discretization schemes to numerically approximate the spatial derivatives of the diffusion equation in spherical coordinates for any functional form of variable diffusivity, especially cases where the diffusivity is a function of position. PMID:25642003

  19. TVD scheme for computing open channel wave flows

    NASA Astrophysics Data System (ADS)

    Buntina, M. V.; Ostapenko, V. V.

    2008-12-01

    For the shallow water equations in the first approximation (Saint-Venant equations), a TVD scheme is developed for shock-capturing computations of open channel flows with discontinuous waves. The scheme is based on a special nondivergence approximation of the total momentum equation that does not involve integrals related to the cross-section pressure force and the channel wall reaction. In standard divergence difference schemes, most of the CPU time is spent on the computation of these integrals. Test computations demonstrate that the discontinuity relations reproduced by the scheme are accurate enough for actual discontinuous wave propagation to be numerically simulated. All the qualitatively distinct solutions for a dam collapsing in a trapezoidal channel with a contraction in the tailwater area are constructed as an example.

  20. 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.

  1. Accuracy study of the IDO scheme by Fourier analysis

    NASA Astrophysics Data System (ADS)

    Imai, Yohsuke; Aoki, Takayuki

    2006-09-01

    The numerical accuracy of the Interpolated Differential Operator (IDO) scheme is studied with Fourier analysis for the solutions of Partial Differential Equations (PDEs): advection, diffusion, and Poisson equations. The IDO scheme solves governing equations not only for physical variable but also for first-order spatial derivative. Spatial discretizations are based on Hermite interpolation functions with both of them. In the Fourier analysis for the IDO scheme, the Fourier coefficients of the physical variable and the first-order derivative are coupled by the equations derived from the governing equations. The analysis shows the IDO scheme resolves all the wavenumbers with higher accuracy than the fourth-order Finite Difference (FD) and Compact Difference (CD) schemes for advection equation. In particular, for high wavenumbers, the accuracy is superior to that of the sixth-order Combined Compact Difference (CCD) scheme. The diffusion and Poisson equations are also more accurately solved in comparison with the FD and CD schemes. These results show that the IDO scheme guarantees highly resolved solutions for all the terms of fluid flow equations.

  2. Detection and accurate localization of harmonic chipless tags

    NASA Astrophysics Data System (ADS)

    Dardari, Davide

    2015-12-01

    We investigate the detection and localization properties of harmonic tags working at microwave frequencies. A two-tone interrogation signal and a dedicated signal processing scheme at the receiver are proposed to eliminate phase ambiguities caused by the short signal wavelength and to provide accurate distance/position estimation even in the presence of clutter and multipath. The theoretical limits on tag detection and localization accuracy are investigated starting from a concise characterization of harmonic backscattered signals. Numerical results show that accuracies in the order of centimeters are feasible within an operational range of a few meters in the RFID UHF band.

  3. Trefftz difference schemes on irregular stencils

    SciTech Connect

    Tsukerman, Igor

    2010-04-20

    The recently developed Flexible Local Approximation MEthod (FLAME) produces accurate difference schemes by replacing the usual Taylor expansion with Trefftz functions - local solutions of the underlying differential equation. This paper advances and casts in a general form a significant modification of FLAME proposed recently by Pinheiro and Webb: a least-squares fit instead of the exact match of the approximate solution at the stencil nodes. As a consequence of that, FLAME schemes can now be generated on irregular stencils with the number of nodes substantially greater than the number of approximating functions. The accuracy of the method is preserved but its robustness is improved. For demonstration, the paper presents a number of numerical examples in 2D and 3D: electrostatic (magnetostatic) particle interactions, scattering of electromagnetic (acoustic) waves, and wave propagation in a photonic crystal. The examples explore the role of the grid and stencil size, of the number of approximating functions, and of the irregularity of the stencils.

  4. Multi-moment advection scheme in three dimension for Vlasov simulations of magnetized plasma

    SciTech Connect

    Minoshima, Takashi; Matsumoto, Yosuke; Amano, Takanobu

    2013-03-01

    We present an extension of the multi-moment advection scheme [T. Minoshima, Y. Matsumoto, T. Amano, Multi-moment advection scheme for Vlasov simulations, Journal of Computational Physics 230 (2011) 6800–6823] to the three-dimensional case, for full electromagnetic Vlasov simulations of magnetized plasma. The scheme treats not only point values of a profile but also its zeroth to second order piecewise moments as dependent variables, and advances them on the basis of their governing equations. Similar to the two-dimensional scheme, the three-dimensional scheme can accurately solve the solid body rotation problem of a gaussian profile with little numerical dispersion or diffusion. This is a very important property for Vlasov simulations of magnetized plasma. We apply the scheme to electromagnetic Vlasov simulations. Propagation of linear waves and nonlinear evolution of the electron temperature anisotropy instability are successfully simulated with a good accuracy of the energy conservation.

  5. Development of comprehensive numerical schemes for predicting evaporating gas-droplets flow processes of a liquid-fueled combustor. Semiannual report, 15 June 1988-30 November 1988

    SciTech Connect

    Chen, C.P.

    1990-01-01

    An existing Computational Fluid Dynamics code for simulating complex turbulent flows inside a liquid rocket combustion chamber was validated and further developed. The Advanced Rocket Injector/Combustor Code (ARICC) is simplified and validated against benchmark flow situations for laminar and turbulent flows. The numerical method used in ARICC Code is re-examined for incompressible flow calculations. For turbulent flows, both the subgrid and the two equation k-epsilon turbulence models are studied. Cases tested include idealized Burger's equation in complex geometries and boundaries, a laminar pipe flow, a high Reynolds number turbulent flow, and a confined coaxial jet with recirculations. The accuracy of the algorithm is examined by comparing the numerical results with the analytical solutions as well as experimented data with different grid sizes.

  6. Saturation-free numerical scheme for computing the flow past a lattice of airfoils and the determination of separation points in a viscous fluid

    NASA Astrophysics Data System (ADS)

    Petrov, A. G.

    2011-07-01

    A numerical method for computing the potential flow past a lattice of airfoils is described. The problem is reduced to a linear integrodifferential equation on the lattice contour, which is then approximated by a linear system of equations with the help of specially derived quadrature formulas. The quadrature formulas exhibit exponential convergence in the number of points on an airfoil and have a simple analytical form. Due to its fast convergence and high accuracy, the method can be used to directly optimize the airfoils as based on any given integral characteristics. The shear stress distribution and the separation points are determined from the velocity distribution at the airfoil boundary calculated by solving the boundary layer equations. The method proposed is free of laborious grid generation procedures and does not involve difficulties associated with numerical viscosity at high Reynolds numbers.

  7. A numerical study of the 2- and 3-dimensional unsteady Navier-Stokes equations in velocity-vorticity variables using compact difference schemes

    NASA Technical Reports Server (NTRS)

    Gatski, T. B.; Grosch, C. E.

    1984-01-01

    A compact finite-difference approximation to the unsteady Navier-Stokes equations in velocity-vorticity variables is used to numerically simulate a number of flows. These include two-dimensional laminar flow of a vortex evolving over a flat plate with an embedded cavity, the unsteady flow over an elliptic cylinder, and aspects of the transient dynamics of the flow over a rearward facing step. The methodology required to extend the two-dimensional formulation to three-dimensions is presented.

  8. 3D models of slow motions in the Earth's crust and upper mantle in the source zones of seismically active regions and their comparison with highly accurate observational data: II. Results of numerical calculations

    NASA Astrophysics Data System (ADS)

    Molodenskii, S. M.; Molodenskii, M. S.; Begitova, T. A.

    2016-09-01

    In the first part of the paper, a new method was developed for solving the inverse problem of coseismic and postseismic deformations in the real (imperfectly elastic, radially and horizontally heterogeneous, self-gravitating) Earth with hydrostatic initial stresses from highly accurate modern satellite data. The method is based on the decomposition of the sought parameters in the orthogonalized basis. The method was suggested for estimating the ambiguity of the solution of the inverse problem for coseismic and postseismic deformations. For obtaining this estimate, the orthogonal complement is constructed to the n-dimensional space spanned by the system of functional derivatives of the residuals in the system of n observed and model data on the coseismic and postseismic displacements at a variety of sites on the ground surface with small variations in the models. Below, we present the results of the numerical modeling of the elastic displacements of the ground surface, which were based on calculating Green's functions of the real Earth for the plane dislocation surface and different orientations of the displacement vector as described in part I of the paper. The calculations were conducted for the model of a horizontally homogeneous but radially heterogeneous selfgravitating Earth with hydrostatic initial stresses and the mantle rheology described by the Lomnitz logarithmic creep function according to (M. Molodenskii, 2014). We compare our results with the previous numerical calculations (Okado, 1985; 1992) for the simplest model of a perfectly elastic nongravitating homogeneous Earth. It is shown that with the source depths starting from the first hundreds of kilometers and with magnitudes of about 8.0 and higher, the discrepancies significantly exceed the errors of the observations and should therefore be taken into account. We present the examples of the numerical calculations of the creep function of the crust and upper mantle for the coseismic deformations. We

  9. 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.

  10. Information field dynamics for simulation scheme construction

    NASA Astrophysics Data System (ADS)

    Enßlin, Torsten A.

    2013-01-01

    Information field dynamics (IFD) is introduced here as a framework to derive numerical schemes for the simulation of physical and other fields without assuming a particular subgrid structure as many schemes do. IFD constructs an ensemble of nonparametric subgrid field configurations from the combination of the data in computer memory, representing constraints on possible field configurations, and prior assumptions on the subgrid field statistics. Each of these field configurations can formally be evolved to a later moment since any differential operator of the dynamics can act on fields living in continuous space. However, these virtually evolved fields need again a representation by data in computer memory. The maximum entropy principle of information theory guides the construction of updated data sets via entropic matching, optimally representing these field configurations at the later time. The field dynamics thereby become represented by a finite set of evolution equations for the data that can be solved numerically. The subgrid dynamics is thereby treated within auxiliary analytic considerations. The resulting scheme acts solely on the data space. It should provide a more accurate description of the physical field dynamics than simulation schemes constructed ad hoc, due to the more rigorous accounting of subgrid physics and the space discretization process. Assimilation of measurement data into an IFD simulation is conceptually straightforward since measurement and simulation data can just be merged. The IFD approach is illustrated using the example of a coarsely discretized representation of a thermally excited classical Klein-Gordon field. This should pave the way towards the construction of schemes for more complex systems like turbulent hydrodynamics.

  11. Information field dynamics for simulation scheme construction.

    PubMed

    Ensslin, Torsten A

    2013-01-01

    Information field dynamics (IFD) is introduced here as a framework to derive numerical schemes for the simulation of physical and other fields without assuming a particular subgrid structure as many schemes do. IFD constructs an ensemble of nonparametric subgrid field configurations from the combination of the data in computer memory, representing constraints on possible field configurations, and prior assumptions on the subgrid field statistics. Each of these field configurations can formally be evolved to a later moment since any differential operator of the dynamics can act on fields living in continuous space. However, these virtually evolved fields need again a representation by data in computer memory. The maximum entropy principle of information theory guides the construction of updated data sets via entropic matching, optimally representing these field configurations at the later time. The field dynamics thereby become represented by a finite set of evolution equations for the data that can be solved numerically. The subgrid dynamics is thereby treated within auxiliary analytic considerations. The resulting scheme acts solely on the data space. It should provide a more accurate description of the physical field dynamics than simulation schemes constructed ad hoc, due to the more rigorous accounting of subgrid physics and the space discretization process. Assimilation of measurement data into an IFD simulation is conceptually straightforward since measurement and simulation data can just be merged. The IFD approach is illustrated using the example of a coarsely discretized representation of a thermally excited classical Klein-Gordon field. This should pave the way towards the construction of schemes for more complex systems like turbulent hydrodynamics.

  12. TVD schemes for open channel flow

    NASA Astrophysics Data System (ADS)

    Delis, A. I.; Skeels, C. P.

    1998-04-01

    The Saint Venant equations for modelling flow in open channels are solved in this paper, using a variety of total variation diminishing (TVD) schemes. The performance of second- and third-order-accurate TVD schemes is investigated for the computation of free-surface flows, in predicting dam-breaks and extreme flow conditions created by the river bed topography. Convergence of the schemes is quantified by comparing error norms between subsequent iterations. Automatically calculated time steps and entropy corrections allow high CFL numbers and smooth transition between different conditions. In order to compare different approaches with TVD schemes, the most accurate of each type was chosen. All four schemes chosen proved acceptably accurate. However, there are important differences between the schemes in the occurrence of clipping, overshooting and oscillating behaviour and in the highest CFL numbers allowed by a scheme. These variations in behaviour stem from the different orders and inherent properties of the four schemes.

  13. A RANS/DES Numerical Procedure for Axisymmetric Flows with and without Strong Rotation

    SciTech Connect

    Andrade, Andrew Jacob

    2007-01-01

    A RANS/DES numerical procedure with an extended Lax-Wendroff control-volume scheme and turbulence model is described for the accurate simulation of internal/external axisymmetric flow with and without strong rotation. This new procedure is an extension, from Cartesian to cylindrical coordinates, of (1) a second order accurate multi-grid, control-volume integration scheme, and (2) a k-ω turbulence model. This paper outlines both the axisymmetric corrections to the mentioned numerical schemes and the developments of techniques pertaining to numerical dissipation, multi-block connectivity, parallelization, etc. Furthermore, analytical and experimental case studies are presented to demonstrate accuracy and computational efficiency. Notes are also made toward numerical stability of highly rotational flows.

  14. Analysis and Improvement of Upwind and Centered Schemes on Quadrilateral and Triangular Meshes

    NASA Technical Reports Server (NTRS)

    Huynh, H. T.

    2003-01-01

    Second-order accurate upwind and centered schemes are presented in a framework that facilitates their analysis and comparison. The upwind scheme employed consists of a reconstruction step (MUSCL approach) followed by an upwind step (Roe's flux-difference splitting). The two centered schemes are of Lax-Friedrichs (L-F) type. They are the nonstaggered versions of the Nessyahu-Tadmor (N-T) scheme and the CE/SE method with epilson = 1/2. The upwind scheme is extended to the case of two spatial dimensions (2D) in a straightforward manner. The N-T and CE/SE schemes are extended in a manner similar to the 2D extensions of the CE/SE scheme by Wang and Chang for a triangular mesh and by Zhang, Yu, and Chang for a quadrilateral mesh. The slope estimates, however, are simplified. Fourier stability and accuracy analyses are carried out for these schemes for the standard 1D and the 2D quadrilateral mesh cases. In the nonstandard case of a triangular mesh, the triangles must be paired up when analyzing the upwind and N-T schemes. An observation resulting in an extended N-T scheme which is faster and uses only one-third of the storage for flow data compared with the CE/SE method is presented. Numerical results are shown. Other improvements to the schemes are discussed.

  15. 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.

  16. 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

  17. Numerical simulations of cryogenic cavitating flows

    NASA Astrophysics Data System (ADS)

    Kim, Hyunji; Kim, Hyeongjun; Min, Daeho; Kim, Chongam

    2015-12-01

    The present study deals with a numerical method for cryogenic cavitating flows. Recently, we have developed an accurate and efficient baseline numerical scheme for all-speed water-gas two-phase flows. By extending such progress, we modify the numerical dissipations to be properly scaled so that it does not show any deficiencies in low Mach number regions. For dealing with cryogenic two-phase flows, previous EOS-dependent shock discontinuity sensing term is replaced with a newly designed EOS-free one. To validate the proposed numerical method, cryogenic cavitating flows around hydrofoil are computed and the pressure and temperature depression effect in cryogenic cavitation are demonstrated. Compared with Hord's experimental data, computed results are turned out to be satisfactory. Afterwards, numerical simulations of flow around KARI turbopump inducer in liquid rocket are carried out under various flow conditions with water and cryogenic fluids, and the difference in inducer flow physics depending on the working fluids are examined.

  18. Accurate thermoelastic tensor and acoustic velocities of NaCl

    NASA Astrophysics Data System (ADS)

    Marcondes, Michel L.; Shukla, Gaurav; da Silveira, Pedro; Wentzcovitch, Renata M.

    2015-12-01

    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 by 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.

  19. Accurate thermoelastic tensor and acoustic velocities of NaCl

    SciTech Connect

    Marcondes, Michel L.; Shukla, Gaurav; Silveira, Pedro da; Wentzcovitch, Renata M.

    2015-12-15

    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 by 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.

  20. Liquid propellant rocket engine combustion simulation with a time-accurate CFD method

    NASA Technical Reports Server (NTRS)

    Chen, Y. S.; Shang, H. M.; Liaw, Paul; Hutt, J.

    1993-01-01

    Time-accurate computational fluid dynamics (CFD) algorithms are among the basic requirements as an engineering or research tool for realistic simulations of transient combustion phenomena, such as combustion instability, transient start-up, etc., inside the rocket engine combustion chamber. A time-accurate pressure based method is employed in the FDNS code for combustion model development. This is in connection with other program development activities such as spray combustion model development and efficient finite-rate chemistry solution method implementation. In the present study, a second-order time-accurate time-marching scheme is employed. For better spatial resolutions near discontinuities (e.g., shocks, contact discontinuities), a 3rd-order accurate TVD scheme for modeling the convection terms is implemented in the FDNS code. Necessary modification to the predictor/multi-corrector solution algorithm in order to maintain time-accurate wave propagation is also investigated. Benchmark 1-D and multidimensional test cases, which include the classical shock tube wave propagation problems, resonant pipe test case, unsteady flow development of a blast tube test case, and H2/O2 rocket engine chamber combustion start-up transient simulation, etc., are investigated to validate and demonstrate the accuracy and robustness of the present numerical scheme and solution algorithm.

  1. On symmetric and upwind TVD schemes

    NASA Technical Reports Server (NTRS)

    Yee, H. C.

    1986-01-01

    The performance of the upwind and symmetric total variation diminishing (TVD) schemes in viscous and inviscid airfoil steady-state calculations is considered, and the extension of the implicit second-order-accurate TVD scheme for hyperbolic systems of conservative laws in curvilinear coordinates is discussed. For two-dimensional steady-state applications, schemes are implemented in a conservative noniterative alternating direction implicit form, and results illustrate that the algorithm produces a fairly good solution for an RAE2822 airfoil calculation. The study demonstrates that the symmetric TVD scheme is as accurate as the upwind TVD scheme, while requiring less computational effort than it.

  2. A modified Rusanov scheme for shallow water equations with topography and two phase flows

    NASA Astrophysics Data System (ADS)

    Mohamed, Kamel; Benkhaldoun, F.

    2016-06-01

    In this work, we introduce a finite volume method for numerical simulation of shallow water equations with source terms in one and two space dimensions, and one-pressure model of two-phase flows in one space dimension. The proposed method is composed of two steps. The first, called predictor step, depends on a local parameter allowing to control the numerical diffusion. A strategy based on limiters theory enables to control this parameter. The second step recovers the conservation equation. The scheme can thus be turned to order 1 in the regions where the flow has a strong variation, and order 2 in the regions where the flow is regular. The numerical scheme is applied to several test cases in one and two space dimensions. This scheme demonstrates its well-balanced property, and that it is an efficient and accurate approach for solving shallow water equations with and without source terms, and water faucet problem.

  3. Conservative form of interpolated differential operator scheme for compressible and incompressible fluid dynamics

    NASA Astrophysics Data System (ADS)

    Imai, Yohsuke; Aoki, Takayuki; Takizawa, Kenji

    2008-02-01

    The proposed scheme, which is a conservative form of the interpolated differential operator scheme (IDO-CF), can provide high accurate solutions for both compressible and incompressible fluid equations. Spatial discretizations with fourth-order accuracy are derived from interpolation functions locally constructed by both cell-integrated values and point values. These values are coupled and time-integrated by solving fluid equations in the flux forms for the cell-integrated values and in the derivative forms for the point values. The IDO-CF scheme exactly conserves mass, momentum, and energy, retaining the high resolution more than the non-conservative form of the IDO scheme. A direct numerical simulation of turbulence is carried out with comparable accuracy to that of spectral methods. Benchmark tests of Riemann problems and lid-driven cavity flows show that the IDO-CF scheme is immensely promising in compressible and incompressible fluid dynamics studies.

  4. TE/TM scheme for computation of electromagnetic fields in accelerators

    SciTech Connect

    Zagorodnov, Igor . E-mail: zagor@temf.de; Weiland, Thomas . E-mail: thomas.weiland@temf.de

    2005-07-20

    We propose a new two-level economical conservative scheme for short-range wake field calculation in three dimensions. The scheme does not have dispersion in the longitudinal direction and is staircase free (second order convergent). Unlike the finite-difference time domain method (FDTD), it is based on a TE/TM like splitting of the field components in time. Additionally, it uses an enhanced alternating direction splitting of the transverse space operator that makes the scheme computationally as effective as the conventional FDTD method. Unlike the FDTD ADI and low-order Strang methods, the splitting error in our scheme is only of fourth order. As numerical examples show, the new scheme is much more accurate on the long-time scale than the conventional FDTD approach.

  5. 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.

  6. 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.

  7. High order WENO scheme for computational cosmology

    NASA Astrophysics Data System (ADS)

    Roy, Ishani

    2010-11-01

    This doctoral dissertation is concerned with the formulation and application of a high order accurate numerical algorithm suitable in solving complex multi dimensional equations and the application of this algorithm to a problem in Astrophysics. The algorithm is designed with the aim of resolving solutions of partial differential equations with sharp fronts propagating with time. This high order accurate class of numerical technique is called a Weighted Essentially Non Oscillatory (WENO) method and is well suited for shock capturing in solving conservation laws. The numerical approximation method, in the algorithm, is coupled with high order time marching as well as integration techniques designed to reduce computational cost. This numerical algorithm is used in several applications in computational cosmology to help understand questions about certain physical phenomena which occurred during the formation and evolution of first generation stars. The thesis is divided broadly in terms of the algorithm and its application to the different galactic processes. The first chapter deals with the astrophysical problem and offers an introduction to the numerical algorithm. In chapter 2 we outline the mathematical model and the various functions and parameters associated with the model. We also give a brief description of the relevant physical phenomena and the conservation laws associated with them. In chapter 3, we give a detailed description of the higher order algorithm and its formulation. We also highlight the special techniques incorporated in the algorithm in order to make it more suitable for handling cases which are computationally intensive. In the later chapters, 4-7, we explore in detail the physical processes and the different applications of our numerical scheme. We calculate different results such as the time scale of a temperature coupling mechanism, radiation and intensity changes etc. Different tests are also performed to illustrate the stability and

  8. 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.

  9. Accurate upwind-monotone (nonoscillatory) methods for conservation laws

    NASA Technical Reports Server (NTRS)

    Huynh, Hung T.

    1992-01-01

    The well known MUSCL scheme of Van Leer is constructed using a piecewise linear approximation. The MUSCL scheme is second order accurate at the smooth part of the solution except at extrema where the accuracy degenerates to first order due to the monotonicity constraint. To construct accurate schemes which are free from oscillations, the author introduces the concept of upwind monotonicity. Several classes of schemes, which are upwind monotone and of uniform second or third order accuracy are then presented. Results for advection with constant speed are shown. It is also shown that the new scheme compares favorably with state of the art methods.

  10. A semi-implicit gas-kinetic scheme for smooth flows

    NASA Astrophysics Data System (ADS)

    Wang, Peng; Guo, Zhaoli

    2016-08-01

    In this paper, a semi-implicit gas-kinetic scheme (SIGKS) is derived for smooth flows based on the Bhatnagar-Gross-Krook (BGK) equation. As a finite-volume scheme, the evolution of the average flow variables in a control volume is under the Eulerian framework, whereas the construction of the numerical flux across the cell interface comes from the Lagrangian perspective. The adoption of the Lagrangian aspect makes the collision and the transport mechanisms intrinsically coupled together in the flux evaluation. As a result, the time step size is independent of the particle collision time and solely determined by the Courant-Friedrichs-Lewy (CFL) condition. An analysis of the reconstructed distribution function at the cell interface shows that the SIGKS can be viewed as a modified Lax-Wendroff type scheme with an additional term. Furthermore, the addition term coming from the implicitness in the reconstruction is expected to be able to enhance the numerical stability of the scheme. A number of numerical tests of smooth flows with low and moderate Mach numbers are performed to benchmark the SIGKS. The results show that the method has second-order spatial accuracy, and can give accurate numerical solutions in comparison with benchmark results. It is also demonstrated that the numerical stability of the proposed scheme is better than the original GKS for smooth flows.

  11. 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.

  12. Frozen core potential scheme with a relativistic electronic Hamiltonian: Theoretical connection between the model potential and all-electron treatments

    NASA Astrophysics Data System (ADS)

    Seino, Junji; Tarumi, Moto; Nakai, Hiromi

    2014-01-01

    This Letter proposes an accurate scheme using frozen core orbitals, called the frozen core potential (FCP) method, to theoretically connect model potential calculations to all-electron (AE) ones. The present scheme is based on the Huzinaga-Cantu equation combined with spin-free relativistic Douglas-Kroll-Hess Hamiltonians. The local unitary transformation scheme for efficiently constructing the Hamiltonian produces a seamless extension to the FCP method in a relativistic framework. Numerical applications to coinage diatomic molecules illustrate the high accuracy of this FCP method, as compared to AE calculations. Furthermore, the efficiency of the FCP method is also confirmed by these calculations.

  13. Well-balanced high-order centred schemes for non-conservative hyperbolic systems. Applications to shallow water equations with fixed and mobile bed

    NASA Astrophysics Data System (ADS)

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

    2009-06-01

    This paper concerns the development of high-order accurate centred schemes for the numerical solution of one-dimensional hyperbolic systems containing non-conservative products and source terms. Combining the PRICE-T method developed in [Toro E, Siviglia A. PRICE: primitive centred schemes for hyperbolic system of equations. Int J Numer Methods Fluids 2003;42:1263-91] with the theoretical insights gained by the recently developed path-conservative schemes [Castro M, Gallardo J, Parés C. High-order finite volume schemes based on reconstruction of states for solving hyperbolic systems with nonconservative products applications to shallow-water systems. Math Comput 2006;75:1103-34; Parés C. Numerical methods for nonconservative hyperbolic systems: a theoretical framework. SIAM J Numer Anal 2006;44:300-21], we propose the new PRICE-C scheme that automatically reduces to a modified conservative FORCE scheme if the underlying PDE system is a conservation law. The resulting first-order accurate centred method is then extended to high order of accuracy in space and time via the ADER approach together with a WENO reconstruction technique. The well-balanced properties of the PRICE-C method are investigated for the shallow water equations. Finally, we apply the new scheme to the shallow water equations with fix bottom topography and with variable bottom solving an additional sediment transport equation.

  14. A fast, time-accurate unsteady full potential scheme

    NASA Technical Reports Server (NTRS)

    Shankar, V.; Ide, H.; Gorski, J.; Osher, S.

    1985-01-01

    The unsteady form of the full potential equation is solved in conservation form by an implicit method based on approximate factorization. At each time level, internal Newton iterations are performed to achieve time accuracy and computational efficiency. A local time linearization procedure is introduced to provide a good initial guess for the Newton iteration. A novel flux-biasing technique is applied to generate proper forms of the artificial viscosity to treat hyperbolic regions with shocks and sonic lines present. The wake is properly modeled by accounting not only for jumps in phi, but also for jumps in higher derivatives of phi, obtained by imposing the density to be continuous across the wake. The far field is modeled using the Riemann invariants to simulate nonreflecting boundary conditions. The resulting unsteady method performs well which, even at low reduced frequency levels of 0.1 or less, requires fewer than 100 time steps per cycle at transonic Mach numbers. The code is fully vectorized for the CRAY-XMP and the VPS-32 computers.

  15. Development of an explicit non-staggered scheme for solving three-dimensional Maxwell's equations

    NASA Astrophysics Data System (ADS)

    Sheu, Tony W. H.; Chung, Y. W.; Li, J. H.; Wang, Y. C.

    2016-10-01

    An explicit finite-difference scheme for solving the three-dimensional Maxwell's equations in non-staggered grids is presented. We aspire to obtain time-dependent solutions of the Faraday's and Ampère's equations and predict the electric and magnetic fields within the discrete zero-divergence context (or Gauss's law). The local conservation laws in Maxwell's equations are numerically preserved using the explicit second-order accurate symplectic partitioned Runge-Kutta temporal scheme. Following the method of lines, the spatial derivative terms in the semi-discretized Faraday's and Ampère's equations are approximated theoretically to obtain a highly accurate numerical phase velocity. The proposed fourth-order accurate space-centered finite difference scheme minimizes the discrepancy between the exact and numerical phase velocities. This minimization process considerably reduces the dispersion and anisotropy errors normally associated with finite difference time-domain methods. The computational efficiency of getting the same level of accuracy at less computing time and the ability of preserving the symplectic property have been numerically demonstrated through several test problems.

  16. A semi-Lagrangian finite difference WENO scheme for scalar nonlinear conservation laws

    NASA Astrophysics Data System (ADS)

    Huang, Chieh-Sen; Arbogast, Todd; Hung, Chen-Hui

    2016-10-01

    For a nonlinear scalar conservation law in one-space dimension, we develop a locally conservative semi-Lagrangian finite difference scheme based on weighted essentially non-oscillatory reconstructions (SL-WENO). This scheme has the advantages of both WENO and semi-Lagrangian schemes. It is a locally mass conservative finite difference scheme, it is formally high-order accurate in space, it has small time truncation error, and it is essentially non-oscillatory. The scheme is nearly free of a CFL time step stability restriction for linear problems, and it has a relaxed CFL condition for nonlinear problems. The scheme can be considered as an extension of the SL-WENO scheme of Qiu and Shu (2011) [2] developed for linear problems. The new scheme is based on a standard sliding average formulation with the flux function defined using WENO reconstructions of (semi-Lagrangian) characteristic tracings of grid points. To handle nonlinear problems, we use an approximate, locally frozen trace velocity and a flux correction step. A special two-stage WENO reconstruction procedure is developed that is biased to the upstream direction. A Strang splitting algorithm is used for higher-dimensional problems. Numerical results are provided to illustrate the performance of the scheme and verify its formal accuracy. Included are applications to the Vlasov-Poisson and guiding-center models of plasma flow.

  17. Implicit-explicit Godunov schemes for unsteady gas dynamics

    SciTech Connect

    Collins, J.P.

    1992-12-31

    Hybrid implicit-explicit schemes are developed for Eulerian hydrodynamics in one and two space dimensions. The hybridization is a continuous switch and operates on each characteristic field separately. The explicit scheme is a version of the second order Godunov scheme; the implicit method is only first order accurate in time but leads to second order accurate steady states. This methodology is developed for linear advection, nonlinear scalar problems, hyperbolic constant co-efficient systems, and for gas dynamics. Truncation error and stability analyses are done for the linear cases. This implicit-explicit strategy is intended for problems with spatially or temporally localized stiffness in wave speeds. By stiffness we mean that the high speed modes contain very little energy, yet they determine the explicit time step through the CFL condition. For hydrodynamics, the main examples are nearly incompressible flow, flows with embedded boundary layers, and magnetohydrodynamics; the latter two examples are not treated here. Several numerical results are presented to demonstrate this method. These include, stable numerical shocks at very high CFL numbers, one-dimensional flow in a duct, and low Mach number shear layers.

  18. Wavenumber-extended high-order upwind-biased finite-difference schemes for convective scalar transport

    SciTech Connect

    Li, Y.

    1997-05-15

    This paper proposes some new wavenumber-extended high-order upwind-biased schemes. The dispersion and dissipation errors of upwind-biased finite-difference schemes are assessed and compared by means of a Fourier analysis of the difference schemes. Up to 11th-order upwind-biased schemes are analyzed. It is shown that both the upwind-biased scheme of order 2N - 1 and the corresponding centered differencing scheme of order 2N have the same dispersion characteristics; thus the former can be considered to be the latter plus a correction that reduces the numerical dissipation. The new second-order wavenumber-extended scheme is tested and compared with some well-known schemes. The range of wavenumbers that are accurately treated by the upwind-biased schemes is improved by using additional constraints from the Fourier analysis to construct the new schemes. The anisotropic behavior of the dispersion and dissipation errors is also analyzed for both the conventional and the new wavenumber-extended upwind-biased finite-difference schemes.

  19. A Quadrature Free Discontinuous Galerkin Conservative Level Set Scheme

    NASA Astrophysics Data System (ADS)

    Czajkowski, Mark; Desjardins, Olivier

    2010-11-01

    In an effort to improve the scalability and accuracy of the Accurate Conservative Level Set (ACLS) scheme [Desjardins et al., J COMPUT PHYS 227 (2008)], a scheme based on the quadrature free discontinuous Galerkin (DG) methodology has been developed. ACLS relies on a hyperbolic tangent level set function that is transported and reinitialized using conservative schemes in order to alleviate mass conservation issues known to plague level set methods. DG allows for an arbitrarily high order representation of the interface by using a basis of high order polynomials while only using data from the faces of neighboring cells. The small stencil allows DG to have excellent parallel scalability. The diffusion term present in the conservative reinitialization equation is handled using local DG method [Cockburn et al., SIAM J NUMER ANAL 39, (2001)] while the normals are computed from a limited form of the level set function in order to avoid spurious oscillations. The resulting scheme is shown to be both robust, accurate, and highly scalable, making it a method of choice for large-scale simulations of multiphase flows with complex interfacial topology.

  20. Time-Space Decoupled Explicit Method for Fast Numerical Simulation of Tsunami Propagation

    NASA Astrophysics Data System (ADS)

    Guo, Anxin; Xiao, Shengchao; Li, Hui

    2015-02-01

    This study presents a novel explicit numerical scheme for simulating tsunami propagation using the exact solution of the wave equations. The objective of this study is to develop a fast and stable numerical scheme by decoupling the wave equation in both the time and space domains. First, the finite difference scheme of the shallow-water equations for tsunami simulation are briefly introduced. The time-space decoupled explicit method based on the exact solution of the wave equation is given for the simulation of tsunami propagation without including frequency dispersive effects. Then, to consider wave dispersion, the second-order accurate numerical scheme to solve the shallow-water equations, which mimics the physical frequency dispersion with numerical dispersion, is derived. Lastly, the computation efficiency and the accuracy of the two types of numerical schemes are investigated by the 2004 Indonesia tsunami and the solution of the Boussinesq equation for a tsunami with Gaussian hump over both uniform and varying water depths. The simulation results indicate that the proposed numerical scheme can achieve a fast and stable tsunami propagation simulation while maintaining computation accuracy.

  1. A third-order compact gas-kinetic scheme on unstructured meshes for compressible Navier-Stokes solutions

    NASA Astrophysics Data System (ADS)

    Pan, Liang; Xu, Kun

    2016-08-01

    In this paper, for the first time a third-order compact gas-kinetic scheme is proposed on unstructured meshes for the compressible viscous flow computations. The possibility to design such a third-order compact scheme is due to the high-order gas evolution model, where a time-dependent gas distribution function at cell interface not only provides the fluxes across a cell interface, but also presents a time accurate solution for flow variables at cell interface. As a result, both cell averaged and cell interface flow variables can be used for the initial data reconstruction at the beginning of next time step. A weighted least-square procedure has been used for the initial reconstruction. Therefore, a compact third-order gas-kinetic scheme with the involvement of neighboring cells only can be developed on unstructured meshes. In comparison with other conventional high-order schemes, the current method avoids the Gaussian point integration for numerical fluxes along a cell interface and the multi-stage Runge-Kutta method for temporal accuracy. The third-order compact scheme is numerically stable under CFL condition CFL ≈ 0.5. Due to its multidimensional gas-kinetic formulation and the coupling of inviscid and viscous terms, even with unstructured meshes, the boundary layer solution and vortex structure can be accurately captured by the current scheme. At the same time, the compact scheme can capture strong shocks as well.

  2. Linearized form of implicit TVD schemes for the multidimensional Euler and Navier-Stokes equations

    NASA Technical Reports Server (NTRS)

    Yee, H. C.

    1986-01-01

    Linearized alternating direction implicit (ADI) forms of a class of total variation diminishing (TVD) schemes for the Euler and Navier-Stokes equations have been developed. These schemes are based on the second-order-accurate TVD schemes for hyperbolic conservation laws developed by Harten (1983, 1984). They have the property of not generating spurious oscillations across shocks and contact discontinuities. In general, shocks can be captured within 1-2 grid points. These schemes are relatively simple to understand and easy to implement into a new or existing computer code. One can modify a standard three-point central-difference code by simply changing the conventional numerical dissipation term into the one designed for the TVD scheme. For steady-state applications, the only difference in computation is that the current schemes require a more elaborate dissipation term for the explicit operator; no extra computation is required for the implicit operator. Numerical experiments with the proposed algorithms on a variety of steady-state airfoil problems illustrate the versatility of the schemes.

  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. High resolution finite volume scheme for the quantum hydrodynamic equations

    NASA Astrophysics Data System (ADS)

    Lin, Chin-Tien; Yeh, Jia-Yi; Chen, Jiun-Yeu

    2009-03-01

    The theory of quantum fluid dynamics (QFD) helps nanotechnology engineers to understand the physical effect of quantum forces. Although the governing equations of quantum fluid dynamics and classical fluid mechanics have the same form, there are two numerical simulation problems must be solved in QFD. The first is that the quantum potential term becomes singular and causes a divergence in the numerical simulation when the probability density is very small and close to zero. The second is that the unitarity in the time evolution of the quantum wave packet is significant. Accurate numerical evaluations are critical to the simulations of the flow fields that are generated by various quantum fluid systems. A finite volume scheme is developed herein to solve the quantum hydrodynamic equations of motion, which significantly improve the accuracy and stability of this method. The QFD equation is numerically implemented within the Eulerian method. A third-order modified Osher-Chakravarthy (MOC) upwind-centered finite volume scheme was constructed for conservation law to evaluate the convective terms, and a second-order central finite volume scheme was used to map the quantum potential field. An explicit Runge-Kutta method is used to perform the time integration to achieve fast convergence of the proposed scheme. In order to meet the numerical result can conform to the physical phenomenon and avoid numerical divergence happening due to extremely low probability density, the minimum value setting of probability density must exceed zero and smaller than certain value. The optimal value was found in the proposed numerical approach to maintain a converging numerical simulation when the minimum probability density is 10 -5 to 10 -12. The normalization of the wave packet remains close to unity through a long numerical simulation and the deviations from 1.0 is about 10 -4. To check the QFD finite difference numerical computations, one- and two-dimensional particle motions were

  5. High resolution finite volume scheme for the quantum hydrodynamic equations

    SciTech Connect

    Lin, C.-T. Yeh, J.-Y. Chen, J.-Y.

    2009-03-20

    The theory of quantum fluid dynamics (QFD) helps nanotechnology engineers to understand the physical effect of quantum forces. Although the governing equations of quantum fluid dynamics and classical fluid mechanics have the same form, there are two numerical simulation problems must be solved in QFD. The first is that the quantum potential term becomes singular and causes a divergence in the numerical simulation when the probability density is very small and close to zero. The second is that the unitarity in the time evolution of the quantum wave packet is significant. Accurate numerical evaluations are critical to the simulations of the flow fields that are generated by various quantum fluid systems. A finite volume scheme is developed herein to solve the quantum hydrodynamic equations of motion, which significantly improve the accuracy and stability of this method. The QFD equation is numerically implemented within the Eulerian method. A third-order modified Osher-Chakravarthy (MOC) upwind-centered finite volume scheme was constructed for conservation law to evaluate the convective terms, and a second-order central finite volume scheme was used to map the quantum potential field. An explicit Runge-Kutta method is used to perform the time integration to achieve fast convergence of the proposed scheme. In order to meet the numerical result can conform to the physical phenomenon and avoid numerical divergence happening due to extremely low probability density, the minimum value setting of probability density must exceed zero and smaller than certain value. The optimal value was found in the proposed numerical approach to maintain a converging numerical simulation when the minimum probability density is 10{sup -5} to 10{sup -12}. The normalization of the wave packet remains close to unity through a long numerical simulation and the deviations from 1.0 is about 10{sup -4}. To check the QFD finite difference numerical computations, one- and two-dimensional particle

  6. 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.

  7. Curvilinear finite-volume schemes using high-order compact interpolation

    SciTech Connect

    Fosso P, Arnaud Deniau, Hugues; Sicot, Frederic; Sagaut, Pierre

    2010-07-01

    During the last years, the need of high fidelity simulations on complex geometries for aeroacoustics predictions has grown. Most of high fidelity numerical schemes, in terms of low dissipative and low dispersive effects, lie on finite-difference (FD) approach. But for industrial applications, FD schemes are less robust compared to finite-volume (FV) ones. Thus the present study focuses on the development of a new compact FV scheme for two- and three-dimensional applications. The proposed schemes are formulated in the physical space and not in the computational space as it is the case in most of the known works. Therefore, they are more appropriate for general grids. They are based on compact interpolation to approximate interface-averaged field values using known cell-averaged values. For each interface, the interpolation coefficients are determined by matching Taylor series expansions around the interface center. Two types of schemes can be distinguished. The first one uses only the curvilinear abscissa along a mesh line to derive a sixth-order compact interpolation formulae while the second, more general, uses coordinates in a spatial three-dimensional frame well chosen. This latter is formally sixth-order accurate in a preferred direction almost orthogonal to the interface and at most fourth-order accurate in transversal directions. For non-linear problems, different approaches can be used to keep the high-order scheme. However, in the present paper, a MUSCL-like formulation was sufficient to address the presented test cases. All schemes have been modified to treat multiblock and periodic interfaces in such a way that high-order accuracy, stability, good spectral resolution, conservativeness and low computational costs are guaranteed. This is a first step to insure good scalability of the schemes although parallel performances issues are not addressed. As high frequency waves, badly resolved, could be amplified and then destabilize the scheme, compact filtering

  8. Discrete unified gas kinetic scheme for all Knudsen number flows: low-speed isothermal case.

    PubMed

    Guo, Zhaoli; Xu, Kun; Wang, Ruijie

    2013-09-01

    Based on the Boltzmann-BGK (Bhatnagar-Gross-Krook) equation, in this paper a discrete unified gas kinetic scheme (DUGKS) is developed for low-speed isothermal flows. The DUGKS is a finite-volume scheme with the discretization of particle velocity space. After the introduction of two auxiliary distribution functions with the inclusion of collision effect, the DUGKS becomes a fully explicit scheme for the update of distribution function. Furthermore, the scheme is an asymptotic preserving method, where the time step is only determined by the Courant-Friedricks-Lewy condition in the continuum limit. Numerical results demonstrate that accurate solutions in both continuum and rarefied flow regimes can be obtained from the current DUGKS. The comparison between the DUGKS and the well-defined lattice Boltzmann equation method (D2Q9) is presented as well.

  9. The Nonlinear Characteristic scheme in X-Y geometries

    SciTech Connect

    Walters, W.F.; Wareing, T.A.

    1994-08-01

    The Nonlinear Characteristic (NC) scheme for solving the discrete-ordinates form of the transport equation has recently been introduced and used to analyze one-dimensional slab transport problems. The purpose of this paper is to determine the accuracy and positivity of the NC scheme as extended to solve two-dimensional X-Y problems. We compare the results obtained using the NC scheme to those obtained using the Bilinear Discontinuous (BLD) scheme, the Bilinear Nodal (BLN) scheme, Linear Characteristic scheme, and the Diamond Difference with Fixup (DD/F) scheme. As was found in one-dimensional applications, the NC scheme is strictly positive and as accurate or more accurate than the other schemes for all meshes examined. The accuracy of the NC scheme for coarse meshes is particularity outstanding compared to that of the other schemes.

  10. A Spatial Discretization Scheme for Solving the Transport Equation on Unstructured Grids of Polyhedra

    SciTech Connect

    Thompson, K.G.

    2000-11-01

    In this work, we develop a new spatial discretization scheme that may be used to numerically solve the neutron transport equation. This new discretization extends the family of corner balance spatial discretizations to include spatial grids of arbitrary polyhedra. This scheme enforces balance on subcell volumes called corners. It produces a lower triangular matrix for sweeping, is algebraically linear, is non-negative in a source-free absorber, and produces a robust and accurate solution in thick diffusive regions. Using an asymptotic analysis, we design the scheme so that in thick diffusive regions it will attain the same solution as an accurate polyhedral diffusion discretization. We then refine the approximations in the scheme to reduce numerical diffusion in vacuums, and we attempt to capture a second order truncation error. After we develop this Upstream Corner Balance Linear (UCBL) discretization we analyze its characteristics in several limits. We complete a full diffusion limit analysis showing that we capture the desired diffusion discretization in optically thick and highly scattering media. We review the upstream and linear properties of our discretization and then demonstrate that our scheme captures strictly non-negative solutions in source-free purely absorbing media. We then demonstrate the minimization of numerical diffusion of a beam and then demonstrate that the scheme is, in general, first order accurate. We also note that for slab-like problems our method actually behaves like a second-order method over a range of cell thicknesses that are of practical interest. We also discuss why our scheme is first order accurate for truly 3D problems and suggest changes in the algorithm that should make it a second-order accurate scheme. Finally, we demonstrate 3D UCBL's performance on several very different test problems. We show good performance in diffusive and streaming problems. We analyze truncation error in a 3D problem and demonstrate robustness in a

  11. Implicit Total Variation Diminishing (TVD) schemes for steady-state calculations. [in gas dynamics

    NASA Technical Reports Server (NTRS)

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

    1985-01-01

    The novel implicit and unconditionally stable, high resolution Total Variation Diminishing (TVD) scheme whose application to steady state calculations is presently examined is a member of a one-parameter family of implicit, second-order accurate systems developed by Harten (1983) for the computation of weak solutions for one-dimensional hyperbolic conservation laws. The scheme will not generate spurious oscillations for a nonlinear scalar equation and a constant coefficient system. Numerical experiments for a quasi-one-dimensional nozzle problem show that the experimentally determined stability limit correlates exactly with the theoretical stability limit for the nonlinear scalar hyberbolic conservation laws.

  12. A critical comparison of the numerical solution of the 1D filtered Vlasov-Poisson equation

    NASA Astrophysics Data System (ADS)

    Viñas, A. F.; Klimas, A. J.

    2003-04-01

    We present a comparison of the numerical solution of the filtered Vlasov-Poisson system of equations using the Fourier-Fourier and the Flux-Balance-MacCormack methods in the electrostatic, non-relativistic case. We show that the splitting method combined with the Flux-Balance-MacCormack scheme provides an efficient and accurate scheme for integrating the filtered Vlasov-Poisson system in their self-consistent field. Finally we present various typical problems of interest in plasma physics research which can be studied with the scheme presented here.

  13. Finite-volume component-wise TVD schemes for 2D shallow water equations

    NASA Astrophysics Data System (ADS)

    Lin, Gwo-Fong; Lai, Jihn-Sung; Guo, Wen-Dar

    Four finite-volume component-wise total variation diminishing (TVD) schemes are proposed for solving the two-dimensional shallow water equations. In the framework of the finite volume method, a proposed algorithm using the flux-splitting technique is established by modifying the MacCormack scheme to preserve second-order accuracy in both space and time. Based on this algorithm, four component-wise TVD schemes, including the Liou-Steffen splitting (LSS), van Leer splitting, Steger-Warming splitting and local Lax-Friedrichs splitting schemes, are developed. These schemes are verified through the simulations of the 1D dam-break, the oblique hydraulic jump, the partial dam-break and circular dam-break problems. It is demonstrated that the proposed schemes are accurate, efficient and robust to capture the discontinuous shock waves without any spurious oscillations in the complex flow domains with dry-bed situation, bottom slope or friction. The simulated results also show that the LSS scheme has the best numerical accuracy among the schemes tested.

  14. 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.

  15. 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

  16. FORCE schemes on unstructured meshes I: Conservative hyperbolic systems

    NASA Astrophysics Data System (ADS)

    Toro, Eleuterio F.; Hidalgo, Arturo; Dumbser, Michael

    2009-05-01

    This paper is about the construction of numerical fluxes of the centred type for one-step schemes in conservative form for solving general systems of conservation laws in multiple space dimensions on structured and unstructured meshes. The work is a multi-dimensional extension of the one-dimensional FORCE flux and is closely related to the work of Nessyahu-Tadmor and Arminjon. The resulting basic flux is first-order accurate and monotone; it is then extended to arbitrary order of accuracy in space and time on unstructured meshes in the framework of finite volume and discontinuous Galerkin methods. The performance of the schemes is assessed on a suite of test problems for the multi-dimensional Euler and Magnetohydrodynamics equations on unstructured meshes.

  17. 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

  18. Construction of weighted upwind compact scheme

    NASA Astrophysics Data System (ADS)

    Wang, Zhengjie

    Enormous endeavor has been devoted in spatial high order high resolution schemes in more than twenty five years previously, like total variation diminishing (TVD), essentially non-oscillatory scheme, weighted essentially non-oscillatory scheme for finite difference, and Discontinuous Galerkin methods for finite element and the finite volume. In this dissertation, a high order finite difference Weighted Upwind Compact Scheme has been constructed by dissipation and dispersion analysis. Secondly, a new method to construct global weights has been tested. Thirdly, a methodology to compromise dissipation and dispersion in constructing Weighted Upwind Compact Scheme has been derived. Finally, several numerical test cases have been shown.

  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

    NASA Astrophysics Data System (ADS)

    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 Navie-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. Analysis of triangular C-grid finite volume scheme for shallow water flows

    NASA Astrophysics Data System (ADS)

    Shirkhani, Hamidreza; Mohammadian, Abdolmajid; Seidou, Ousmane; Qiblawey, Hazim

    2015-08-01

    In this paper, a dispersion relation analysis is employed to investigate the finite volume triangular C-grid formulation for two-dimensional shallow-water equations. In addition, two proposed combinations of time-stepping methods with the C-grid spatial discretization are investigated. In the first part of this study, the C-grid spatial discretization scheme is assessed, and in the second part, fully discrete schemes are analyzed. Analysis of the semi-discretized scheme (i.e. only spatial discretization) shows that there is no damping associated with the spatial C-grid scheme, and its phase speed behavior is also acceptable for long and intermediate waves. The analytical dispersion analysis after considering the effect of time discretization shows that the Leap-Frog time stepping technique can improve the phase speed behavior of the numerical method; however it could not damp the shorter decelerated waves. The Adams-Bashforth technique leads to slower propagation of short and intermediate waves and it damps those waves with a slower propagating speed. The numerical solutions of various test problems also conform and are in good agreement with the analytical dispersion analysis. They also indicate that the Adams-Bashforth scheme exhibits faster convergence and more accurate results, respectively, when the spatial and temporal step size decreases. However, the Leap-Frog scheme is more stable with higher CFL numbers.

  2. Upwind Compact Finite Difference Schemes

    NASA Astrophysics Data System (ADS)

    Christie, I.

    1985-07-01

    It was shown by Ciment, Leventhal, and Weinberg ( J. Comput. Phys.28 (1978), 135) that the standard compact finite difference scheme may break down in convection dominated problems. An upwinding of the method, which maintains the fourth order accuracy, is suggested and favorable numerical results are found for a number of test problems.

  3. 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

  4. Stable and accurate hybrid finite volume methods based on pure convexity arguments for hyperbolic systems of conservation law

    NASA Astrophysics Data System (ADS)

    De Vuyst, Florian

    2004-01-01

    This exploratory work tries to present first results of a novel approach for the numerical approximation of solutions of hyperbolic systems of conservation laws. The objective is to define stable and "reasonably" accurate numerical schemes while being free from any upwind process and from any computation of derivatives or mean Jacobian matrices. That means that we only want to perform flux evaluations. This would be useful for "complicated" systems like those of two-phase models where solutions of Riemann problems are hard, see impossible to compute. For Riemann or Roe-like solvers, each fluid model needs the particular computation of the Jacobian matrix of the flux and the hyperbolicity property which can be conditional for some of these models makes the matrices be not R-diagonalizable everywhere in the admissible state space. In this paper, we rather propose some numerical schemes where the stability is obtained using convexity considerations. A certain rate of accuracy is also expected. For that, we propose to build numerical hybrid fluxes that are convex combinations of the second-order Lax-Wendroff scheme flux and the first-order modified Lax-Friedrichs scheme flux with an "optimal" combination rate that ensures both minimal numerical dissipation and good accuracy. The resulting scheme is a central scheme-like method. We will also need and propose a definition of local dissipation by convexity for hyperbolic or elliptic-hyperbolic systems. This convexity argument allows us to overcome the difficulty of nonexistence of classical entropy-flux pairs for certain systems. We emphasize the systematic feature of the method which can be fastly implemented or adapted to any kind of systems, with general analytical or data-tabulated equations of state. The numerical results presented in the paper are not superior to many existing state-of-the-art numerical methods for conservation laws such as ENO, MUSCL or central scheme of Tadmor and coworkers. The interest is rather

  5. The basic function scheme of polynomial type

    SciTech Connect

    WU, Wang-yi; Lin, Guang

    2009-12-01

    A new numerical method---Basic Function Method is proposed. This method can directly discrete differential operator on unstructured grids. By using the expansion of basic function to approach the exact function, the central and upwind schemes of derivative are constructed. By using the second-order polynomial as basic function and applying the technique of flux splitting method and the combination of central and upwind schemes to suppress the non-physical fluctuation near the shock wave, the second-order basic function scheme of polynomial type for solving inviscid compressible flow numerically is constructed in this paper. Several numerical results of many typical examples for two dimensional inviscid compressible transonic and supersonic steady flow illustrate that it is a new scheme with high accuracy and high resolution for shock wave. Especially, combining with the adaptive remeshing technique, the satisfactory results can be obtained by these schemes.

  6. A fifth-order finite difference scheme for hyperbolic equations on block-adaptive curvilinear grids

    NASA Astrophysics Data System (ADS)

    Chen, Yuxi; Tóth, Gábor; Gombosi, Tamas I.

    2016-01-01

    We present a new fifth-order accurate finite difference method for hyperbolic equations on block-adaptive curvilinear grids. The scheme employs the 5th order accurate monotonicity preserving limiter MP5 to construct high order accurate face fluxes. The fifth-order accuracy of the spatial derivatives is ensured by a flux correction step. The method is generalized to curvilinear grids with a free-stream preserving discretization. It is also extended to block-adaptive grids using carefully designed ghost cell interpolation algorithms. Only three layers of ghost cells are required, and the grid blocks can be as small as 6 × 6 × 6 cells. Dynamic grid refinement and coarsening are also fifth-order accurate. All interpolation algorithms employ a general limiter based on the principles of the MP5 limiter. The finite difference scheme is fully conservative on static uniform grids. Conservation is only maintained at the truncation error level at grid resolution changes and during grid adaptation, but our numerical tests indicate that the results are still very accurate. We demonstrate the capabilities of the new method on a number of numerical tests, including smooth but non-linear problems as well as simulations involving discontinuities.

  7. A High-Order Accurate Parallel Solver for Maxwell's Equations on Overlapping Grids

    SciTech Connect

    Henshaw, W D

    2005-09-23

    A scheme for the solution of the time dependent Maxwell's equations on composite overlapping grids is described. The method uses high-order accurate approximations in space and time for Maxwell's equations written as a second-order vector wave equation. High-order accurate symmetric difference approximations to the generalized Laplace operator are constructed for curvilinear component grids. The modified equation approach is used to develop high-order accurate approximations that only use three time levels and have the same time-stepping restriction as the second-order scheme. Discrete boundary conditions for perfect electrical conductors and for material interfaces are developed and analyzed. The implementation is optimized for component grids that are Cartesian, resulting in a fast and efficient method. The solver runs on parallel machines with each component grid distributed across one or more processors. Numerical results in two- and three-dimensions are presented for the fourth-order accurate version of the method. These results demonstrate the accuracy and efficiency of the approach.

  8. A generalized procedure for constructing an upwind based TVD scheme

    NASA Technical Reports Server (NTRS)

    Liou, Meng-Sing

    1987-01-01

    A generalized formulation for constructing second- and higher-order accurate TVD (total variation diminishing) schemes is presented. A given scheme is made TVD by limiting antidiffusive flux differences with some linear functions, so-called limiters. The general idea of the formulation and its mathematical proof of Harten's TVD conditions is shown by applying the Lax-Wendroff method to scalar nonlinear equations and a constant-coefficient system of conservation laws. For the system of equations, several definitions are derived for the argument used in the limiter function and present their performance in numerical experiments. The formulation is extended to the nonlinear system. It is demonstrated that the present procedure can easily convert existing central or upwind, and second- or higher-order differencing schemes to preserve monotonicity and yield physically admissible solutions. The formulation is simple mathematically as well as numerically; both matrix-vector multiplication and Riemann solver are avoided. Although the notion of TVD is based on the initial value problem, application to the steady Euler equations of the formulation is also made.

  9. Minimal dissipation hybrid bicompact schemes for hyperbolic equations

    NASA Astrophysics Data System (ADS)

    Bragin, M. D.; Rogov, B. V.

    2016-06-01

    New monotonicity-preserving hybrid schemes are proposed for multidimensional hyperbolic equations. They are convex combinations of high-order accurate central bicompact schemes and upwind schemes of first-order accuracy in time and space. The weighting coefficients in these combinations depend on the local difference between the solutions produced by the high- and low-order accurate schemes at the current space-time point. The bicompact schemes are third-order accurate in time, while having the fourth order of accuracy and the first difference order in space. At every time level, they can be solved by marching in each spatial variable without using spatial splitting. The upwind schemes have minimal dissipation among all monotone schemes constructed on a minimum space-time stencil. The hybrid schemes constructed has been successfully tested as applied to a number of two-dimensional gas dynamics benchmark problems.

  10. Compact high order schemes for the Euler equations

    NASA Technical Reports Server (NTRS)

    Abarbanel, Saul; Kumar, Ajay

    1988-01-01

    An implicit approximate factorization (AF) algorithm is constructed which has the following characteistics. In 2-D: The scheme is unconditionally stable, has a 3 x 3 stencil and at steady state has a fourth order spatial accuracy. The temporal evolution is time accurate either to first or second order through choice of parameter. In 3-D: The scheme has almost the same properties as in 2-D except that it is now only conditionally stable, with the stability condition (the CFL number) being dependent on the cell aspect ratios, delta y/delta x and delta z/delta x. The stencil is still compact and fourth order accuracy at steady state is maintained. Numerical experiments on a 2-D shock-reflection problem show the expected improvement over lower order schemes, not only in accuracy (measured by the L sub 2 error) but also in the dispersion. It is also shown how the same technique is immediately extendable to Runge-Kutta type schemes resulting in improved stability in addition to the enhanced accuracy.

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

    NASA Astrophysics Data System (ADS)

    Cui, Xia; Yuan, Guang-wei; Shen, Zhi-jun

    2016-05-01

    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-order 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.

  12. Direct Eulerian MUSCL scheme for gas dynamics

    SciTech Connect

    Colella, P.

    1985-01-01

    The authors present a second order extension of Godunov's method for gas dynamics in Eulerian coordinates patterned after van Leer's MUSCL scheme for gas dynamics in Lagrangian coordinates. The present method performs the Eulerian calculation in a single step by solving Riemann problems and characteristic equations for the fluxes in the Eulerian frame. The authors also make several modifications in the formulation of MUSCL, applicable to both this scheme and to the original Lagrangian scheme, all aimed at making a more robust and accurate scheme. The authors present the results of test calculations in one and two space variables. 12 references, 5 figures.

  13. High-Order Energy Stable WENO Schemes

    NASA Technical Reports Server (NTRS)

    Yamaleev, Nail K.; Carpenter, Mark H.

    2008-01-01

    A new third-order Energy Stable Weighted Essentially NonOscillatory (ESWENO) finite difference scheme for scalar and vector linear hyperbolic equations with piecewise continuous initial conditions is developed. The new scheme is proven to be stable in the energy norm for both continuous and discontinuous solutions. In contrast to the existing high-resolution shock-capturing schemes, no assumption that the reconstruction should be total variation bounded (TVB) is explicitly required to prove stability of the new scheme. A rigorous truncation error analysis is presented showing that the accuracy of the 3rd-order ESWENO scheme is drastically improved if the tuning parameters of the weight functions satisfy certain criteria. Numerical results show that the new ESWENO scheme is stable and significantly outperforms the conventional third-order WENO finite difference scheme of Jiang and Shu in terms of accuracy, while providing essentially nonoscillatory solutions near strong discontinuities.

  14. High resolution TVD schemes for interface tracking

    NASA Astrophysics Data System (ADS)

    Nandi, K.; Walker, S. P.; Date, A. W.

    2016-06-01

    A first order upwind difference scheme (UDS) is routinely adopted for representing convection terms in a discretised space. UDS provides stable solutions. However it also introduces false diffusion in situations in which the flow direction is oblique relative to the numerical grid or when the cell-Peclet number is large. In order to predict sharp interface, higher order upwind schemes are preferred because of they reduce numerical dissipation. In interfacial flows, density and viscosity vary sharply in space. Representation of convective terms by Total variation diminishing (TVD) schemes ensures reduced smearing without impairing convergence property. TVD schemes develop formulae for interpolation of a cell-face value of the transported variable. If the interpolated value is bounded by the neighbouring nodal values then the scheme is `Bounded'. However, not all TVD schemes possess this property of `Boundedness'. The Normalised Variable Diagram (NVD) defines a domain within which the TVD scheme is bounded. Thus by combining the features of both TVD schemes and ensuring that they fall with the defined area of NVD, the convergence as well as the boundedness of a computational scheme can be ensured. In this paper, six different higher order schemes are considered some which are TVD bounded or unbounded, to solve the well known interface tracking problem of Rayleigh-Taylor Instability. To the best of our knowledge, a comparison of combined TVD/NVD principles in the case of interface tracking problems has not been reported in published literature.

  15. Comparison of SMAC, PISO, and iterative time-advancing schemes for unsteady flows

    NASA Technical Reports Server (NTRS)

    Kim, Sang-Wook; Benson, Thomas J.

    1991-01-01

    Calculations of unsteady flows using a simplified marker and cell (SMAC), a pressure implicit splitting of operators (PSIO), and an iterative time advancing scheme (ITA) are presented. A partial differential equation for incremental pressure is used in each time advancing scheme. Example flows considered are a polar cavity flow starting from rest and self-sustained oscillating flows over a circular and a square cylinder. For a large time step size, the SMAC and ITA are more strongly convergent and yield more accurate results than PSIO. The SMAC is the most efficient computationally. For a small time step size, the three time advancing schemes yield equally accurate Strouhal numbers. The capability of each time advancing scheme to accurately resolve unsteady flows is attributed to the use of new pressure correction algorithm that can strongly enforce the conservation of mass. The numerical results show that the low frequency of the vortex shedding is caused by the growth time of each vortex shed into the wake region.

  16. Comparison of the tangent linear properties of tracer transport schemes applied to geophysical problems

    NASA Astrophysics Data System (ADS)

    Kent, James; Holdaway, Daniel

    2015-04-01

    Data assimilation is one of the most common inverse problems encountered in geophysical models. One of the leading techniques used for data assimilation in numerical weather prediction is four dimensional variational data assimilation (4DVAR). In 4DVAR the tangent linear and adjoint versions of the nonlinear model are used to perform a minimization with time dependent observations. In order for the minimization to perform well requires a certain degree of linearity in both the underlying equations and numerical methods used to solve them. Advection is central to the underlying equations used for numerical weather prediction, as well as many other geophysical models. From the advection of momentum, temperature and moisture to passive tracers such as smoke from wildfires, accurate transport is paramount. Over recent decades much effort has been directed toward the development of positive definite, non-oscillatory, mass conserving advection schemes. These schemes are capable of giving excellent representation of transport, but by definition introduce nonlinearity into equations that are otherwise quite linear. One such example is the flux limited piecewise parabolic method (PPM) used in NASA's Goddard Earth Observing System version 5 (GEOS-5), which can perform very poorly when linearized. With a view to an optimal representation of transport in the linear versions of atmospheric models and 4DVAR we analyse the performance of a number of different linear and nonlinear advection schemes. The schemes are analysed using a one dimensional case study, a passive tracer in GEOS-5 experiment and using the full linearized version of GEOS-5. Using the three studies it is shown that higher order linear schemes provide the best representation of the transport of perturbations and sensitivities. In certain situations the nonlinear schemes give the best performance but are subject to issues. It is also shown that many of the desirable properties of the nonlinear schemes are

  17. Dissipative issue of high-order shock capturing schemes with non-convex equations of state

    NASA Astrophysics Data System (ADS)

    Heuzé, Olivier; Jaouen, Stéphane; Jourdren, Hervé

    2009-02-01

    It is well known that, closed with a non-convex equation of state (EOS), the Riemann problem for the Euler equations allows non-standard waves, such as split shocks, sonic isentropic compressions or rarefaction shocks, to occur. Loss of convexity then leads to non-uniqueness of entropic or Lax solutions, which can only be resolved via the Liu-Oleinik criterion (equivalent to the existence of viscous profiles for all admissible shock waves). This suggests that in order to capture the physical solution, a numerical scheme must provide an appropriate level of dissipation. A legitimate question then concerns the ability of high-order shock capturing schemes to naturally select such a solution. To investigate this question and evaluate modern as well as future high-order numerical schemes, there is therefore a crucial need for well-documented benchmarks. A thermodynamically consistent C∞ non-convex EOS that can be easily introduced in Eulerian as well as Lagrangian hydrocodes for test purposes is here proposed, along with a reference solution for an initial value problem exhibiting a complex composite wave pattern (the Bizarrium test problem). Two standard Lagrangian numerical approaches, both based on a finite volume method, are then reviewed (vNR and Godunov-type schemes) and evaluated on this Riemann problem. In particular, a complete description of several state-of-the-art high-order Godunov-type schemes applicable to general EOSs is provided. We show that this particular test problem reveals quite severe when working on high-order schemes, and recommend it as a benchmark for devising new limiters and/or next-generation highly accurate schemes.

  18. High-resolution shock-capturing schemes for inviscid and viscous hypersonic flows

    NASA Technical Reports Server (NTRS)

    Yee, H. C.; Klopfer, G. H.; Montagne, J.-L.

    1988-01-01

    A class of implicit Total Variation Diminishing (TVD) type algorithms suitable for transonic and supersonic multidimensional Euler and Navier-Stokes equations was extended to hypersonic computations. The improved conservative shock-capturing schemes are spatially second- and third-order, and are fully implicit. They can be first- or second-order accurate in time and are suitable for either steady or unsteady calculations. Enhancement of stability and convergence rate for hypersonic flows is discussed. With the proper choice of the temporal discretization and suitable implicit linearization, these schemes are fairly efficient and accurate for very complex two-dimensional hypersonic inviscid and viscous shock interactions. This study is complimented by a variety of steady and unsteady viscous and inviscid hypersonic blunt-body flow computations. Due to the inherent stiffness of viscous flow problems, numerical experiments indicated that the convergence rate is in general slower for viscous flows than for inviscid steady flows.

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

    SciTech Connect

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

    1995-08-01

    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 been 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.

  20. Supercomputing of supersonic flows using upwind relaxation and MacCormack schemes

    NASA Technical Reports Server (NTRS)

    Baysal, O.

    1987-01-01

    The performance of two numerical solution schemes, (1) an implicit upwind relaxation with a finite-volume discretization (Thomas and Walters, 1985) and (2) an explicit-implicit MacCormack (1981) scheme with a finite-difference discretization, is compared in two-dimensional simulations of supersonic flow past a flat plate with leading edge, a rearward-facing step, a 10-deg compression corner, a NACA 0012 airfoil at high angle of attack, and a cavity. The algebraic turbulence model, the solution methods, and the boundary conditions and SIMD coding are explained, and the results are presented in tables and graphs and characterized with reference to published experimental data. Scheme (1) is found to converge more rapidly and to give more accurate results than (2) in a wide range of problem types.

  1. Accurate deterministic solutions for the classic Boltzmann shock profile

    NASA Astrophysics Data System (ADS)

    Yue, Yubei

    The Boltzmann equation or Boltzmann transport equation is a classical kinetic equation devised by Ludwig Boltzmann in 1872. It is regarded as a fundamental law in rarefied gas dynamics. Rather than using macroscopic quantities such as density, temperature, and pressure to describe the underlying physics, the Boltzmann equation uses a distribution function in phase space to describe the physical system, and all the macroscopic quantities are weighted averages of the distribution function. The information contained in the Boltzmann equation is surprisingly rich, and the Euler and Navier-Stokes equations of fluid dynamics can be derived from it using series expansions. Moreover, the Boltzmann equation can reach regimes far from the capabilities of fluid dynamical equations, such as the realm of rarefied gases---the topic of this thesis. Although the Boltzmann equation is very powerful, it is extremely difficult to solve in most situations. Thus the only hope is to solve it numerically. But soon one finds that even a numerical simulation of the equation is extremely difficult, due to both the complex and high-dimensional integral in the collision operator, and the hyperbolic phase-space advection terms. For this reason, until few years ago most numerical simulations had to rely on Monte Carlo techniques. In this thesis I will present a new and robust numerical scheme to compute direct deterministic solutions of the Boltzmann equation, and I will use it to explore some classical gas-dynamical problems. In particular, I will study in detail one of the most famous and intrinsically nonlinear problems in rarefied gas dynamics, namely the accurate determination of the Boltzmann shock profile for a gas of hard spheres.

  2. Numerical simulation of flows from free molecular regime to continuum regime by a DVM with streaming and collision processes

    NASA Astrophysics Data System (ADS)

    Yang, L. M.; Shu, C.; Wu, J.; Wang, Y.

    2016-02-01

    A discrete velocity method (DVM) with streaming and collision processes is presented in this work for simulation of flows from free molecular regime to continuum regime. The present scheme can be considered as a semi-Lagrangian like scheme. At first, we follow the conventional DVM to discretize the phase velocity space by a number of discrete velocities. Then, for each discrete velocity, the kinetic equation with BGK-Shakhov model is integrated in space and time within one time step. As a result, a simple algebraic formulation can be obtained, and its solution can be marched in time by the streaming and collision processes. However, differently from the conventional semi-Lagrangian scheme, the present scheme uses the MUSCL approach with van Albada limiter in the process of reconstructing the distribution function at the surrounding points of the cell center, and the transport distance is controlled in order to avoid extrapolation. This makes the present scheme be capable of simulating the hypersonic rarefied flows. In addition, as compared to the unified gas kinetic scheme (UGKS), the present scheme is simpler and easier for implementation. Thus, the computational efficiency can be improved accordingly. To validate the proposed numerical scheme, test examples from free molecular regime to continuum regime are simulated. Numerical results showed that the present scheme can predict the flow properties accurately even for hypersonic rarefied flows.

  3. A classification scheme for chimera states

    NASA Astrophysics Data System (ADS)

    Kemeth, Felix P.; Haugland, Sindre W.; Schmidt, Lennart; Kevrekidis, Ioannis G.; Krischer, Katharina

    2016-09-01

    We present a universal characterization scheme for chimera states applicable to both numerical and experimental data sets. The scheme is based on two correlation measures that enable a meaningful definition of chimera states as well as their classification into three categories: stationary, turbulent, and breathing. In addition, these categories can be further subdivided according to the time-stationarity of these two measures. We demonstrate that this approach is both consistent with previously recognized chimera states and enables us to classify states as chimeras which have not been categorized as such before. Furthermore, the scheme allows for a qualitative and quantitative comparison of experimental chimeras with chimeras obtained through numerical simulations.

  4. An accurate parameterization of the infrared radiative properties of cirrus clouds for climate models

    SciTech Connect

    Fu, Q.; Sun, W.B.; Yang, P.

    1998-09-01

    An accurate parameterization is presented for the infrared radiative properties of cirrus clouds. For the single-scattering calculations, a composite scheme is developed for randomly oriented hexagonal ice crystals by comparing results from Mie theory, anomalous diffraction theory (ADT), the geometric optics method (GOM), and the finite-difference time domain technique. This scheme employs a linear combination of single-scattering properties from the Mie theory, ADT, and GOM, which is accurate for a wide range of size parameters. Following the approach of Q. Fu, the extinction coefficient, absorption coefficient, and asymmetry factor are parameterized as functions of the cloud ice water content and generalized effective size (D{sub ge}). The present parameterization of the single-scattering properties of cirrus clouds is validated by examining the bulk radiative properties for a wide range of atmospheric conditions. Compared with reference results, the typical relative error in emissivity due to the parameterization is {approximately}2.2%. The accuracy of this parameterization guarantees its reliability in applications to climate models. The present parameterization complements the scheme for the solar radiative properties of cirrus clouds developed by Q. Fu for use in numerical models.

  5. An Accurate Parameterization of the Infrared Radiative Properties of Cirrus Clouds for Climate Models.

    NASA Astrophysics Data System (ADS)

    Fu, Qiang; Yang, Ping; Sun, W. B.

    1998-09-01

    An accurate parameterization is presented for the infrared radiative properties of cirrus clouds. For the single-scattering calculations, a composite scheme is developed for randomly oriented hexagonal ice crystals by comparing results from Mie theory, anomalous diffraction theory (ADT), the geometric optics method (GOM), and the finite-difference time domain technique. This scheme employs a linear combination of single-scattering properties from the Mie theory, ADT, and GOM, which is accurate for a wide range of size parameters. Following the approach of Q. Fu, the extinction coefficient, absorption coefficient, and asymmetry factor are parameterized as functions of the cloud ice water content and generalized effective size (Dge). The present parameterization of the single-scattering properties of cirrus clouds is validated by examining the bulk radiative properties for a wide range of atmospheric conditions. Compared with reference results, the typical relative error in emissivity due to the parameterization is 2.2%. The accuracy of this parameterization guarantees its reliability in applications to climate models. The present parameterization complements the scheme for the solar radiative properties of cirrus clouds developed by Q. Fu for use in numerical models.

  6. Accurate monotone cubic interpolation

    NASA Technical Reports Server (NTRS)

    Huynh, Hung T.

    1991-01-01

    Monotone piecewise cubic interpolants are simple and effective. They are generally third-order accurate, except near strict local extrema where accuracy degenerates to second-order due to the monotonicity constraint. Algorithms for piecewise cubic interpolants, which preserve monotonicity as well as uniform third and fourth-order accuracy are presented. The gain of accuracy is obtained by relaxing the monotonicity constraint in a geometric framework in which the median function plays a crucial role.

  7. Accurate Finite Difference Algorithms

    NASA Technical Reports Server (NTRS)

    Goodrich, John W.

    1996-01-01

    Two families of finite difference algorithms for computational aeroacoustics are presented and compared. All of the algorithms are single step explicit methods, they have the same order of accuracy in both space and time, with examples up to eleventh order, and they have multidimensional extensions. One of the algorithm families has spectral like high resolution. Propagation with high order and high resolution algorithms can produce accurate results after O(10(exp 6)) periods of propagation with eight grid points per wavelength.

  8. A higher-order implicit IDO scheme and its CFD application to local mesh refinement method

    NASA Astrophysics Data System (ADS)

    Imai, Yohsuke; Aoki, Takayuki

    2006-08-01

    The Interpolated Differential Operator (IDO) scheme has been developed for the numerical solution of the fluid motion equations, and allows to produce highly accurate results by introducing the spatial derivative of the physical value as an additional dependent variable. For incompressible flows, semi-implicit time integration is strongly affected by the Courant and diffusion number limitation. A high-order fully-implicit IDO scheme is presented, and the two-stage implicit Runge-Kutta time integration keeps over third-order accuracy. The application of the method to the direct numerical simulation of turbulence demonstrates that the proposed scheme retains a resolution comparable to that of spectral methods even for relatively large Courant numbers. The scheme is further applied to the Local Mesh Refinement (LMR) method, where the size of the time step is often restricted by the dimension of the smallest meshes. In the computation of the Karman vortex street problem, the implicit IDO scheme with LMR is shown to allow a conspicuous saving of computational resources.

  9. Aspects of a high-resolution scheme for the Navier-Stokes equations

    NASA Technical Reports Server (NTRS)

    Swanson, R. C.; Turkel, E.

    1993-01-01

    In this paper we emphasize the importance of the form of the numerical dissipation model in computing accurate viscous flow solutions. A high-resolution scheme for viscous flows based on three-point central differencing and a matrix dissipation is considered. The various components of this scheme, including 'entropy fix', limiter function, and boundary-point dissipation are discussed. By analyzing boundary-point dissipation stencils, we confirm that with the matrix dissipation model the normal numerical dissipation terms in the streamwise momentum equation are independent of the Reynolds number. Such independence is not achieved with a scalar dissipation form. The accuracy of the central-difference scheme, with and without matrix dissipation, and the flux-difference split scheme of Roe, which is classified as a high-resolution scheme, is compared. For this comparison, three high Reynolds number laminar flows are considered. Solutions of the Navier-Stokes equations are obtained for low-speed flow over a flat plate, transonic flow over an airfoil with transition near the leading edge, and hypersonic flow over a compression ramp. The emphasis of the comparison is primarily on the details of the viscous flows. The necessity of the high-resolution property is revealed.

  10. 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.

  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. On Tenth Order Central Spatial Schemes

    SciTech Connect

    Sjogreen, B; Yee, H C

    2007-05-14

    This paper explores the performance of the tenth-order central spatial scheme and derives the accompanying energy-norm stable summation-by-parts (SBP) boundary operators. The objective is to employ the resulting tenth-order spatial differencing with the stable SBP boundary operators as a base scheme in the framework of adaptive numerical dissipation control in high order multistep filter schemes of Yee et al. (1999), Yee and Sj{umlt o}green (2002, 2005, 2006, 2007), and Sj{umlt o}green and Yee (2004). These schemes were designed for multiscale turbulence flows including strong shock waves and combustion.

  13. 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.

  14. A generalized procedure for constructing an upwind-based TVD scheme

    NASA Technical Reports Server (NTRS)

    Liou, Meng-Sing

    1987-01-01

    A generalized formulation for constructing second- and higher-order accurate TVD (total variation diminishing) schemes is presented. A given scheme is made TVD by limiting antidiffusive flux differences with some nonlinear functions, so-called limiters. The general idea of the formulation and its mathematical proof of Harten's TVD conditions is shown by applying the Lax-Wendroff method to a scalar nonlinear equation and constant-coefficient system of conservation laws. For the system of equations, several definitions are derived for the argument used in the limiter function and present their performance to numerical experiments. Then the formulation is formally extended to the nonlinear system of equations. It is demonstrated that use of the present procedure allows easy conversion of existing central or upwind, and second- or higher-order differencing schemes so as to preserve monotonicity and to yield physically admissible solutions. The formulation is simple mathematically as well as numerically; neither matrix-vector multiplication nor Riemann solver is required. Roughly twice as much computational effort is needed as compared to conventional scheme. Although the notion of TVD is based on the initial value problem, application to the steady Euler equations of the formulation is also made. Numerical examples including various ranges of problems show both time- and spatial-accuracy in comparison with exact solutions.

  15. 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

  16. Asynchronous and corrected-asynchronous numerical solutions of parabolic PDES on MIMD multiprocessors

    NASA Technical Reports Server (NTRS)

    Amitai, Dganit; Averbuch, Amir; Itzikowitz, Samuel; Turkel, Eli

    1991-01-01

    A major problem in achieving significant speed-up on parallel machines is the overhead involved with synchronizing the concurrent process. Removing the synchronization constraint has the potential of speeding up the computation. The authors present asynchronous (AS) and corrected-asynchronous (CA) finite difference schemes for the multi-dimensional heat equation. Although the discussion concentrates on the Euler scheme for the solution of the heat equation, it has the potential for being extended to other schemes and other parabolic partial differential equations (PDEs). These schemes are analyzed and implemented on the shared memory multi-user Sequent Balance machine. Numerical results for one and two dimensional problems are presented. It is shown experimentally that the synchronization penalty can be about 50 percent of run time: in most cases, the asynchronous scheme runs twice as fast as the parallel synchronous scheme. In general, the efficiency of the parallel schemes increases with processor load, with the time level, and with the problem dimension. The efficiency of the AS may reach 90 percent and over, but it provides accurate results only for steady-state values. The CA, on the other hand, is less efficient, but provides more accurate results for intermediate (non steady-state) values.

  17. Numerical experiments for advection equation

    SciTech Connect

    Sun, Wen-Yih )

    1993-10-01

    We propose to combine the Crowley fourth-order scheme and the Gadd scheme for solving the linear advection equation. Two new schemes will be presented: the first is to integrate the Crowley scheme and the Gadd scheme alternately (referred to as New1); the second is to integrate the Crowley scheme twice before we apply the Gadd scheme once (referred to as New2). The new schemes are designed such that no additional restriction is placed on the CFL criterion in an integration. The performance of the new schemes is better than that of the original Crowley or Gadd schemes. It is noted that the amplitude obtained from New2 is more accurate than that from New1 for long waves, but less accurate for short waves. The phase speed calculated from New2 is very close to the real phase speed in most cases tested here, but the phase speed of New 1 is faster than the real phase speed. Hence, New2 is a better choice, especially for a model that includes horizontal smoothing to dampen the short waves. 9 refs., 5 figs., 8 tabs.

  18. 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

  19. Implicit - symplectic partitioned (IMSP) Runge-Kutta schemes for predator-prey dynamics

    NASA Astrophysics Data System (ADS)

    Diele, F.; Marangi, C.; Ragni, S.

    2012-09-01

    In the study of the effects of habitat fragmentation on biodiversity the role of spatial processes reveals of great interest since both the variation of size of the domains as well as their heterogeneity largely affects the dynamics of species. In order to begin a preliminary study about the effects of habitat fragmentation on wolf - wild boar pair populating the Italian "Alta Murgia" Natura 2000 site, object of interest for FP7 project BIOSOS, (BIOdiversity multi-SOurce Monitoring System: from Space TO Species), spatially explicit models described by reaction-diffusion partial differential equations are considered. Numerical methods based on partitioned Runge-Kutta schemes which use an implicit scheme for the stiff diffusive term and a partitioned symplectic scheme for the reaction function are here proposed. We are motivated by the classical results about Lotka-Volterra model described by ordinary differential equations to which the spatially explicit model reduces for diffusion coefficients tending to zero: for their accurate solution symplectic schemes have to be used for an optimal long run preservation of the dynamics invariant. Moreover, for models based on logistic growth and Holling type II functional predator response we verify the better performance of our schemes when compared with classical implicit-explicit (IMEX) schemes on chaotic dynamics given in literature.

  20. On the Dynamics of TVD Schemes

    NASA Technical Reports Server (NTRS)

    Yee, H. C.; Sweby, P. K.; Kutler, Paul (Technical Monitor)

    1994-01-01

    The dynamics of a class of TVD schemes for model hyperbolic and parabolic equations is studied numerically using a highly parallel supercomputer (CM-5). The objective is to utilize the highly parallel property of the CM-5 to reveal the reliable time step and entropy parameter ranges, and the degree of compressible flux limiters to avoid slow convergence and the production of nonphysical numerical solutions. We choose to study the nonlinear stability property of TVD schemes numerically since it is otherwise not amenable analytically.

  1. An adaptive high-order hybrid scheme for compressive, viscous flows with detailed chemistry

    NASA Astrophysics Data System (ADS)

    Ziegler, Jack L.; Deiterding, Ralf; Shepherd, Joseph E.; Pullin, D. I.

    2011-08-01

    A hybrid weighted essentially non-oscillatory (WENO)/centered-difference numerical method, with low numerical dissipation, high-order shock-capturing, and structured adaptive mesh refinement (SAMR), has been developed for the direct numerical simulation of the multicomponent, compressible, reactive Navier-Stokes equations. The method enables accurate resolution of diffusive processes within reaction zones. The approach combines time-split reactive source terms with a high-order, shock-capturing scheme specifically designed for diffusive flows. A description of the order-optimized, symmetric, finite difference, flux-based, hybrid WENO/centered-difference scheme is given, along with its implementation in a high-order SAMR framework. The implementation of new techniques for discontinuity flagging, scheme-switching, and high-order prolongation and restriction is described. In particular, the refined methodology does not require upwinded WENO at grid refinement interfaces for stability, allowing high-order prolongation and thereby eliminating a significant source of numerical diffusion within the overall code performance. A series of one-and two-dimensional test problems is used to verify the implementation, specifically the high-order accuracy of the diffusion terms. One-dimensional benchmarks include a viscous shock wave and a laminar flame. In two-space dimensions, a Lamb-Oseen vortex and an unstable diffusive detonation are considered, for which quantitative convergence is demonstrated. Further, a two-dimensional high-resolution simulation of a reactive Mach reflection phenomenon with diffusive multi-species mixing is presented.

  2. 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.

  3. Dispersion-relation-preserving schemes for computational aeroacoustics

    NASA Technical Reports Server (NTRS)

    Tam, Christopher K. W.; Webb, Jay C.

    1992-01-01

    Finite difference schemes that have the same dispersion relations as the original partial differential equations are referred to as dispersion-relation-preserving (DRP) schemes. A method to construct time marching DRP schemes by optimizing the finite difference approximations of the space and time derivatives in the wave number and frequency space is presented. A sequence of numerical simulations is then performed.

  4. Direct Arbitrary-Lagrangian-Eulerian ADER-MOOD finite volume schemes for multidimensional hyperbolic conservation laws

    NASA Astrophysics Data System (ADS)

    Boscheri, Walter; Loubère, Raphaël; Dumbser, Michael

    2015-07-01

    In this paper we present a new family of efficient high order accurate direct Arbitrary-Lagrangian-Eulerian (ALE) one-step ADER-MOOD finite volume schemes for the solution of nonlinear hyperbolic systems of conservation laws for moving unstructured triangular and tetrahedral meshes. This family is the next generation of the ALE ADER-WENO schemes presented in [16,20]. Here, we use again an element-local space-time Galerkin finite element predictor method to achieve a high order accurate one-step time discretization, while the somewhat expensive WENO approach on moving meshes, used to obtain high order of accuracy in space, is replaced by an a posteriori MOOD loop which is shown to be less expensive but still as accurate. This a posteriori MOOD loop ensures the numerical solution in each cell at any discrete time level to fulfill a set of user-defined detection criteria. If a cell average does not satisfy the detection criteria, then the solution is locally re-computed by progressively decrementing the order of the polynomial reconstruction, following a so-called cascade of predefined schemes with decreasing approximation order. A so-called parachute scheme, typically a very robust first order Godunov-type finite volume method, is employed as a last resort for highly problematic cells. The cascade of schemes defines how the decrementing process is carried out, i.e. how many schemes are tried and which orders are adopted for the polynomial reconstructions. The cascade and the parachute scheme are choices of the user or the code developer. Consequently the iterative MOOD loop allows the numerical solution to maintain some interesting properties such as positivity, mesh validity, etc., which are otherwise difficult to ensure. We have applied our new high order unstructured direct ALE ADER-MOOD schemes to the multi-dimensional Euler equations of compressible gas dynamics. A large set of test problems has been simulated and analyzed to assess the validity of our approach

  5. Accurate numerical solutions for elastic-plastic models. [LMFBR

    SciTech Connect

    Schreyer, H. L.; Kulak, R. F.; Kramer, J. M.

    1980-03-01

    The accuracy of two integration algorithms is studied for the common engineering condition of a von Mises, isotropic hardening model under plane stress. Errors in stress predictions for given total strain increments are expressed with contour plots of two parameters: an angle in the pi plane and the difference between the exact and computed yield-surface radii. The two methods are the tangent-predictor/radial-return approach and the elastic-predictor/radial-corrector algorithm originally developed by Mendelson. The accuracy of a combined tangent-predictor/radial-corrector algorithm is also investigated.

  6. Study of longwave radiative transfer in stratocumulus clouds by using bin optical properties and bin microphysics scheme

    NASA Astrophysics Data System (ADS)

    Lábó, E.; Geresdi, I.

    2016-01-01

    Infrared radiative cooling at the cloud top is the major driving force for stratocumulus-topped boundary layer turbulence and the major source of buoyancy within a convective mixed layer. However, there is still large uncertainty about the rate of longwave cooling at the cloud top in recent numerical models. Radiative transfer calculations within stratocumulus clouds can be further improved by using bin scheme in the calculation of longwave extinction coefficients. A method to calculate bin optical properties was developed and was implemented in the RRTM LW radiative transfer model. This bin-type radiation scheme allows us more accurate calculation of the optical properties of clouds, because it does not need any arbitrary assumption for the size distribution of the hydrometeors. The number concentrations and mixing ratios in 36 size-bins provided by bin microphysical scheme are used for calculation of the extinction coefficient. In this paper results of this new scheme were compared to that of one-moment and two-moment bulk radiation schemes where the size distributions were supposed to follow a gamma-function. It was found that the application of the two-moment bulk scheme had no advantage against the one-moment bulk scheme in simulation of radiation profiles, if radiation feedback on cloud processes was not taken into account. Although the gamma function used by bulk schemes fitted relatively well to the size distribution of the water drops calculated by the bin scheme, the longwave radiation fluxes calculated by the two schemes (bulk vs. bin) were significantly different. The bin radiation scheme gave at least 50% larger warming rates both at the cloud base and at the cloud top than the bulk schemes did. The cooling/warming occurred in a thinner vertical layer in the case of the bin scheme than in the case of bulk schemes. The shape of the net radiation profile strongly depended on the CCN concentration. Continental clouds were found to have horizontally less

  7. 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.

  8. Accurate quantum chemical calculations

    NASA Technical Reports Server (NTRS)

    Bauschlicher, Charles W., Jr.; Langhoff, Stephen R.; Taylor, Peter R.

    1989-01-01

    An important goal of quantum chemical calculations is to provide an understanding of chemical bonding and molecular electronic structure. A second goal, the prediction of energy differences to chemical accuracy, has been much harder to attain. First, the computational resources required to achieve such accuracy are very large, and second, it is not straightforward to demonstrate that an apparently accurate result, in terms of agreement with experiment, does not result from a cancellation of errors. Recent advances in electronic structure methodology, coupled with the power of vector supercomputers, have made it possible to solve a number of electronic structure problems exactly using the full configuration interaction (FCI) method within a subspace of the complete Hilbert space. These exact results can be used to benchmark approximate techniques that are applicable to a wider range of chemical and physical problems. The methodology of many-electron quantum chemistry is reviewed. Methods are considered in detail for performing FCI calculations. The application of FCI methods to several three-electron problems in molecular physics are discussed. A number of benchmark applications of FCI wave functions are described. Atomic basis sets and the development of improved methods for handling very large basis sets are discussed: these are then applied to a number of chemical and spectroscopic problems; to transition metals; and to problems involving potential energy surfaces. Although the experiences described give considerable grounds for optimism about the general ability to perform accurate calculations, there are several problems that have proved less tractable, at least with current computer resources, and these and possible solutions are discussed.

  9. An adaptive additive inflation scheme for Ensemble Kalman Filters

    NASA Astrophysics Data System (ADS)

    Sommer, Matthias; Janjic, Tijana

    2016-04-01

    Data assimilation for atmospheric dynamics requires an accurate estimate for the uncertainty of the forecast in order to obtain an optimal combination with available observations. This uncertainty has two components, firstly the uncertainty which originates in the the initial condition of that forecast itself and secondly the error of the numerical model used. While the former can be approximated quite successfully with an ensemble of forecasts (an additional sampling error will occur), little is known about the latter. For ensemble data assimilation, ad-hoc methods to address model error include multiplicative and additive inflation schemes, possibly also flow-dependent. The additive schemes rely on samples for the model error e.g. from short-term forecast tendencies or differences of forecasts with varying resolutions. However since these methods work in ensemble space (i.e. act directly on the ensemble perturbations) the sampling error is fixed and can be expected to affect the skill substiantially. In this contribution we show how inflation can be generalized to take into account more degrees of freedom and what improvements for future operational ensemble data assimilation can be expected from this, also in comparison with other inflation schemes.

  10. Asymptotically Correct Finite Difference Schemes for Highly Oscillatory ODEs

    SciTech Connect

    Arnold, Anton; Geier, Jens

    2010-09-30

    We are concerned with the numerical integration of ODE-initial value problems of the form {epsilon}{sup 2{phi}}{sub xx}+a(x){phi} = 0 with given a(x){>=}a{sub 0}>0 in the highly oscillatory regime 0<{epsilon}(appearing as a stationary Schroedinger equation, e.g.). In two steps we derive an accurate finite difference scheme that does not need to resolve each oscillation: With a WKB-ansatz the dominant oscillations are ''transformed out'', yielding a much smoother ODE. For the resulting oscillatory integrals we devise an asymptotic expansion both in {epsilon} and h. The resulting scheme typically has a step size restriction of h = o({radical}({epsilon})). If the phase of the WKB-transformation can be computed explicitly, then the scheme is asymptotically correct with an error bound of the order o({epsilon}{sup 3}h{sup 2}). As an application we present simulations of a 1D-model for ballistic quantum transport in a MOSFET (metal oxide semiconductor field-effect transistor).

  11. Soil Moisture Prediction in the Soil, Vegetation and Snow (SVS) Scheme

    NASA Astrophysics Data System (ADS)

    Alavi, Nasim; Bélair, Stéphane; Fortin, Vincent; Zhang, Shunli; Husain, Syed; Carrera, Marco; Abrahamowicz, Maria

    2016-04-01

    A new land surface scheme has been developed at Environment of Canada to provide surface fluxes of momentum, heat and moisture for the Global Environmental Multiscale (GEM) atmospheric model. In this study, the performance of the soil, vegetation and snow (SVS) scheme in estimating surface and root-zone soil moisture is evaluated against the ISBA (Interactions between Surface, Biosphere, and Atmosphere) scheme currently used operationally within GEM for numerical weather prediction. In addition, the sensitivity of SVS soil moisture results to soil texture and vegetation data sources (type and fractional coverage) has been explored. The performance of SVS and ISBA was assessed against a large set of in situ as well as brightness temperature data from the Soil Moisture and Ocean Salinity (SMOS) satellite over North America. The results indicate that SVS estimates the time evolution of soil moisture more accurately, and compared to ISBA results in higher correlations with observations and reduced errors. The sensitivity tests carried out during this study revealed that SVS soil moisture results are not affected significantly by the soil texture data from different sources. The vegetation data source, however, has a major impact on the soil moisture results predicted by SVS, and accurate specification of vegetation characteristics is crucial for accurate soil moisture prediction.

  12. 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.

  13. Stabilized second-order convex splitting schemes for Cahn-Hilliard models with application to diffuse-interface tumor-growth models.

    PubMed

    Wu, X; van Zwieten, G J; van der Zee, K G

    2014-02-01

    We present unconditionally energy-stable second-order time-accurate schemes for diffuse-interface (phase-field) models; in particular, we consider the Cahn-Hilliard equation and a diffuse-interface tumor-growth system consisting of a reactive Cahn-Hilliard equation and a reaction-diffusion equation. The schemes are of the Crank-Nicolson type with a new convex-concave splitting of the free energy and an artificial-diffusivity stabilization. The case of nonconstant mobility is treated using extrapolation. For the tumor-growth system, a semi-implicit treatment of the reactive terms and additional stabilization are discussed. For suitable free energies, all schemes are linear. We present numerical examples that verify the second-order accuracy, unconditional energy-stability, and superiority compared with their first-order accurate variants. PMID:24023005

  14. Accurate Optical Reference Catalogs

    NASA Astrophysics Data System (ADS)

    Zacharias, N.

    2006-08-01

    Current and near future all-sky astrometric catalogs on the ICRF are reviewed with the emphasis on reference star data at optical wavelengths for user applications. The standard error of a Hipparcos Catalogue star position is now about 15 mas per coordinate. For the Tycho-2 data it is typically 20 to 100 mas, depending on magnitude. The USNO CCD Astrograph Catalog (UCAC) observing program was completed in 2004 and reductions toward the final UCAC3 release are in progress. This all-sky reference catalogue will have positional errors of 15 to 70 mas for stars in the 10 to 16 mag range, with a high degree of completeness. Proper motions for the about 60 million UCAC stars will be derived by combining UCAC astrometry with available early epoch data, including yet unpublished scans of the complete set of AGK2, Hamburg Zone astrograph and USNO Black Birch programs. Accurate positional and proper motion data are combined in the Naval Observatory Merged Astrometric Dataset (NOMAD) which includes Hipparcos, Tycho-2, UCAC2, USNO-B1, NPM+SPM plate scan data for astrometry, and is supplemented by multi-band optical photometry as well as 2MASS near infrared photometry. The Milli-Arcsecond Pathfinder Survey (MAPS) mission is currently being planned at USNO. This is a micro-satellite to obtain 1 mas positions, parallaxes, and 1 mas/yr proper motions for all bright stars down to about 15th magnitude. This program will be supplemented by a ground-based program to reach 18th magnitude on the 5 mas level.

  15. High order asymptotic preserving nodal discontinuous Galerkin IMEX schemes for the BGK equation

    NASA Astrophysics Data System (ADS)

    Xiong, Tao; Jang, Juhi; Li, Fengyan; Qiu, Jing-Mei

    2015-03-01

    In this paper, we develop high-order asymptotic preserving (AP) schemes for the BGK equation in a hyperbolic scaling, which leads to the macroscopic models such as the Euler and compressible Navier-Stokes equations in the asymptotic limit. Our approaches are based on the so-called micro-macro formulation of the kinetic equation which involves a natural decomposition of the problem to the equilibrium and the non-equilibrium parts. The proposed methods are formulated for the BGK equation with constant or spatially variant Knudsen number. The new ingredients for the proposed methods to achieve high order accuracy are the following: we introduce discontinuous Galerkin (DG) discretization of arbitrary order of accuracy with nodal Lagrangian basis functions in space; we employ a high order globally stiffly accurate implicit-explicit (IMEX) Runge-Kutta (RK) scheme as time discretization. Two versions of the schemes are proposed: Scheme I is a direct formulation based on the micro-macro decomposition of the BGK equation, while Scheme II, motivated by the asymptotic analysis for the continuous problem, utilizes certain properties of the projection operator. Compared with Scheme I, Scheme II not only has better computational efficiency (the computational cost is reduced by half roughly), but also allows the establishment of a formal asymptotic analysis. Specifically, it is demonstrated that when 0 < ε ≪ 1, Scheme II, up to O (ε2), becomes a local DG discretization with an explicit RK method for the macroscopic compressible Navier-Stokes equations, a method in a similar spirit to the ones in Bassi and Rebay (1997) [3], Cockburn and Shu (1998) [16]. Numerical results are presented for a wide range of Knudsen number to illustrate the effectiveness and high order accuracy of the methods.

  16. 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. PMID:27078488

  17. High order accurate solutions of viscous problems

    NASA Technical Reports Server (NTRS)

    Hayder, M. E.; Turkel, Eli

    1993-01-01

    We consider a fourth order extension to MacCormack's scheme. The original extension was fourth order only for the inviscid terms but was second order for the viscous terms. We show how to modify the viscous terms so that the scheme is uniformly fourth order in the spatial derivatives. Applications are given to some boundary layer flows. In addition, for applications to shear flows the effect of the outflow boundary conditions are very important. We compare the accuracy of several of these different boundary conditions for both boundary layer and shear flows. Stretching at the outflow usually increases the oscillations in the numerical solution but the addition of a filtered sponge layer (with or without stretching) reduces such oscillations. The oscillations are generated by insufficient resolution of the shear layer. When the shear layer is sufficiently resolved then oscillations are not generated and there is less of a need for a nonreflecting boundary condition.

  18. A comparison of ENO and TVD schemes

    NASA Technical Reports Server (NTRS)

    Chang, Shih-Hung; Liou, Meng-Sing

    1988-01-01

    The numerical performance of a second-order upwind-based TVD scheme is compared with that of a uniform second-order ENO scheme on shock capturing. The cases considered include flows with Mach numbers of 2.9, 5.0, and 10.0. For cases with Mach numbers of 5.0 and 10.0, the computed ENO results are inferior to the corresponding TVD results.

  19. Dynamic Restarting Schemes for Eigenvalue Problems

    SciTech Connect

    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.

  20. Numerical solution of under-resolved detonations

    NASA Astrophysics Data System (ADS)

    Tosatto, Luca; Vigevano, Luigi

    2008-02-01

    A new fractional-step method is proposed for the numerical solution of high speed reacting flows, where the chemical time scales are often much smaller than the fluid dynamical time scales. When the problem is stiff, because of insufficient spatial/temporal resolution, a well-known spurious numerical phenomenon occurs in standard finite volume schemes: the incorrect calculation of the speed of propagation of discontinuities. The new method is first illustrated considering a one-dimensional scalar hyperbolic advection/reaction equation with stiff source term, which may be considered as a model problem to under-resolved detonations. During the reaction step, the proposed scheme replaces the cell average representation with a two-value reconstruction, which allows us to locate the discontinuity position inside the cell during the computation of the source term. This results in the correct propagation of discontinuities even in the stiff case. The method is proved to be second-order accurate for smooth solutions of scalar equations and is applied successfully to the solution of the one-dimensional reactive Euler equations for Chapman-Jouguet detonations.

  1. A diagonally inverted LU implicit multigrid scheme

    NASA Technical Reports Server (NTRS)

    Yokota, Jeffrey W.; Caughey, David A.; Chima, Rodrick V.

    1988-01-01

    A new Diagonally Inverted LU Implicit scheme is developed within the framework of the multigrid method for the 3-D unsteady Euler equations. The matrix systems that are to be inverted in the LU scheme are treated by local diagonalizing transformations that decouple them into systems of scalar equations. Unlike the Diagonalized ADI method, the time accuracy of the LU scheme is not reduced since the diagonalization procedure does not destroy time conservation. Even more importantly, this diagonalization significantly reduces the computational effort required to solve the LU approximation and therefore transforms it into a more efficient method of numerically solving the 3-D Euler equations.

  2. Renormalization schemes: Where do we stand

    SciTech Connect

    Ward, B.F.L.

    1989-07-01

    We consider the status of the current approaches to the application of the renormalization program to the standard SU/sub 2L/ /times/ U/sub 1/ theory from the standpoint of the interplay of the scheme chosen for such an application and the attendant high-precision tests of the respective loop effects. We thus review the available schemes and discuss their theoretical relationships. We also show how such schemes stand in numerical relation to one another in the context of high-precision Z/sup 0/ physics, as an illustration. 15 refs., 2 figs., 2 tabs.

  3. TVD finite difference schemes and artificial viscosity

    NASA Technical Reports Server (NTRS)

    Davis, S. F.

    1984-01-01

    The total variation diminishing (TVD) finite difference scheme can be interpreted as a Lax-Wendroff scheme plus an upwind weighted artificial dissipation term. If a particular flux limiter is chosen and the requirement for upwind weighting is removed, an artificial dissipation term which is based on the theory of TVD schemes is obtained which does not contain any problem dependent parameters and which can be added to existing MacCormack method codes. Numerical experiments to examine the performance of this new method are discussed.

  4. An accurate conservative level set/ghost fluid method for simulating turbulent atomization

    SciTech Connect

    Desjardins, Olivier Moureau, Vincent; Pitsch, Heinz

    2008-09-10

    This paper presents a novel methodology for simulating incompressible two-phase flows by combining an improved version of the conservative level set technique introduced in [E. Olsson, G. Kreiss, A conservative level set method for two phase flow, J. Comput. Phys. 210 (2005) 225-246] with a ghost fluid approach. By employing a hyperbolic tangent level set function that is transported and re-initialized using fully conservative numerical schemes, mass conservation issues that are known to affect level set methods are greatly reduced. In order to improve the accuracy of the conservative level set method, high order numerical schemes are used. The overall robustness of the numerical approach is increased by computing the interface normals from a signed distance function reconstructed from the hyperbolic tangent level set by a fast marching method. The convergence of the curvature calculation is ensured by using a least squares reconstruction. The ghost fluid technique provides a way of handling the interfacial forces and large density jumps associated with two-phase flows with good accuracy, while avoiding artificial spreading of the interface. Since the proposed approach relies on partial differential equations, its implementation is straightforward in all coordinate systems, and it benefits from high parallel efficiency. The robustness and efficiency of the approach is further improved by using implicit schemes for the interface transport and re-initialization equations, as well as for the momentum solver. The performance of the method is assessed through both classical level set transport tests and simple two-phase flow examples including topology changes. It is then applied to simulate turbulent atomization of a liquid Diesel jet at Re=3000. The conservation errors associated with the accurate conservative level set technique are shown to remain small even for this complex case.

  5. Integration of Full Particle Orbit in Toroidal Plasmas Using Boris Scheme

    NASA Astrophysics Data System (ADS)

    Wei, Xishuo; Xiao, Yong

    2014-10-01

    When studying particle dynamics in high frequency electromagnetic waves, such as low hybrid wave heating, it is important to integrate full particle orbit accurately to very long time in tokamaks. Here we derived a formulation under magnetic coordinate based on the Boris Scheme, which can be used effectively to push particles in long time scale. After several hundred gyro-periods, the banana orbit can be observed and the toroidal precession frequency can be measured. The toroidal precession frequency is found to match that from the guiding center simulation. This new method shows superior numeric properties than the traditional Runge-Kutta method in terms of conserving particle energy and magnetic moment.

  6. Accurate direct Eulerian simulation of dynamic elastic-plastic flow

    SciTech Connect

    Kamm, James R; Walter, John W

    2009-01-01

    The simulation of dynamic, large strain deformation is an important, difficult, and unsolved computational challenge. Existing Eulerian schemes for dynamic material response are plagued by unresolved issues. We present a new scheme for the first-order system of elasto-plasticity equations in the Eulerian frame. This system has an intrinsic constraint on the inverse deformation gradient. Standard Godunov schemes do not satisfy this constraint. The method of Flux Distributions (FD) was devised to discretely enforce such constraints for numerical schemes with cell-centered variables. We describe a Flux Distribution approach that enforces the inverse deformation gradient constraint. As this approach is new and novel, we do not yet have numerical results to validate our claims. This paper is the first installment of our program to develop this new method.

  7. An improved CE/SE scheme and its application to dilute gas-particle flows

    NASA Astrophysics Data System (ADS)

    Wang, Gang; Zhu, Huiyu; Sun, Quanhua; Zhang, Deliang; Liu, Kaixin

    2011-08-01

    An improved space-time Conservation Element and Solution Element (CE/SE) scheme is constructed by proposing a new structure of solution elements and conservation elements based on the rectangular mesh. Furthermore, the improved CE/SE scheme was applied to dilute gas-particle two-phase flows. A two-fluid model and two corresponding chemical reaction models, i.e., two-step reaction model and detailed chemical reaction model, were used to describe the physical and chemical characteristics in the two-phase flows. Shock wave reflection in gas, shock wave diffraction in air-sand mixture, explosive synthesis of TiO2 nanoparticle and air-fuel two-phase detonation were simulated by the improved CE/SE scheme and appropriate physical and chemical models. All the numerical results were compared and discussed carefully. The results show that the improved CE/SE scheme is clear in physical concept, easy to be implemented and high accurate for the above-mentioned problems. Thus, the improved CE/SE scheme can be applied to gas-particle flows widely.

  8. 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.

  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. A fast accurate approximation method with multigrid solver for two-dimensional fractional sub-diffusion equation

    NASA Astrophysics Data System (ADS)

    Lin, Xue-lei; Lu, Xin; Ng, Micheal K.; Sun, Hai-Wei

    2016-10-01

    A fast accurate approximation method with multigrid solver is proposed to solve a two-dimensional fractional sub-diffusion equation. Using the finite difference discretization of fractional time derivative, a block lower triangular Toeplitz matrix is obtained where each main diagonal block contains a two-dimensional matrix for the Laplacian operator. Our idea is to make use of the block ɛ-circulant approximation via fast Fourier transforms, so that the resulting task is to solve a block diagonal system, where each diagonal block matrix is the sum of a complex scalar times the identity matrix and a Laplacian matrix. We show that the accuracy of the approximation scheme is of O (ɛ). Because of the special diagonal block structure, we employ the multigrid method to solve the resulting linear systems. The convergence of the multigrid method is studied. Numerical examples are presented to illustrate the accuracy of the proposed approximation scheme and the efficiency of the proposed solver.

  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. 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

    2016-08-01

    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.

  13. Toward Hamiltonian Adaptive QM/MM: Accurate Solvent Structures Using Many-Body Potentials.

    PubMed

    Boereboom, Jelle M; Potestio, Raffaello; Donadio, Davide; Bulo, Rosa E

    2016-08-01

    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. PMID:27332140

  14. Compact finite difference schemes with spectral-like resolution

    NASA Technical Reports Server (NTRS)

    Lele, Sanjiva K.

    1992-01-01

    The present finite-difference schemes for the evaluation of first-order, second-order, and higher-order derivatives yield improved representation of a range of scales and may be used on nonuniform meshes. Various boundary conditions may be invoked, and both accurate interpolation and spectral-like filtering can be accomplished by means of schemes for derivatives at mid-cell locations. This family of schemes reduces to the Pade schemes when the maximal formal accuracy constraint is imposed with a specific computational stencil. Attention is given to illustrative applications of these schemes in fluid dynamics.

  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. Advanced numerics for multi-dimensional fluid flow calculations

    SciTech Connect

    Vanka, S.P.

    1984-04-01

    In recent years, there has been a growing interest in the development and use of mathematical models for the simulation of fluid flow, heat transfer and combustion processes in engineering equipment. The equations representing the multi-dimensional transport of mass, momenta and species are numerically solved by finite-difference or finite-element techniques. However despite the multiude of differencing schemes and solution algorithms, and the advancement of computing power, the calculation of multi-dimensional flows, especially three-dimensional flows, remains a mammoth task. The following discussion is concerned with the author's recent work on the construction of accurate discretization schemes for the partial derivatives, and the efficient solution of the set of nonlinear algebraic equations resulting after discretization. The present work has been jointly supported by the Ramjet Engine Division of the Wright Patterson Air Force Base, Ohio, and the NASA Lewis Research Center.

  17. Advanced numerics for multi-dimensional fluid flow calculations

    NASA Technical Reports Server (NTRS)

    Vanka, S. P.

    1984-01-01

    In recent years, there has been a growing interest in the development and use of mathematical models for the simulation of fluid flow, heat transfer and combustion processes in engineering equipment. The equations representing the multi-dimensional transport of mass, momenta and species are numerically solved by finite-difference or finite-element techniques. However despite the multiude of differencing schemes and solution algorithms, and the advancement of computing power, the calculation of multi-dimensional flows, especially three-dimensional flows, remains a mammoth task. The following discussion is concerned with the author's recent work on the construction of accurate discretization schemes for the partial derivatives, and the efficient solution of the set of nonlinear algebraic equations resulting after discretization. The present work has been jointly supported by the Ramjet Engine Division of the Wright Patterson Air Force Base, Ohio, and the NASA Lewis Research Center.

  18. A numerical method for solving the Vlasov equation

    NASA Technical Reports Server (NTRS)

    Satofuka, N.

    1982-01-01

    A numerical procedure is derived for the solution of the Vlasov-Poisson system of equations in two phase-space variables. Derivatives with respect to the phase-space variables are approximated by a weighted sum of the values of the distribution function at property chosen neighboring points. The resulting set of ordinary differential equations is then solved by using an appropriate time intergration scheme. The accuracy of the proposed method is tested with some simple model problems. The results for the free streaming case, linear Landau damping, and nonlinear Landau damping are investigated and compared with those of the splitting scheme. The proposed method is found to be very accurate and efficient.

  19. 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

  20. Nonlinear wave propagation using three different finite difference schemes (category 2 application)

    NASA Technical Reports Server (NTRS)

    Pope, D. Stuart; Hardin, J. C.

    1995-01-01

    Three common finite difference schemes are used to examine the computation of one-dimensional nonlinear wave propagation. The schemes are studied for their responses to numerical parameters such as time step selection, boundary condition implementation, and discretization of governing equations. The performance of the schemes is compared and various numerical phenomena peculiar to each is discussed.

  1. Analysis and application of high order implicit Runge-Kutta schemes for unsteady conjugate heat transfer: A strongly-coupled approach

    NASA Astrophysics Data System (ADS)

    Kazemi-Kamyab, V.; van Zuijlen, A. H.; Bijl, H.

    2014-09-01

    Thermal interaction of fluids and solids, or conjugate heat transfer (CHT), is encountered in many engineering applications. Since time-accurate computations of unsteady CHT can be computationally demanding, we consider the use of high order implicit time integration schemes which have the potential to be more efficient relative to the commonly used second order implicit schemes. We present a strongly-coupled solution algorithm where the high order L-stable explicit first-stage singly diagonally implicit Runge-Kutta (ESDIRK) schemes are used to advance the solution in time within each separate fluid and solid subdomains. Furthermore, the stability and rate of convergence of performing (Gauss-Seidel) subiterations at each stage of the ESDIRK schemes are analyzed. The results from solving a numerical example (an unsteady conjugate natural convection in an enclosure) show good agreement with the performed analytical stability analysis. In addition, the (computational) work-(temporal) precision character of several schemes in solving a strongly coupled CHT problem is compared over a range of accuracy requirements. From the efficiency investigation, it is observed that performing subiterations with the strongly-coupled ESDIRK algorithm is more efficient than lowering time-step size using a high order loosely-coupled IMEX algorithm. In addition, by using the ESDIRK schemes, gain in computational efficiency relative to Crank-Nicolson is observed for time-accurate solutions (a factor of 1.4 using the fourth order ESDIRK). The computational gain is higher for smaller tolerances.

  2. Implicit and explicit schemes for mass consistency preservation in hybrid particle/finite-volume algorithms for turbulent reactive flows

    SciTech Connect

    Popov, Pavel P. Pope, Stephen B.

    2014-01-15

    This work addresses the issue of particle mass consistency in Large Eddy Simulation/Probability Density Function (LES/PDF) methods for turbulent reactive flows. Numerical schemes for the implicit and explicit enforcement of particle mass consistency (PMC) are introduced, and their performance is examined in a representative LES/PDF application, namely the Sandia–Sydney Bluff-Body flame HM1. A new combination of interpolation schemes for velocity and scalar fields is found to better satisfy PMC than multilinear and fourth-order Lagrangian interpolation. A second-order accurate time-stepping scheme for stochastic differential equations (SDE) is found to improve PMC relative to Euler time stepping, which is the first time that a second-order scheme is found to be beneficial, when compared to a first-order scheme, in an LES/PDF application. An explicit corrective velocity scheme for PMC enforcement is introduced, and its parameters optimized to enforce a specified PMC criterion with minimal corrective velocity magnitudes.

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

    SciTech Connect

    Cheng, Juan; Shu, Chi-Wang

    2014-09-01

    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, based 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.

  4. Hybrid undulator numerical optimization

    SciTech Connect

    Hairetdinov, A.H.; Zukov, A.A.

    1995-12-31

    3D properties of the hybrid undulator scheme arc studied numerically using PANDIRA code. It is shown that there exist two well defined sets of undulator parameters which provide either maximum on-axis field amplitude or minimal higher harmonics amplitude of the basic undulator field. Thus the alternative between higher field amplitude or pure sinusoidal field exists. The behavior of the undulator field amplitude and harmonics structure for a large set of (undulator gap)/(undulator wavelength) values is demonstrated.

  5. Numerical simulations in combustion

    NASA Technical Reports Server (NTRS)

    Chung, T. J.

    1989-01-01

    This paper reviews numerical simulations in reacting flows in general and combustion phenomena in particular. It is shown that use of implicit schemes and/or adaptive mesh strategies can improve convergence, stability, and accuracy of the solution. Difficulties increase as turbulence and multidimensions are considered, particularly when finite-rate chemistry governs the given combustion problem. Particular attention is given to the areas of solid-propellant combustion dynamics, turbulent diffusion flames, and spray droplet vaporization.

  6. A stable scheme for a nonlinear, multiphase tumor growth model with an elastic membrane.

    PubMed

    Chen, Ying; Wise, Steven M; Shenoy, Vivek B; Lowengrub, John S

    2014-07-01

    In this paper, we extend the 3D multispecies diffuse-interface model of the tumor growth, which was derived in Wise et al. (Three-dimensional multispecies nonlinear tumor growth-I: model and numerical method, J. Theor. Biol. 253 (2008) 524-543), and incorporate the effect of a stiff membrane to model tumor growth in a confined microenvironment. We then develop accurate and efficient numerical methods to solve the model. When the membrane is endowed with a surface energy, the model is variational, and the numerical scheme, which involves adaptive mesh refinement and a nonlinear multigrid finite difference method, is demonstrably shown to be energy stable. Namely, in the absence of cell proliferation and death, the discrete energy is a nonincreasing function of time for any time and space steps. When a simplified model of membrane elastic energy is used, the resulting model is derived analogously to the surface energy case. However, the elastic energy model is actually nonvariational because certain coupling terms are neglected. Nevertheless, a very stable numerical scheme is developed following the strategy used in the surface energy case. 2D and 3D simulations are performed that demonstrate the accuracy of the algorithm and illustrate the shape instabilities and nonlinear effects of membrane elastic forces that may resist or enhance growth of the tumor. Compared with the standard Crank-Nicholson method, the time step can be up to 25 times larger using the new approach.

  7. A stable scheme for a nonlinear, multiphase tumor growth model with an elastic membrane

    PubMed Central

    Chen, Ying; Wise, Steven M.; Shenoy, Vivek B.; Lowengrub, John S.

    2014-01-01

    Summary In this paper, we extend the 3D multispecies diffuse-interface model of the tumor growth, which was derived in Wise et al. (Three-dimensional multispecies nonlinear tumor growth-I: model and numerical method, J. Theor. Biol. 253 (2008) 524–543), and incorporate the effect of a stiff membrane to model tumor growth in a confined microenvironment. We then develop accurate and efficient numerical methods to solve the model. When the membrane is endowed with a surface energy, the model is variational, and the numerical scheme, which involves adaptive mesh refinement and a nonlinear multigrid finite difference method, is demonstrably shown to be energy stable. Namely, in the absence of cell proliferation and death, the discrete energy is a nonincreasing function of time for any time and space steps. When a simplified model of membrane elastic energy is used, the resulting model is derived analogously to the surface energy case. However, the elastic energy model is actually nonvariational because certain coupling terms are neglected. Nevertheless, a very stable numerical scheme is developed following the strategy used in the surface energy case. 2D and 3D simulations are performed that demonstrate the accuracy of the algorithm and illustrate the shape instabilities and nonlinear effects of membrane elastic forces that may resist or enhance growth of the tumor. Compared with the standard Crank–Nicholson method, the time step can be up to 25 times larger using the new approach. PMID:24443369

  8. 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.

  9. On the monotonicity of multidimensional finite difference schemes

    NASA Astrophysics Data System (ADS)

    Kovyrkina, O.; Ostapenko, V.

    2016-10-01

    The classical concept of monotonicity, introduced by Godunov for linear one-dimensional difference schemes, is extended to multidimensional case. Necessary and sufficient conditions of monotonicity are obtained for linear multidimensional difference schemes of first order. The constraints on the numerical viscosity are given that ensure the monotonicity of a difference scheme in the multidimensional case. It is proposed a modification of the second order multidimensional CABARET scheme that preserves the monotonicity of one-dimensional discrete solutions and, as a result, ensures higher smoothness in the computation of multidimensional discontinuous solutions. The results of two-dimensional test computations illustrating the advantages of the modified CABARET scheme are presented.

  10. 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.

  11. Numerical investigation of tail buffet on F-18 aircraft

    NASA Technical Reports Server (NTRS)

    Rizk, Yehia M.; Guruswamy, Guru P.; Gee, Ken

    1992-01-01

    Numerical investigation of vortex induced tail buffet is conducted on the F-18 aircraft at high angles of attack. The Reynolds-averaged Navier-Stokes equations are integrated using a time-accurate, implicit procedure. A generalized overset zonal grid scheme is used to decompose the computational space around the complete aircraft with faired-over inlet. A weak coupling between the aerodynamics and structures is assumed to compute the structural oscillation of the flexible vertical tail. Time-accurate computations of the turbulent flow around the F-18 aircraft at 30 degrees angle of attack show the surface and off-surface flowfield details, including the unsteadiness created by the vortex burst and its interaction with the vertical twin tail which causes the tail buffet. The effect of installing a LEX fence on modifying the vortex structure upstream of the tail is also examined.

  12. Comparisons of TVD schemes applied to the Navier-Stokes equations. [total variation diminishing

    NASA Technical Reports Server (NTRS)

    Buelow, Philip E.

    1989-01-01

    In this study, the following total variation diminishing (TVD) schemes for solving the Navier-Stokes equations have been tested: the Chakravarthy and Szema (1985) upwind biased TVD scheme, the Harten's upwind TVD scheme described by Yee et al. (1983), and the Yee's (1985) symmetric TVD scheme. The schemes have been compared using three test cases. The first case was the one-dimensional shock tube problem which tested the shock-capturing abilities of the schemes. Chakravarthy's and Harten's schemes gave similar results which were found to be more accurate than the results from Yee's scheme. The second case was a compressible boundary layer which tested the schemes's abilities to solve fiscous flows. In this case, the three schemes yielded almost identical results. Finally, the shock/boundary-layer interaction case studied experimentally by Hakkinen et al. (1959) was computed. Here, Chakravarthy's and Yee's schemes compared most favorably with the published data, with Yee's scheme giving slightly better results.

  13. 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.

  14. Accurate description of argon and water adsorption on surfaces of graphene-based carbon allotropes.

    PubMed

    Kysilka, Jiří; Rubeš, Miroslav; Grajciar, Lukáš; Nachtigall, Petr; Bludský, Ota

    2011-10-20

    Accurate interaction energies of nonpolar (argon) and polar (water) adsorbates with graphene-based carbon allotropes were calculated by means of a combined density functional theory (DFT)-ab initio computational scheme. The calculated interaction energy of argon with graphite (-9.7 kJ mol(-1)) is in excellent agreement with the available experimental data. The calculated interaction energy of water with graphene and graphite is -12.8 and -14.6 kJ mol(-1), respectively. The accuracy of combined DFT-ab initio methods is discussed in detail based on a comparison with the highly precise interaction energies of argon and water with coronene obtained at the coupled-cluster CCSD(T) level extrapolated to the complete basis set (CBS) limit. A new strategy for a reliable estimate of the CBS limit is proposed for systems where numerical instabilities occur owing to basis-set near-linear dependence. The most accurate estimate of the argon and water interaction with coronene (-8.1 and -14.0 kJ mol(-1), respectively) is compared with the results of other methods used for the accurate description of weak intermolecular interactions.

  15. A nonconservative scheme for isentropic gas dynamics

    SciTech Connect

    Chen, Gui-Qiang |; Liu, Jian-Guo

    1994-05-01

    In this paper, we construct a second-order nonconservative for the system of isentropic gas dynamics to capture the physical invariant regions for preventing negative density, to treat the vacuum singularity, and to control the local entropy from dramatically increasing near shock waves. The main difference in the construction of the scheme discussed here is that we use piecewise linear functions to approximate the Riemann invariants w and z instead of the physical variables {rho} and m. Our scheme is a natural extension of the schemes for scalar conservation laws and it can be numerical implemented easily because the system is diagonalized in this coordinate system. Another advantage of using Riemann invariants is that the Hessian matrix of any weak entropy has no singularity in the Riemann invariant plane w-z, whereas the Hessian matrices of the weak entropies have singularity at the vacuum points in the physical plane p-m. We prove that this scheme converges to an entropy solution for the Cauchy problem with L{sup {infinity}} initial data. By convergence here we mean that there is a subsequent convergence to a generalized solution satisfying the entrophy condition. As long as the entropy solution is unique, the whole sequence converges to a physical solution. This shows that this kind of scheme is quite reliable from theoretical view of point. In addition to being interested in the scheme itself, we wish to provide an approach to rigorously analyze nonconservative finite difference schemes.

  16. 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.

  17. 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.

  18. An Improved Bulk Microphysical Scheme for Studying Precipitation Processes: Comparisons with Other Schemes

    NASA Technical Reports Server (NTRS)

    Tao, W. K.; Shi, J. J.; Lang, S.; Chen, S.; Hong, S-Y.; Peters-Lidard, C.

    2007-01-01

    Cloud microphysical processes play an important role in non-hydrostatic high-resolution simulations. Over the past decade both research and operational numerical weather prediction models have started using more complex cloud microphysical schemes that were originally developed for high-resolution cloud-resolving models. An improved bulk microphysical parameterization (adopted from the Goddard microphysics schemes) has recently implemented into the Weather Research and Forecasting (WRF) model. This bulk microphysical scheme has three different options --- 2ICE (cloud ice & snow), 3ICE-graupel (cloud ice, snow & graupel) and 3ICE-hail (cloud ice, snow & hail). 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 Atlantic hurricane). In addition, this bulk microphysical parameterization is compared with WIRF's three other bulk microphysical schemes.

  19. Application of Spectral Filtering scheme for Spherical Limited-Area domain to Regional forecast model

    NASA Astrophysics Data System (ADS)

    Park, J.-R.; Cheong, H.-. B.; Kang, H.-. G.

    2012-04-01

    The spectral filter for spherical limited-area domain was applied to time integration procedure of regional model as a numerical scheme to remove small scale noises, which cannot be properly resolved in numerical models. This filter is designed to provide the sharp filter response, selective scale decomposition, and the isotropy on the limited-area domain by using the filter equation with high-order spherical Laplacian operator. The high-order filter equation is solved by low-order elliptic equations with the first or the second spherical Laplacian operator. It is controlled by the order of the spherical Laplacian operator and wave cutoff scale parameter. For the application to the regional weather forecast model, the filter is reconstructed into the regional map projection, e.g., Mercator map projection. The weather research and forecasting (WRF) model is used and the spectral filter works on the vertical velocity field in which the unresolved kinematic features appear prominently. The filter parameters are set to damp the amplitude of wave component with wavelength of two times the grid interval by half in every time step. The effect of the filter on the removal of small-scale waves was evaluated through the tropical cyclone (TC) track and intensity prediction. For the accurate prediction of typhoon, the TC initialization scheme, named the structure adjustable balanced vortex (SABV) scheme, is used for all test cases. In comparison with the simulated result using the diffusion scheme provided in the model for the same purpose, the model performance was improved, especially in track prediction. The 1-day accumulated precipitation of the test simulation using the spectral filter exhibits the most similar pattern to the observation. The spectra analysis of vertical velocity field showed that the spectral filtering scheme restrains the undesirable small upturned spectral energy usually produced in limited-area models.

  20. Direct simulations of turbulent flow using finite-difference schemes

    NASA Technical Reports Server (NTRS)

    Rai, Man Mohan; Moin, Parviz

    1989-01-01

    A high-order accurate finite-difference approach is presented for calculating incompressible turbulent flow. The methods used include a kinetic energy conserving central difference scheme and an upwind difference scheme. The methods are evaluated in test cases for the evolution of small-amplitude disturbances and fully developed turbulent channel flow. It is suggested that the finite-difference approach can be applied to complex geometries more easilty than highly accurate spectral methods. It is concluded that the upwind scheme is a good candidate for direct simulations of turbulent flows over complex geometries.

  1. Boundary Variation Diminishing (BVD) reconstruction: A new approach to improve Godunov schemes

    NASA Astrophysics Data System (ADS)

    Sun, Ziyao; Inaba, Satoshi; Xiao, Feng

    2016-10-01

    This paper presents a new approach, so-called boundary variation diminishing (BVD), for reconstructions that minimize the discontinuities (jumps) at cell interfaces in Godunov type schemes. It is motivated by the observation that diminishing the jump at the cell boundary can effectively reduce the dissipation in numerical flux. Differently from the existing practices which seek high-order polynomials within mesh cells while assuming discontinuities being always at the cell interfaces, the BVD strategy presented in this paper switches between a high-order polynomial and a jump-like reconstruction that allows a discontinuity being partly represented within the mesh cell rather than at the interface. Excellent numerical results have been obtained for both scalar and Euler conservation laws with substantially improved solution quality in comparison with the existing methods. It is shown that new schemes of high fidelity for both continuous and discontinuous solutions can be devised by the BVD guideline with properly-chosen candidate reconstruction schemes. This work provides a simple and accurate alternative of great practical significance to the current high-order Godunov paradigm which overly pursues the smoothness within mesh cells under the questionable premiss that discontinuities only appear at cell interfaces.

  2. Band structure and transmission characteristics of complex phononic crystals by multi-level substructure scheme

    NASA Astrophysics Data System (ADS)

    Yin, J.; Zhang, S.; Zhang, H. W.; Chen, B. S.

    2015-10-01

    A fast scheme based on the multi-level substructure technique is proposed for the band structure and transmission characteristics calculation of phononic crystals uniformly. The main idea is that finite element models of phononic crystals are divided into several domains by a special multi-level decomposition. For the band structure calculation, the upscaling calculation is employed to condense the internal stiffness matrix of the unit cell into the Bloch boundary. Due to the internal stiffness matrix does not change along with reduced wave vectors in an iteration process, the scheme can reduce the computational scale and improve the efficiency greatly, meanwhile it does not introduce approximation into the traditional finite element model. For the transmission characteristics calculation, the unit cell of the phononic crystal is periodic which is taken as a substructure with the same coefficient matrix. Moreover, the downscaling calculation of internal displacements can be selected flexibly. Some closely watched examples of the three-dimensional locally resonant, defect state of Lamb wave and Bragg waveguide are analyzed. Numerical results indicate that the proposed scheme is efficient and accurate, which may widely be applicable and suitable for complex phononic crystal problems, and provides a reliable numerical tool to optimize and design crystal devices.

  3. Confined turbulent fluid-particle flow modeling using multiple-realization particle trajectory schemes

    NASA Technical Reports Server (NTRS)

    Adeniji-Fashola, A. A.

    1988-01-01

    A multiple-realization particle trajectory scheme has been developed and applied to the numerical prediction of confined turbulent fluid-particle flows. The example flows investigated include the vertical pipe upflow experimental data of Tsuji et al. and the experimental data of Leavitt for a coaxial jet flow, comprising a particle-laden central jet and a clean annular jet, into a large recirculation chamber. The results obtained from the numerical scheme agree well with the experimental data, lending confidence to the modeling approach. The multiple-realization particle trajectory turbulent flow modeling scheme is believed to be a more elegant and accurate approach to the extension of single-particle hydrodynamics to dilute multi-particle systems than the more commonly employed two-fluid modeling approach. It is also better able to incorporate additional force items such as lift, virtual mass and Bassett history terms directly into the particle equation of motion as appropriate. This makes it a suitable candidate for particle migration studies and an extension to situations involving liquid particulate phases with possible propulsion applications, such as in spray combustion, follows naturally.

  4. 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

  5. A novel correction scheme for DFT: A combined vdW-DF/CCSD(T) approach

    NASA Astrophysics Data System (ADS)

    Hermann, Jan; Bludský, Ota

    2013-07-01

    A system-specific but very accurate density functional theory (DFT) correction scheme is proposed for precise calculations of adsorbent-adsorbate interactions by combining the non-empirical van der Waals density functional (vdW-DF) method and the empirical DFT/CC correction scheme to reach accuracy of the coupled clusters method with single, double and perturbative triple excitations (CCSD(T)). The new approach is applied to small molecules (CH4, CO2, H2, H2O, N2) interacting with silica surfaces and purely siliceous microporous solids. The vdW-DF/CC results for a perfectly reconstructed α-quartz surface are consistent with other dispersion-corrected DFT methods. Corrected for ZPVE, the vdW-DF/CC enthalpies of adsorption in pure-silica zeolite LTA (ΔHads(0 K)) of 3.6 and 5.2 kcal/mol for methane and carbon dioxide, respectively, are in excellent agreement with experimental values of 3.6 and 5.0 kcal/mol. The very high accuracy of the new scheme and its relatively easy use and numerical stability as compared to the earlier DFT/CC scheme offer a straightforward solution for obtaining reliable predictions of adsorption energies.

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

    PubMed

    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.

  7. A high-order time formulation of the RBC schemes for unsteady compressible Euler equations

    NASA Astrophysics Data System (ADS)

    Lerat, A.

    2015-12-01

    Residual-Based Compact (RBC) schemes can approximate the compressible Euler equations with a high space-accuracy on a very compact stencil. For instance on a 2-D Cartesian mesh, the 5th- and 7th-order accuracy can be reached on a 5 × 5-point stencil. The time integration of the RBC schemes uses a fully implicit method of 2nd-order accuracy (Gear method) usually solved by a dual-time approach. This method is efficient for computing compressible flows in slow unsteady regimes, but for quick unsteady flows, it may be costly and not accurate enough. A new time-formulation is proposed in the present paper. Unusually, in a RBC scheme the time derivative occurs, through linear discrete operators due to compactness, not only in the main residual but also in the other two residuals (in 2-D) involved in the numerical dissipation. To extract the time derivative, a space-factorization method which preserves the high accuracy in space is developed for reducing the algebra to the direct solution of simple linear systems on the mesh lines. Then a time-integration of high accuracy is selected for the RBC schemes by comparing the efficiency of four classes of explicit methods. The new time-formulation is validated for the diagonal advection of a Gaussian shape, the rotation of a hump, the advection of a vortex for a long time and the interaction of a vortex with a shock.

  8. High Order Finite Volume Nonlinear Schemes for the Boltzmann Transport Equation

    SciTech Connect

    Bihari, B L; Brown, P N

    2005-03-29

    The authors apply the nonlinear WENO (Weighted Essentially Nonoscillatory) scheme to the spatial discretization of the Boltzmann Transport Equation modeling linear particle transport. The method is a finite volume scheme which ensures not only conservation, but also provides for a more natural handling of boundary conditions, material properties and source terms, as well as an easier parallel implementation and post processing. It is nonlinear in the sense that the stencil depends on the solution at each time step or iteration level. By biasing the gradient calculation towards the stencil with smaller derivatives, the scheme eliminates the Gibb's phenomenon with oscillations of size O(1) and reduces them to O(h{sup r}), where h is the mesh size and r is the order of accuracy. The current implementation is three-dimensional, generalized for unequally spaced meshes, fully parallelized, and up to fifth order accurate (WENO5) in space. For unsteady problems, the resulting nonlinear spatial discretization yields a set of ODE's in time, which in turn is solved via high order implicit time-stepping with error control. For the steady-state case, they need to solve the non-linear system, typically by Newton-Krylov iterations. There are several numerical examples presented to demonstrate the accuracy, non-oscillatory nature and efficiency of these high order methods, in comparison with other fixed-stencil schemes.

  9. 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

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

    NASA Astrophysics Data System (ADS)

    Owkes, Mark; Desjardins, Olivier

    2013-09-01

    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 the 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.

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

    SciTech Connect

    Owkes, Mark 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 the 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.

  12. FRESCO: flexible alignment with rectangle scoring schemes.

    PubMed

    Dalca, A V; Brudno, M

    2008-01-01

    While the popular DNA sequence alignment tools incorporate powerful heuristics to allow for fast and accurate alignment of DNA, most of them still optimize the classical Needleman Wunsch scoring scheme. The development of novel scoring schemes is often hampered by the difficulty of finding an optimizing algorithm for each non-trivial scheme. In this paper we define the broad class of rectangle scoring schemes, and describe an algorithm and tool that can align two sequences with an arbitrary rectangle scoring scheme in polynomial time. Rectangle scoring schemes encompass some of the popular alignment scoring metrics currently in use, as well as many other functions. We investigate a novel scoring function based on minimizing the expected number of random diagonals observed with the given scores and show that it rivals the LAGAN and Clustal-W aligners, without using any biological or evolutionary parameters. The FRESCO program, freely available at http://compbio.cs.toronto.edu/fresco, gives bioinformatics researchers the ability to quickly compare the performance of other complex scoring formulas without having to implement new algorithms to optimize them.

  13. NNLOPS accurate associated HW production

    NASA Astrophysics Data System (ADS)

    Astill, William; Bizon, Wojciech; Re, Emanuele; Zanderighi, Giulia

    2016-06-01

    We present a next-to-next-to-leading order accurate description of associated HW production consistently matched to a parton shower. The method is based on reweighting events obtained with the HW plus one jet NLO accurate calculation implemented in POWHEG, extended with the MiNLO procedure, to reproduce NNLO accurate Born distributions. Since the Born kinematics is more complex than the cases treated before, we use a parametrization of the Collins-Soper angles to reduce the number of variables required for the reweighting. We present phenomenological results at 13 TeV, with cuts suggested by the Higgs Cross section Working Group.

  14. On the novel chaotic secure communication scheme design

    NASA Astrophysics Data System (ADS)

    Wang, B.; Zhong, S. M.; Dong, X. C.

    2016-10-01

    In this paper, the problem on the chaotic secure communication is discussed. First a new dual channel transmission mechanism is presented and used in secure communication scheme design, then the channel-switching techniques are adopted to further improve the security of information transmission. Finally some typical numerical simulations are carried out to demonstrate the effectiveness of the proposed secure communication scheme.

  15. 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.

  16. Tabled Execution in Scheme

    SciTech Connect

    Willcock, J J; Lumsdaine, A; Quinlan, D J

    2008-08-19

    Tabled execution is a generalization of memorization developed by the logic programming community. It not only saves results from tabled predicates, but also stores the set of currently active calls to them; tabled execution can thus provide meaningful semantics for programs that seemingly contain infinite recursions with the same arguments. In logic programming, tabled execution is used for many purposes, both for improving the efficiency of programs, and making tasks simpler and more direct to express than with normal logic programs. However, tabled execution is only infrequently applied in mainstream functional languages such as Scheme. We demonstrate an elegant implementation of tabled execution in Scheme, using a mix of continuation-passing style and mutable data. We also show the use of tabled execution in Scheme for a problem in formal language and automata theory, demonstrating that tabled execution can be a valuable tool for Scheme users.

  17. The NEC Link Scheme

    ERIC Educational Resources Information Center

    Noakes, Peter

    1976-01-01

    Describes the operation of the National Electronics Council (NEC) Link Scheme for schools in Great Britain. The service is intended to provide technical assistance, information concerning surplus equipment, and guest speakers for school aspiring professional electronic counsel. (CP)

  18. Matching multistage schemes to viscous flow

    NASA Astrophysics Data System (ADS)

    Kleb, William Leonard

    A method to accelerate convergence to steady state by explicit time-marching schemes for the compressible Navier-Stokes equations is presented. The combination of cell-Reynolds-number-based multistage time stepping and local preconditioning makes solving steady-state viscous flow problems competitive with the convergence rates typically associated with implicit methods, without the associated memory penalty. Initially, various methods are investigated to extend the range of multistage schemes to diffusion-dominated cases. It is determined that the Chebyshev polynomials are well suited to serve as amplification factors for these schemes; however, creating a method that can bridge the continuum from convection-dominated to diffusion-dominated regimes proves troublesome, until the Manteuffel family of polynomials is uncovered. This transformation provides a smooth transition between the two extremes; and armed with this information, sets of multistage coefficients are created for a given spatial discretization as a function of cell Reynolds number according to various design criteria. As part of this process, a precise definition for the numerical time step is hammered out, something which up to this time, has been set via algebraic arguments only. Next are numerical tests of these sets of variable multistage coefficients. To isolate the effects of the variable multistage coefficients, the test case chosen is very simple: circular advection-diffusion. The numerical results support the analytical analysis by demonstrating an order of magnitude improvement in convergence rate for single-grid relaxation and a factor of three for multigrid relaxation. Building upon the success of the scalar case, preconditioning is applied to make the Navier-Stokes system of equations behave more nearly as a single scalar equation. Then, by applying the variable multistage coefficient scheme to a typical boundary-layer flow problem, the results affirm the benefits of local preconditioning

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

    SciTech Connect

    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 an 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.

  20. 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.

  1. The Linear Bicharacteristic Scheme for Electromagnetics

    NASA Technical Reports Server (NTRS)

    Beggs, John H.

    2001-01-01

    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 model 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 for perfect electrical conductors. Heterogeneous media are modeled 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.

  2. Triangular tessellation scheme for the adsorption free energy at the liquid-liquid interface: Towards nonconvex patterned colloids.

    PubMed

    de Graaf, Joost; Dijkstra, Marjolein; van Roij, René

    2009-11-01

    We present a numerical technique, namely, triangular tessellation, to calculate the free energy associated with the adsorption of a colloidal particle at a flat interface. The theory and numerical scheme presented here are sufficiently general to handle nonconvex patchy colloids with arbitrary surface patterns characterized by a wetting angle, e.g., amphiphilicity. We ignore interfacial deformation due to capillary, electrostatic, or gravitational forces, but the method can be extended to take such effects into account. It is verified that the numerical method presented is accurate and sufficiently stable to be applied to more general situations than presented in this paper. The merits of the tessellation method prove to outweigh those of traditionally used semianalytic approaches, especially when it comes to generality and applicability. PMID:20364983

  3. Engineering images designed by fractal subdivision scheme.

    PubMed

    Mustafa, Ghulam; Bari, Mehwish; Jamil, Saba

    2016-01-01

    This paper is concerned with the modeling of engineering images by the fractal properties of 6-point binary interpolating scheme. Association between the fractal behavior of the limit curve/surface and the parameter is obtained. The relationship between the subdivision parameter and the fractal dimension of the limit fractal curve of subdivision fractal is also presented. Numerical examples and visual demonstrations show that 6-point scheme is good choice for the generation of fractals for the modeling of fractal antennas, bearings, garari's and rock etc. PMID:27652066

  4. Accurate determination of characteristic relative permeability curves

    NASA Astrophysics Data System (ADS)

    Krause, Michael H.; Benson, Sally M.

    2015-09-01

    A recently developed technique to accurately characterize sub-core scale heterogeneity is applied to investigate the factors responsible for flowrate-dependent effective relative permeability curves measured on core samples in the laboratory. The dependency of laboratory measured relative permeability on flowrate has long been both supported and challenged by a number of investigators. Studies have shown that this apparent flowrate dependency is a result of both sub-core scale heterogeneity and outlet boundary effects. However this has only been demonstrated numerically for highly simplified models of porous media. In this paper, flowrate dependency of effective relative permeability is demonstrated using two rock cores, a Berea Sandstone and a heterogeneous sandstone from the Otway Basin Pilot Project in Australia. Numerical simulations of steady-state coreflooding experiments are conducted at a number of injection rates using a single set of input characteristic relative permeability curves. Effective relative permeability is then calculated from the simulation data using standard interpretation methods for calculating relative permeability from steady-state tests. Results show that simplified approaches may be used to determine flowrate-independent characteristic relative permeability provided flow rate is sufficiently high, and the core heterogeneity is relatively low. It is also shown that characteristic relative permeability can be determined at any typical flowrate, and even for geologically complex models, when using accurate three-dimensional models.

  5. Solving turbulent diffusion flame in cylindrical frame applying an improved advective kinetics scheme

    NASA Astrophysics Data System (ADS)

    Darbandi, Masoud; Ghafourizadeh, Majid

    2015-12-01

    In this work, we derive a few new advective flux approximation expressions, apply them in a hybrid finite-volume-element (FVE) formulation, and solve the turbulent reacting flow governing equations in the cylindrical frame. To derive these advective-kinetic-based expressions, we benefit from the advantages of a physical influence scheme (PIS) basically, extend it to the cylindrical frame suitably, and approximate the required advective flux terms at the cell faces more accurately. The present numerical scheme not only respects the physics of flow correctly but also resolves the pressure-velocity coupling problem automatically. We also suggest a bi-implicit algorithm to solve the set of coupled turbulent reacting flow governing equations, in which the turbulence and chemistry governing equations are solved simultaneously. To evaluate the accuracy of new derived FVE-PIS expressions, we compare the current solutions with other available numerical solutions and experimental data. The comparisons show that the new derived expressions provide some more advantages over the past numerical approaches in solving turbulent diffusion flame in the cylindrical frame. Indeed, the current method and formulations can be used to solve and analyze the turbulent diffusion flames in the cylindrical coordinates very reliably.

  6. 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.

  7. An efficient high-order compact scheme for the unsteady compressible Euler and Navier-Stokes equations

    NASA Astrophysics Data System (ADS)

    Lerat, A.

    2016-10-01

    Residual-Based Compact (RBC) schemes approximate the 3-D compressible Euler equations with a 5th- or 7th-order accuracy on a 5 × 5 × 5-point stencil and capture shocks pretty well without correction. For unsteady flows however, they require a costly algebra to extract the time-derivative occurring at several places in the scheme. A new high-order time formulation has been recently proposed [13] for simplifying the RBC schemes and increasing their temporal accuracy. The present paper goes much further in this direction and deeply reconsiders the method. An avatar of the RBC schemes is presented that greatly reduces the computing time and the memory requirements while keeping the same type of successful numerical dissipation. Two and three-dimensional linear stability are analyzed and the method is extended to the 3-D compressible Navier-Stokes equations. The new compact scheme is validated for several unsteady problems in two and three dimension. In particular, an accurate DNS at moderate cost is presented for the evolution of the Taylor-Green Vortex at Reynolds 1600 and Prandtl 0.71. The effects of the mesh size and of the accuracy order in the approximation of Euler and viscous terms are discussed.

  8. ICPP: Numerical Fokker-Planck calculations in nonuniform grids

    NASA Astrophysics Data System (ADS)

    Bizarro, João P. S.

    2000-10-01

    The Fokker-Planck equation arises in a wide class of problems in plasma physics, so numerical schemes that provide efficient, accurate, and stable solutions to that equation are always welcome. One way to accomplish this is via nonuniform grids, which allow the use of different mesh sizes according to the real needs of the physical problem under consideration. The extension of the standard finite-difference approach to general nonuniform grids, taking into account proper weighting coefficients, has already been presented, and the results have been rather conclusive [J. P. S. Bizarro and P. Rodrigues, Nucl. Fusion Vol. 37, 1509 (1997)]. Besides reviewing what has been achieved with nonuniform grids, a numerical scheme that is accurate to second order (both in time step and mesh size) is here extended and detailed. Such an analysis is rigourous for one-dimensional Fokker-Planck equations, and is generalized to two-dimensional equations. The constraints on the design of the nonuniform grid are discussed, as well as the particle and energy conservation properties. The conditions under which the nonuniformity correction in the weighting coefficients is essential to secure physically meaningful solutions are also analyzed. The proposed scheme is shown to efficiently handle both linear and weakly nonlinear problems and, in addition, its ability to provide solutions to stronger nonlinear situations is demonstrated. Some particular problems in the field of plasma physics (e.g., Coulomb collisions, Compton scattering by an electronic population, and the rf heating and current drive of thermonuclear reactors) are solved in order to illustrate several features, most particularly the usefulness of nonuniform grids in reducing computational effort and in increasing accuracy.

  9. An Accurately Stable Thermo-Hydro-Mechanical Model for Geo-Environmental Simulations

    NASA Astrophysics Data System (ADS)

    Gambolati, G.; Castelletto, N.; Ferronato, M.

    2011-12-01

    In real-world applications involving complex 3D heterogeneous domains the use of advanced numerical algorithms is of paramount importance to stabily, accurately and efficiently solve the coupled system of partial differential equations governing the mass and the energy balance in deformable porous media. The present communication discusses a novel coupled 3-D numerical model based on a suitable combination of Finite Elements (FEs), Mixed FEs (MFEs), and Finite Volumes (FVs) developed with the aim at stabilizing the numerical solution. Elemental pressures and temperatures, nodal displacements and face normal Darcy and Fourier fluxes are the selected primary variables. Such an approach provides an element-wise conservative velocity field, with both pore pressure and stress having the same order of approximation, and allows for the accurate prediction of sharp temperature convective fronts. In particular, the flow-deformation problem is addressed jointly by FEs and MFEs and is coupled to the heat transfer equation using an ad hoc time splitting technique that separates the time temperature evolution into two partial differential equations, accounting for the convective and the diffusive contribution, respectively. The convective part is addressed by a FV scheme which proves effective in treating sharp convective fronts, while the diffusive part is solved by a MFE formulation. A staggered technique is then implemented for the global solution of the coupled thermo-hydro-mechanical problem, solving iteratively the flow-deformation and the heat transport at each time step. Finally, the model is successfully experimented with in realistic applications dealing with geothermal energy extraction and injection.

  10. 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.

  11. 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.

  12. 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.

  13. Aerothermal modeling program. Phase 2, element A: Improved numerical methods for turbulent viscous recirculating flows

    NASA Technical Reports Server (NTRS)

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

    1987-01-01

    The objective of this effort is to develop improved numerical schemes for predicting combustor flow fields. Various candidate numerical schemes were evaluated, and promising schemes were selected for detailed assessment. The criteria for evaluation included accuracy, computational efficiency, stability, and ease of extension to multidimensions. The candidate schemes were assessed against a variety of simple one- and two-dimensional problems. These results led to the selection of the following schemes for further evaluation: flux spline schemes (linear and cubic) and controlled numerical diffusion with internal feedback (CONDIF). The incorporation of the flux spline scheme and direct solution strategy in a computer program for three-dimensional flows is in progress.

  14. A composite scheme for gas dynamics in Lagrangian coordinates

    SciTech Connect

    Shashkov, M.; Wendroff, B.

    1999-04-10

    One cycle of a composite finite difference scheme is defined as several time steps of an oscillatory scheme such as Lax-Wendroff followed by one step of a diffusive scheme such as Lax-Friedrichs. The authors apply this idea to gas dynamics in Lagrangian coordinates. They show numerical results in two dimensions for Noh`s infinite strength shock problem and the Sedov blast wave problem, and for several one-dimensional problems including a Riemann problem with a contact discontinuity. For Noh`s problem the composite scheme produces a better result than that obtained with a more conventional Lagrangian code.

  15. Effect of Prandtl number and computational schemes on the oscillatory natural convection in an enclosure

    SciTech Connect

    Tagawa, Toshio; Ozoe, Hiroyuki

    1996-08-23

    Numerical calculations were carried out for natural convection of low-Prandtl-number fluid. These calculations include the inertial terms that were approximated by six kinds of schemes, i.e., upwind scheme, hybrid scheme, second-order central difference method, Kawamura-Kuwahara scheme, Utopia scheme, and fourth-order central difference method. The average Nusselt number depended significantly on the schemes. The occurrence of oscillatory flow also depended on the schemes for inertial terms. Higher order up-winding approximations for inertial terms appear to be required to calculate natural convection of low-Prandtl-number fluids like liquid metal, even if the Rayleigh number is not large enough.

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

    SciTech Connect

    Sun, Wenjun; Jiang, Song; Xu, Kun

    2015-03-15

    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 transport 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.

  17. Numerical Development

    ERIC Educational Resources Information Center

    Siegler, Robert S.; Braithwaite, David W.

    2016-01-01

    In this review, we attempt to integrate two crucial aspects of numerical development: learning the magnitudes of individual numbers and learning arithmetic. Numerical magnitude development involves gaining increasingly precise knowledge of increasing ranges and types of numbers: from non-symbolic to small symbolic numbers, from smaller to larger…

  18. Compact Spreader Schemes

    SciTech Connect

    Placidi, M.; Jung, J. -Y.; Ratti, A.; Sun, C.

    2014-07-25

    This paper describes beam distribution schemes adopting a novel implementation based on low amplitude vertical deflections combined with horizontal ones generated by Lambertson-type septum magnets. This scheme offers substantial compactness in the longitudinal layouts of the beam lines and increased flexibility for beam delivery of multiple beam lines on a shot-to-shot basis. Fast kickers (FK) or transverse electric field RF Deflectors (RFD) provide the low amplitude deflections. Initially proposed at the Stanford Linear Accelerator Center (SLAC) as tools for beam diagnostics and more recently adopted for multiline beam pattern schemes, RFDs offer repetition capabilities and a likely better amplitude reproducibility when compared to FKs, which, in turn, offer more modest financial involvements both in construction and operation. Both solutions represent an ideal approach for the design of compact beam distribution systems resulting in space and cost savings while preserving flexibility and beam quality.

  19. Compact spreader schemes

    NASA Astrophysics Data System (ADS)

    Placidi, M.; Jung, J.-Y.; Ratti, A.; Sun, C.

    2014-12-01

    This paper describes beam distribution schemes adopting a novel implementation based on low amplitude vertical deflections combined with horizontal ones generated by Lambertson-type septum magnets. This scheme offers substantial compactness in the longitudinal layouts of the beam lines and increased flexibility for beam delivery of multiple beam lines on a shot-to-shot basis. Fast kickers (FK) or transverse electric field RF Deflectors (RFD) provide the low amplitude deflections. Initially proposed at the Stanford Linear Accelerator Center (SLAC) as tools for beam diagnostics and more recently adopted for multiline beam pattern schemes, RFDs offer repetition capabilities and a likely better amplitude reproducibility when compared to FKs, which, in turn, offer more modest financial involvements both in construction and operation. Both solutions represent an ideal approach for the design of compact beam distribution systems resulting in space and cost savings while preserving flexibility and beam quality.

  20. A time-accurate multiple-grid algorithm

    NASA Technical Reports Server (NTRS)

    Jespersen, D. C.

    1985-01-01

    A time-accurate multiple-grid algorithm is described. The algorithm allows one to take much larger time steps with an explicit time-marching scheme than would otherwise be the case. Sample calculations of a scalar advection equation and the Euler equations for an oscillating airfoil are shown. For the oscillating airfoil, time steps an order of magnitude larger than the single-grid algorithm are possible.

  1. Numerical approximation of higher-order time-fractional telegraph equation by using a combination of a geometric approach and method of line

    NASA Astrophysics Data System (ADS)

    Hashemi, M. S.; Baleanu, D.

    2016-07-01

    We propose a simple and accurate numerical scheme for solving the time fractional telegraph (TFT) equation within Caputo type fractional derivative. A fictitious coordinate ϑ is imposed onto the problem in order to transform the dependent variable u (x , t) into a new variable with an extra dimension. In the new space with the added fictitious dimension, a combination of method of line and group preserving scheme (GPS) is proposed to find the approximate solutions. This method preserves the geometric structure of the problem. Power and accuracy of this method has been illustrated through some examples of TFT equation.

  2. Campylobacter biotyping scheme of epidemiological value.

    PubMed Central

    Bolton, F J; Holt, A V; Hutchinson, D N

    1984-01-01

    A biotyping scheme has been developed which utilises 12 tests, including growth at 28 degrees C, hippurate hydrolysis, and 10 resistotyping tests. These tests are arranged in groups of three, and by assigning a numerical value to each positive test a four figure code is produced for each strain. The order of the tests is such that campylobacters are both speciated and biotyped . This scheme recognises Campylobacter jejuni, C coli, "C laridis ," C fetus fetus, and C fetus subspecies venerealis. The reproducibility of the biotyping technique and the stability of the biotype code have been determined by testing campylobacter reference strains. The routine application of the scheme has also been evaluated by biotyping 1000 recent campylobacter isolates, and the epidemiological value has been confirmed by testing serotyped isolates from several milk borne outbreaks. PMID:6373839

  3. 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

  4. 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

  5. An improved WENO-Z scheme

    NASA Astrophysics Data System (ADS)

    Acker, F.; B. de R. Borges, R.; Costa, B.

    2016-05-01

    In this article, we show that for a WENO scheme to improve the numerical resolution of smooth waves, increasing to some extent the contribution of the substencils where the solution is less smooth is much more important than improving the accuracy at critical points. WENO-Z, for instance, achieved less dissipative results than classical WENO through the use of a high-order global smoothness measurement, τ, which increased the weights of less-smooth substencils. This time, we present a way of further increasing the relevance of less-smooth substencils by adding a new term to the WENO-Z weights that uses information which is already available in its formula. The improved scheme attains much better resolution at the smooth parts of the solution, while keeping the same numerical stability of the original WENO-Z at shocks and discontinuities.

  6. 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.

  7. Conservation Properties of Numerical Schemes for the Shallow Water Equations

    NASA Astrophysics Data System (ADS)

    Eldred, Chris; Randall, David

    2014-05-01

    The shallow water equations provide a useful analogue of fully compressible Euler equations since they have similar conservation laws, many of the same types of waves and a similar (quasi-) balanced state. With regards to conservation properties, there have been two major thrusts of research: Hamiltonian methods (work done by Salmon and Dubois, primarily) and Discrete Exterior Calculus (DEC; Thuburn, Cotter, Ringler, etc.). In particular, recent work done by Thuburn and Cotter (2011) introduced a generalized framework for energy-conservative C-grid discretizations of the rotating shallow water equation using ideas from Discrete Exterior Calculus. The current research elucidates the connections between the Hamiltonian and DEC approaches, and looks at potential enstrophy conservation in addition to energy conservation. Finally, a generalized framework for mimetic total energy and potential enstrophy conserving discretizations of the rotating shallow water equation in vorticity-divergence form (also using the DEC approach) is developed.

  8. 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).

  9. Splitting based finite volume schemes for ideal MHD equations

    NASA Astrophysics Data System (ADS)

    Fuchs, F. G.; Mishra, S.; Risebro, N. H.

    2009-02-01

    We design finite volume schemes for the equations of ideal magnetohydrodynamics (MHD) and based on splitting these equations into a fluid part and a magnetic induction part. The fluid part leads to an extended Euler system with magnetic forces as source terms. This set of equations are approximated by suitable two- and three-wave HLL solvers. The magnetic part is modeled by the magnetic induction equations which are approximated using stable upwind schemes devised in a recent paper [F. Fuchs, K.H. Karlsen, S. Mishra, N.H. Risebro, Stable upwind schemes for the Magnetic Induction equation. Math. Model. Num. Anal., Available on conservation laws preprint server, submitted for publication, URL: ]. These two sets of schemes can be combined either component by component, or by using an operator splitting procedure to obtain a finite volume scheme for the MHD equations. The resulting schemes are simple to design and implement. These schemes are compared with existing HLL type and Roe type schemes for MHD equations in a series of numerical experiments. These tests reveal that the proposed schemes are robust and have a greater numerical resolution than HLL type solvers, particularly in several space dimensions. In fact, the numerical resolution is comparable to that of the Roe scheme on most test problems with the computational cost being at the level of a HLL type solver. Furthermore, the schemes are remarkably stable even at very fine mesh resolutions and handle the divergence constraint efficiently with low divergence errors.

  10. The development and numerical implementation of approximate inertial manifolds for the Ginzburg-Landau equation

    SciTech Connect

    Promislow, K.S.

    1991-01-01

    In this work the author considers the long-time behavior of dissipative evolution equations; in particular, the construction of Approximate Inertial Manifolds (AIMs) for the Ginzburg-Landau equation (GLE) and their subsequent application to the creation of more efficient and more accurate numerical schemes. In the first part, the time analyticity for the solutions of a class of dissipative evolution equations is shown. This class includes Reaction-Diffusion, GLE, Navier-Stokes, and Cahn-Hilliard equations. Existing methods are generalized and extended, and it is shown that the solutions of these equations have a unique analytic extension to an infinite pencil-shaped domain about the positive real axis in the complex plane. In the second part, the preceding result is applied to develop a new method of construction of AIMs which produces an infinite series of increasingly higher order AIMs for the GLE and associates with each a thin neighborhood into which the orbits enter in finite time and with exponential speed. These manifolds are a substitute for Inertial Manifolds when the existence of the Inertial Manifold is not known and are shown to localize the universal attractor in the phase space. Finally, in the third part, using the explicit non-linear equations of the first two nontrivial AIMs, two numerical schemes are implemented for the GLE, as well as a traditional, linear Galerkin scheme. Comparisons of the accuracy of these three schemes are made, showing gains in stability and accuracy.

  11. Check-Digit Schemes.

    ERIC Educational Resources Information Center

    Wheeler, Mary L.

    1994-01-01

    Discusses the study of identification codes and check-digit schemes as a way to show students a practical application of mathematics and introduce them to coding theory. Examples include postal service money orders, parcel tracking numbers, ISBN codes, bank identification numbers, and UPC codes. (MKR)

  12. Numerical methods for problems in computational aeroacoustics

    NASA Astrophysics Data System (ADS)

    Mead, Jodi Lorraine

    1998-12-01

    A goal of computational aeroacoustics is the accurate calculation of noise from a jet in the far field. This work concerns the numerical aspects of accurately calculating acoustic waves over large distances and long time. More specifically, the stability, efficiency, accuracy, dispersion and dissipation in spatial discretizations, time stepping schemes, and absorbing boundaries for the direct solution of wave propagation problems are determined. Efficient finite difference methods developed by Tam and Webb, which minimize dispersion and dissipation, are commonly used for the spatial and temporal discretization. Alternatively, high order pseudospectral methods can be made more efficient by using the grid transformation introduced by Kosloff and Tal-Ezer. Work in this dissertation confirms that the grid transformation introduced by Kosloff and Tal-Ezer is not spectrally accurate because, in the limit, the grid transformation forces zero derivatives at the boundaries. If a small number of grid points are used, it is shown that approximations with the Chebyshev pseudospectral method with the Kosloff and Tal-Ezer grid transformation are as accurate as with the Chebyshev pseudospectral method. This result is based on the analysis of the phase and amplitude errors of these methods, and their use for the solution of a benchmark problem in computational aeroacoustics. For the grid transformed Chebyshev method with a small number of grid points it is, however, more appropriate to compare its accuracy with that of high- order finite difference methods. This comparison, for an order of accuracy 10-3 for a benchmark problem in computational aeroacoustics, is performed for the grid transformed Chebyshev method and the fourth order finite difference method of Tam. Solutions with the finite difference method are as accurate. and the finite difference method is more efficient than, the Chebyshev pseudospectral method with the grid transformation. The efficiency of the Chebyshev

  13. Assessment of the numerical efficiency of ocean circulation model : Hycom contribution to the COMODO project

    NASA Astrophysics Data System (ADS)

    Lathuilière, Cyril; Baraille, Rémy; Le Boyer, Arnaud

    2015-04-01

    The French navy hydrographic service uses a modified version of the Hybrid coordinate ocean model (HYCOM) for operational oceanographic applications. In the framework of the COMODO project, a series of test cases has been carried out to measure the numerical efficiency of the model. It addresses a wide panel of oceanic processes (baroclinic eddy, baroclinic jet, coastal upwelling, internal tides) and is useful to examine most of numerical schemes (advection schemes, time stepping, pressure gradient, …). The objectives of this study are first to assess the numerical performance of the present model to guide the modelers to make the suitable choices, and second to examine how the performances may be improved in the next years. We examine the sensitivity of the main choices for Hycom (2th or 4th order advection schemes, and viscosity values) in baroclinic eddy and baroclinic jet test cases. Both test cases are run using increasing resolution. The highest resolution provides a reference for studying the coarser resolutions. In the baroclinic vortex test case, the second order vector form scheme is well performing whereas the 4th order scheme appears to be more accurate in the baroclinic jet test case. This is probably due to the lack of fine scale energy in the baroclinic vortex test case allowing simulations with very tiny dissipation rates. We focus then on the sensitivity of the performance to vertical coordinate choices. The ability of Hycom to switch between isopycnal coordinate and quasi geopotential coordinate provides useful insights for example on the sensitivity of numerical diapycnal mixing to remapping scheme. This is particularly visible on the internal tide test case. The type of vertical coordinate is also important for potential vorticity structures. The shape of the baroclinic vortex is found to be different in geopotential and isopycnal coordinates. At coarse resolution, the potential vorticity structures seem to be better resolved in isopycnal

  14. Numerical and experimental study of a rotating magnetic particle chain in a viscous fluid.

    PubMed

    Gao, Y; Hulsen, M A; Kang, T G; den Toonder, J M J

    2012-10-01

    A simple and fast numerical method is developed capable of accurately determining the 3D rotational dynamics of a magnetic particle chain in an infinite fluid domain. The focus is to control the alternating breakup and reformation of the bead chain which we believe is essential to achieve effective fluid mixing at small scales. The numerical scheme makes use of magnetic dipole moments and extended forms of the Oseen-Burgers tensor to account for both the magnetic and hydrodynamic interactions between the particles. It is shown that the inclusion of hydrodynamic interaction between the particles is crucial to obtain a good description of the particle dynamics. Only a small error of deviation is observed when benchmarking the numerical scheme against a more computationally intensive method, the direct simulation method. The numerical results are compared with experiments and the simulated rotational dynamics correspond well with those obtained from video-microscopy experiments qualitatively and quantitatively. In addition, a dimensionless number (R(T)) is derived as the sole control parameter for the rotational bead chain dynamics. Numerically and experimentally, R(T)≈ 1 is the boundary between rigid "rod" and dynamic "breaking and reformation" behaviors. PMID:23214587

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

    NASA Astrophysics Data System (ADS)

    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), 10.1016/j.jcp.2014.06.033]. 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.

  16. 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.

  17. 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.

  18. A flexible gridding scheme for reservoir simulation

    SciTech Connect

    Verma, S.

    1995-12-31

    This paper describes a new control volume based finite difference scheme for petroleum reservoir simulation which can be used with unstructured grids. The numerical scheme to model fluid flow is shown to be easily used for Voronoi grids in 2D. It can also be used with certain geometrical limitations for 3D Voronoi grids. The scheme can be used without any significant limitations for triangle or tetrahedron based grids where control volumes are constructed around their vertices. It assumes uniform properties inside such control volumes. Full, anisotropic and asymmetric permeability tensor can be easily handled with the proposed method. The permeability tensor can vary from block to block. Thus it will be of great value in modeling fluid flow in reservoirs where principal directions of permeability varies between beds or within a bed. The paper also presents an analysis of some of the published flexible gridding schemes which use a control volume type algebraic approximation and demonstrate the advantages of the method presented here. The technique for grid construction is also discussed. Test results presented here demonstrate the need for proper representation of reservoir geometry to predict the correct flow behavior. The gridding scheme described in this paper achieves that purpose.

  19. Validation Study of the Integral-Differential Scheme for Multi-Block Grids

    NASA Astrophysics Data System (ADS)

    Mrema, Honest Frank

    This MS Thesis seeks to validate the accuracy of the Integral-Differential Scheme (IDS). In the attempts to accomplish this task, research efforts were focused on the scheme's ability to capture the physics of known flow fields, as well as the scheme's ability to predict the features of flow field quantities that may be derived from experimental measurements. The IDS was developed with the goal of being computationally efficient, from a programming perspective, as well as being numerically accurate, stable, and robust, from a mathematical perspective. The IDS is designed to solve the full Navier-Stokes equations in their integral forms. Unlike traditional control volume schemes, the IDS is built upon two sets of cells: spatial and temporal cells. For 2-D flows, the IDS considers an elementary control volume as a collection of four spatial cells and a single temporal cell. Similar to other explicit CFD schemes, the IDS relies on the use of the Taylor series expansion and other traditional CFD criteria. It is of interest to note that there are previous IDS validation studies which were conducted at North Carolina A&T State University. These past studies mainly focused on the qualitative aspects of the flow field physics. Furthermore, in all cases, they focused on flow field problems that can be represented by single-block grids. In this analysis, the validation studies are focused on multi-block grids in which the physics of the flow field is made complicated due to the presence of shock waves and flow separation zones. Of interest to this MS Thesis are two supersonic flow field problems that are supported by experimental data; namely, the supersonic flow over a rearward-facing step problem and the supersonic flow over a cavity problem. The validation studies conducted herein demonstrated that the IDS was able to predict the experimental data in both cases.

  20. 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