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Sample records for advanced numerical schemes

  1. On Some Numerical Dissipation Schemes

    NASA Technical Reports Server (NTRS)

    Swanson, R. C.; Radespiel, R.; Turkel, E.

    1998-01-01

    Several schemes for introducing an artificial dissipation into a central difference approximation to the Euler and Navier Stokes equations are considered. The focus of the paper is on the convective upwind and split pressure (CUSP) scheme, which is designed to support single interior point discrete shock waves. This scheme is analyzed and compared in detail with scalar dissipation and matrix dissipation (MATD) schemes. Resolution capability is determined by solving subsonic, transonic, and hypersonic flow problems. A finite-volume discretization and a multistage time-stepping scheme with multigrid are used to compute solutions to the flow equations. Numerical solutions are also compared with either theoretical solutions or experimental data. For transonic airfoil flows the best accuracy on coarse meshes for aerodynamic coefficients is obtained with a simple MATD scheme. The coarse-grid accuracy for the original CUSP scheme is improved by modifying the limiter function used with the scheme, giving comparable accuracy to that obtained with the MATD scheme. The modifications reduce the background dissipation and provide control over the regions where the scheme can become first order.

  2. Multidimensional numerical scheme for resistive relativistic magnetohydrodynamics

    NASA Astrophysics Data System (ADS)

    Komissarov, Serguei S.

    2007-12-01

    The paper describes a new upwind conservative numerical scheme for special relativistic resistive magnetohydrodynamics with scalar resistivity. The magnetic field is kept approximately divergence free and the divergence of the electric field is kept consistent with the electric charge distribution via the method of Generalized Lagrange Multiplier. The hyperbolic fluxes are computed using the Harten-Lax-van Leer (HLL) prescription and the source terms are accounted via the time-splitting technique. The results of test simulations show that the scheme can handle equally well both resistive current sheets and shock waves, and thus can be a useful tool for studying phenomena of relativistic astrophysics that involve both colliding supersonic flows and magnetic reconnection.

  3. 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.

  4. Study on the numerical schemes for hypersonic flow simulation

    NASA Astrophysics Data System (ADS)

    Nagdewe, S. P.; Shevare, G. R.; Kim, Heuy-Dong

    2009-10-01

    Hypersonic flow is full of complex physical and chemical processes, hence its investigation needs careful analysis of existing schemes and choosing a suitable scheme or designing a brand new scheme. The present study deals with two numerical schemes Harten, Lax, and van Leer with Contact (HLLC) and advection upstream splitting method (AUSM) to effectively simulate hypersonic flow fields, and accurately predict shock waves with minimal diffusion. In present computations, hypersonic flows have been modeled as a system of hyperbolic equations with one additional equation for non-equilibrium energy and relaxing source terms. Real gas effects, which appear typically in hypersonic flows, have been simulated through energy relaxation method. HLLC and AUSM methods are modified to incorporate the conservation laws for non-equilibrium energy. Numerical implementation have shown that non-equilibrium energy convect with mass, and hence has no bearing on the basic numerical scheme. The numerical simulation carried out shows good comparison with experimental data available in literature. Both numerical schemes have shown identical results at equilibrium. Present study has demonstrated that real gas effects in hypersonic flows can be modeled through energy relaxation method along with either AUSM or HLLC numerical scheme.

  5. Uplink Access Schemes for LTE-Advanced

    NASA Astrophysics Data System (ADS)

    Liu, Le; Inoue, Takamichi; Koyanagi, Kenji; Kakura, Yoshikazu

    The 3GPP LTE-Advanced has been attracting much attention recently, where the channel bandwidth would be beyond the maximum bandwidth of LTE, 20MHz. In LTE, single carrier-frequency division multiple access (SC-FDMA) was accepted as the uplink access scheme due to its advantage of very low cubic metric (CM). For LTE-A wideband transmission, multicarrier access would be more effective than single carrier access to make use of multi-user diversity and can maintain the physical channel structure of LTE, where the control information is transmitted on the edges of each 20MHz. In this paper, we discuss the access schemes in bandwidth under 20MHz as well as over 20MHz. In the case of bandwidth under 20MHz, we propose the access schemes allowing discontinuous resource allocation to enhance average throughput while maintaining cell-edge user throughput, that is, DFT-spread-OFDM with spectrum division control (SDC) and adaptive selection of SC-FDMA and OFDM (SC+OFDM). The number of discontinuous spectrums is denoted as spectrum division (SD). For DFT-S-OFDM, we define a parameter max SD as the upper limit of SD. We evaluate our proposed schemes in bandwidth under 20MHz and find that SC+OFDM as well as SDC with common max SD or UE-specific max SD can improve average throughput while their cell-edge user throughput can approach that of SC-FDMA. In the case of bandwidth over 20MHz, we consider key factors to decide a feasible access scheme for aggregating several 20MHz-wide bands.

  6. Suppressing the numerical Cherenkov radiation in the Yee numerical scheme

    SciTech Connect

    Nuter, Rachel Tikhonchuk, Vladimir

    2016-01-15

    The next generation of laser facilities will routinely produce relativistic particle beams from the interaction of intense laser pulses with solids and/or gases. Their modeling with Particle-In-Cell (PIC) codes needs dispersion-free Maxwell solvers in order to properly describe the interaction of electromagnetic waves with relativistic particles. A particular attention is devoted to the suppression of the numerical Cherenkov instability, responsible for the noise generation. It occurs when the electromagnetic wave is artificially slowed down because of the finite mesh size, thus allowing for the high energy particles to propagate with super-luminous velocities. In the present paper, we show how a slight increase of the light velocity in the Maxwell's equations enables to suppress this instability while keeping a good overall precision of calculations.

  7. The numerical scheme development of a simplified frozen soil model

    NASA Astrophysics Data System (ADS)

    Li, Qian; Sun, Shufen; Dai, Qiudan

    2009-09-01

    In almost all frozen soil models used currently, three variables of temperature, ice content and moisture content are used as prognostic variables and the rate term, accounting for the contribution of the phase change between water and ice, is shown explicitly in both the energy and mass balance equations. The models must be solved by a numerical method with an iterative process, and the rate term of the phase change needs to be pre-estimated at the beginning in each iteration step. Since the rate term of the phase change in the energy equation is closely related to the release or absorption of the great amount of fusion heat, a small error in the rate term estimation will introduce greater error in the energy balance, which will amplify the error in the temperature calculation and in turn, cause problems for the numerical solution convergence. In this work, in order to first reduce the trouble, the methodology of the variable transformation is applied to a simplified frozen soil model used currently, which leads to new frozen soil scheme used in this work. In the new scheme, the enthalpy and the total water equivalent are used as predictive variables in the governing equations to replace temperature, volumetric soil moisture and ice content used in many current models. By doing so, the rate terms of the phase change are not shown explicitly in both the mass and energy equations and its pre-estimation is avoided. Secondly, in order to solve this new scheme more functionally, the development of the numerical scheme to the new scheme is described and a numerical algorithm appropriate to the numerical scheme is developed. In order to evaluate the new scheme of the frozen soil model and its relevant algorithm, a series of model evaluations are conducted by comparing numerical results from the new model scheme with three observational data sets. The comparisons show that the results from the model are in good agreement with these data sets in both the change trend of

  8. Numerical Testing of Parameterization Schemes for Solving Parameter Estimation Problems

    DTIC Science & Technology

    2008-12-01

    1 NUMERICAL TESTING OF PARAMETERIZATION SCHEMES FOR SOLVING PARAMETER ESTIMATION PROBLEMS L. Velázquez*, M. Argáez and C. Quintero The...performance computing (HPC). 1. INTRODUCTION In this paper we present the numerical performance of three parameterization approaches, SVD...wavelets, and the combination of wavelet-SVD for solving automated parameter estimation problems based on the SPSA described in previous reports of this

  9. A comparative study of advanced shock-capturing schemes applied to Burgers' equation

    NASA Technical Reports Server (NTRS)

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

    1992-01-01

    A systematic evaluation is conducted of all extant numerical schemes for nonlinear scalar transport problems, and several advanced shock-capturing schemes are used to solve the nonlinear Burgers' equation in order to characterize their ability to resolve the sharp discontinuity, expansion zone, and propagation and collision features of shocks. For discontinuous functions, the Warming-Beam scheme generates preshock wiggles, while the Lax-Wendroff scheme generates postshock ones. Such limiters as the MUSCL or the superbee are more compressive than minimod or monotonic limiters. The performance of such TVD schemes as the upwind, the symmetric, and the Roe-Sweby, resemble each other.

  10. Novel discretization schemes for the numerical simulation of membrane dynamics

    NASA Astrophysics Data System (ADS)

    Kolsti, Kyle F.

    Motivated by the demands of simulating flapping wings of Micro Air Vehicles, novel numerical methods were developed and evaluated for the dynamic simulation of membranes. For linear membranes, a mixed-form time-continuous Galerkin method was employed using trilinear space-time elements. Rather than time-marching, the entire space-time domain was discretized and solved simultaneously. Second-order rates of convergence in both space and time were observed in numerical studies. Slight high-frequency noise was filtered during post-processing. For geometrically nonlinear membranes, the model incorporated two new schemes that were independently developed and evaluated. Time marching was performed using quintic Hermite polynomials uniquely determined by end-point jerk constraints. The single-step, implicit scheme was significantly more accurate than the most common Newmark schemes. For a simple harmonic oscillator, the scheme was found to be symplectic, frequency-preserving, and conditionally stable. Time step size was limited by accuracy requirements rather than stability. The spatial discretization scheme employed a staggered grid, grouping of nonlinear terms, and polygon shape functions in a strong-form point collocation formulation. The observed rate of convergence was two for both displacement and strain. Validation against existing experimental data showed the method to be accurate until hyperelastic effects dominate.

  11. Advances in numerical and applied mathematics

    NASA Technical Reports Server (NTRS)

    South, J. C., Jr. (Editor); Hussaini, M. Y. (Editor)

    1986-01-01

    This collection of papers covers some recent developments in numerical analysis and computational fluid dynamics. Some of these studies are of a fundamental nature. They address basic issues such as intermediate boundary conditions for approximate factorization schemes, existence and uniqueness of steady states for time dependent problems, and pitfalls of implicit time stepping. The other studies deal with modern numerical methods such as total variation diminishing schemes, higher order variants of vortex and particle methods, spectral multidomain techniques, and front tracking techniques. There is also a paper on adaptive grids. The fluid dynamics papers treat the classical problems of imcompressible flows in helically coiled pipes, vortex breakdown, and transonic flows.

  12. Direct numerical simulation of scalar transport using unstructured finite-volume schemes

    NASA Astrophysics Data System (ADS)

    Rossi, Riccardo

    2009-03-01

    An unstructured finite-volume method for direct and large-eddy simulations of scalar transport in complex geometries is presented and investigated. The numerical technique is based on a three-level fully implicit time advancement scheme and central spatial interpolation operators. The scalar variable at cell faces is obtained by a symmetric central interpolation scheme, which is formally first-order accurate, or by further employing a high-order correction term which leads to formal second-order accuracy irrespective of the underlying grid. In this framework, deferred-correction and slope-limiter techniques are introduced in order to avoid numerical instabilities in the resulting algebraic transport equation. The accuracy and robustness of the code are initially evaluated by means of basic numerical experiments where the flow field is assigned a priori. A direct numerical simulation of turbulent scalar transport in a channel flow is finally performed to validate the numerical technique against a numerical dataset established by a spectral method. In spite of the linear character of the scalar transport equation, the computed statistics and spectra of the scalar field are found to be significantly affected by the spectral-properties of interpolation schemes. Although the results show an improved spectral-resolution and greater spatial-accuracy for the high-order operator in the analysis of basic scalar transport problems, the low-order central scheme is found superior for high-fidelity simulations of turbulent scalar transport.

  13. A Stable Adaptive Numerical Scheme for Hyperbolic Conservation Laws.

    DTIC Science & Technology

    1983-05-01

    Bradley J. Lucier Mathematics Research Center University of Wisconsin- Madison * 610 Walnut Strest Madison, Wisconsin 53706 *May 1983 (Received April 5... 1983 ) ITO FILE COPY~D Approved for public release D TICTE Ditiuinunlimited JUL 2 0 19N3 Sponsored by E U. S. Army Research office National Science...CENTER A STABLE ADAPTIVE NUMERICAL SCHEME FOR HYPERBOLIC CONSERVATION LAWS * Bradley J. Lucier Technical Summary Report #2517 May 1983 ABSTRACT A new

  14. Recent advances in numerical PDEs

    NASA Astrophysics Data System (ADS)

    Zuev, Julia Michelle

    In this thesis, we investigate four neighboring topics, all in the general area of numerical methods for solving Partial Differential Equations (PDEs). Topic 1. Radial Basis Functions (RBF) are widely used for multi-dimensional interpolation of scattered data. This methodology offers smooth and accurate interpolants, which can be further refined, if necessary, by clustering nodes in select areas. We show, however, that local refinements with RBF (in a constant shape parameter [varepsilon] regime) may lead to the oscillatory errors associated with the Runge phenomenon (RP). RP is best known in the case of high-order polynomial interpolation, where its effects can be accurately predicted via Lebesgue constant L (which is based solely on the node distribution). We study the RP and the applicability of Lebesgue constant (as well as other error measures) in RBF interpolation. Mainly, we allow for a spatially variable shape parameter, and demonstrate how it can be used to suppress RP-like edge effects and to improve the overall stability and accuracy. Topic 2. Although not as versatile as RBFs, cubic splines are useful for interpolating grid-based data. In 2-D, we consider a patch representation via Hermite basis functions s i,j ( u, v ) = [Special characters omitted.] h mn H m ( u ) H n ( v ), as opposed to the standard bicubic representation. Stitching requirements for the rectangular non-equispaced grid yield a 2-D tridiagonal linear system AX = B, where X represents the unknown first derivatives. We discover that the standard methods for solving this NxM system do not take advantage of the spline-specific format of the matrix B. We develop an alternative approach using this specialization of the RHS, which allows us to pre-compute coefficients only once, instead of N times. MATLAB implementation of our fast 2-D cubic spline algorithm is provided. We confirm analytically and numerically that for large N ( N > 200), our method is at least 3 times faster than the

  15. Secret Sharing Schemes and Advanced Encryption Standard

    DTIC Science & Technology

    2015-09-01

    without the selfless support and sacrifice of my wife, Sharon, who took the time to nurture our two children, Rianne and Rayden, during this one-year...polynomial to either a non-linear, or a monic polynomial form. Opportunities for future work of this nature are discussed in Chapter 6. Therefore, it...introduced variables that are protected by any secret sharing scheme cannot be solved using any algebraic transformation that is linear in nature , since

  16. Numerical Schemes for a Model for Nonlinear Dispersive Waves.

    DTIC Science & Technology

    1983-11-01

    2604 November 1983 ABSTRACT A description is given of a number of numerical schemes to solve an evolution equation Athat arises when modelling the...travel at constant speed and whose shape is independent of time. One of the models, the Korteweg -de Vries equation , has been studied extensively, both...inital-value problem for the Korteweg -de Vries equation y~~~-2u 0(I) ut + ux + Buu x +fYu inO, Department of Mathematics, University of Chicago, Chicago

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

    NASA Astrophysics Data System (ADS)

    Liu, Jianjun; Zhang, Feimin; Pu, Zhaoxia

    2017-04-01

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

  18. 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.

  19. 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.

  20. 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.

  1. 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

  2. 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.

  3. Symmetric fast marching schemes for better numerical isotropy.

    PubMed

    Appia, Vikram; Yezzi, Anthony

    2013-09-01

    Existing fast marching methods solve the Eikonal equation using a continuous (first-order) model to estimate the accumulated cost, but a discontinuous (zero-order) model for the traveling cost at each grid point. As a result the estimate of the accumulated cost (calculated numerically) at a given point will vary based on the direction of the arriving front, introducing an anisotropy into the discrete algorithm even though the continuous partial differential equation (PDE) is itself isotropic. To remove this anisotropy, we propose two very different schemes. In the first model, we utilize a continuous interpolation of the traveling cost, which is not biased by the direction of the propagating front. In the second model, we upsample the traveling cost on a higher resolution grid to overcome the directional bias. We show the significance of removing the directional bias in the computation of the cost in some applications of the fast marching method, demonstrating that both methods make the discrete implementation more isotropic, in accordance with the underlying continuous PDE.

  4. Symmetric Fast Marching Schemes for Better Numerical Isotropy.

    PubMed

    Appia, Vikram; Yezzi, Anthony

    2013-03-06

    Existing Fast Marching methods solve the Eikonal equation using a continuous (first order) model to estimate the accumulated cost, but a discontinuous (zero order) model for the traveling cost at each grid point. As a result the estimate of the accumulated cost (calculated numerically) at a given point will vary based on the direction of the arriving front, introducing an anisotropy into the discrete algorithm even though the continuous PDE is itself isotropic. To remove this anisotropy, we propose two very different schemes. In the first model we utilize a continuous interpolation of the traveling cost, which is not biased by the direction of the propagating front. In the second model we upsample the traveling cost on a higher resolution grid to overcome the directional bias. We show the significance of removing the directional bias in the computation of the cost in some applications of fast marching method, demonstrating that both methods make the discrete implementation more isotropic in accordance with the underlying continuous PDE. We also compare the accuracy and computation time of our proposed methods with the existing state of the art fast marching techniques to demonstrate the superiority of our method.

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

    NASA Astrophysics Data System (ADS)

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

    2015-02-01

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

  6. 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.

  7. Verification and comparison of four numerical schemes for a 1D viscoelastic blood flow model.

    PubMed

    Wang, Xiaofei; Fullana, Jose-Maria; Lagrée, Pierre-Yves

    2015-01-01

    A reliable and fast numerical scheme is crucial for the 1D simulation of blood flow in compliant vessels. In this paper, a 1D blood flow model is incorporated with a Kelvin-Voigt viscoelastic arterial wall. This leads to a nonlinear hyperbolic-parabolic system, which is then solved with four numerical schemes, namely: MacCormack, Taylor-Galerkin, monotonic upwind scheme for conservation law and local discontinuous Galerkin. The numerical schemes are tested on a single vessel, a simple bifurcation and a network with 55 arteries. The numerical solutions are checked favorably against analytical, semi-analytical solutions or clinical observations. Among the numerical schemes, comparisons are made in four important aspects: accuracy, ability to capture shock-like phenomena, computational speed and implementation complexity. The suitable conditions for the application of each scheme are discussed.

  8. An Advanced Leakage Scheme for Neutrino Treatment in Astrophysical Simulations

    NASA Astrophysics Data System (ADS)

    Perego, A.; Cabezón, R. M.; Käppeli, R.

    2016-04-01

    We present an Advanced Spectral Leakage (ASL) scheme to model neutrinos in the context of core-collapse supernovae (CCSNe) and compact binary mergers. Based on previous gray leakage schemes, the ASL scheme computes the neutrino cooling rates by interpolating local production and diffusion rates (relevant in optically thin and thick regimes, respectively) separately for discretized values of the neutrino energy. Neutrino trapped components are also modeled, based on equilibrium and timescale arguments. The better accuracy achieved by the spectral treatment allows a more reliable computation of neutrino heating rates in optically thin conditions. The scheme has been calibrated and tested against Boltzmann transport in the context of Newtonian spherically symmetric models of CCSNe. ASL shows a very good qualitative and a partial quantitative agreement for key quantities from collapse to a few hundreds of milliseconds after core bounce. We have proved the adaptability and flexibility of our ASL scheme, coupling it to an axisymmetric Eulerian and to a three-dimensional smoothed particle hydrodynamics code to simulate core collapse. Therefore, the neutrino treatment presented here is ideal for large parameter-space explorations, parametric studies, high-resolution tests, code developments, and long-term modeling of asymmetric configurations, where more detailed neutrino treatments are not available or are currently computationally too expensive.

  9. AN ADVANCED LEAKAGE SCHEME FOR NEUTRINO TREATMENT IN ASTROPHYSICAL SIMULATIONS

    SciTech Connect

    Perego, A.; Cabezón, R. M.; Käppeli, R.

    2016-04-15

    We present an Advanced Spectral Leakage (ASL) scheme to model neutrinos in the context of core-collapse supernovae (CCSNe) and compact binary mergers. Based on previous gray leakage schemes, the ASL scheme computes the neutrino cooling rates by interpolating local production and diffusion rates (relevant in optically thin and thick regimes, respectively) separately for discretized values of the neutrino energy. Neutrino trapped components are also modeled, based on equilibrium and timescale arguments. The better accuracy achieved by the spectral treatment allows a more reliable computation of neutrino heating rates in optically thin conditions. The scheme has been calibrated and tested against Boltzmann transport in the context of Newtonian spherically symmetric models of CCSNe. ASL shows a very good qualitative and a partial quantitative agreement for key quantities from collapse to a few hundreds of milliseconds after core bounce. We have proved the adaptability and flexibility of our ASL scheme, coupling it to an axisymmetric Eulerian and to a three-dimensional smoothed particle hydrodynamics code to simulate core collapse. Therefore, the neutrino treatment presented here is ideal for large parameter-space explorations, parametric studies, high-resolution tests, code developments, and long-term modeling of asymmetric configurations, where more detailed neutrino treatments are not available or are currently computationally too expensive.

  10. A Numerical Homogenization Scheme for Glass Particle-Toughened Polymers Under Dynamic Loading

    NASA Astrophysics Data System (ADS)

    Karamnejad, Amin; Ahmed, Awais; Sluys, Lambertus Johannes

    A numerical homogenization scheme is presented to model glass particle-toughened polymer materials under dynamic loading. A constitutive law is developed for the polymer material and validated by comparing the results to experimental test data. A similar constitutive law as that of the polymer material with unknown material parameters is assumed for the glass particle-toughened polymer. A homogenization scheme is used to determine the unknown material parameters from the boundary value problem (BVP) of a representative volume element. Unlike the standard computational homogenization scheme, the proposed numerical homogenization scheme can be used after localization occurs in the material. The proposed multiscale model is then verified against direct numerical simulation.

  11. HARM: A Numerical Scheme for General Relativistic Magnetohydrodynamics

    NASA Astrophysics Data System (ADS)

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

    2012-09-01

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

  12. Improvements to the RELAP5-3D Nearly-Implicit Numerical Scheme

    SciTech Connect

    Richard A. Riemke; Walter L. Weaver; RIchard R. Schultz

    2005-05-01

    The RELAP5-3D computer program has been improved with regard to its nearly-implicit numerical scheme for twophase flow and single-phase flow. Changes were made to the nearly-implicit numerical scheme finite difference momentum equations as follows: (1) added the velocity flip-flop mass/energy error mitigation logic, (2) added the modified Henry-Fauske choking model, (3) used the new time void fraction in the horizontal stratification force terms and gravity head, and (4) used an implicit form of the artificial viscosity. The code modifications allow the nearly-implicit numerical scheme to be more implicit and lead to enhanced numerical stability.

  13. Brush seal numerical simulation: Concepts and advances

    NASA Technical Reports Server (NTRS)

    Braun, M. J.; Kudriavtsev, V. V.

    1994-01-01

    The development of the brush seal is considered to be most promising among the advanced type seals that are presently in use in the high speed turbomachinery. The brush is usually mounted on the stationary portions of the engine and has direct contact with the rotating element, in the process of limiting the 'unwanted' leakage flows between stages, or various engine cavities. This type of sealing technology is providing high (in comparison with conventional seals) pressure drops due mainly to the high packing density (around 100 bristles/sq mm), and brush compliance with the rotor motions. In the design of modern aerospace turbomachinery leakage flows between the stages must be minimal, thus contributing to the higher efficiency of the engine. Use of the brush seal instead of the labyrinth seal reduces the leakage flow by one order of magnitude. Brush seals also have been found to enhance dynamic performance, cost less, and are lighter than labyrinth seals. Even though industrial brush seals have been successfully developed through extensive experimentation, there is no comprehensive numerical methodology for the design or prediction of their performance. The existing analytical/numerical approaches are based on bulk flow models and do not allow the investigation of the effects of brush morphology (bristle arrangement), or brushes arrangement (number of brushes, spacing between them), on the pressure drops and flow leakage. An increase in the brush seal efficiency is clearly a complex problem that is closely related to the brush geometry and arrangement, and can be solved most likely only by means of a numerically distributed model.

  14. 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.

  15. 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.

  16. 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.

  17. Steady-State Analysis Model for Advanced Fuel Cycle Schemes.

    SciTech Connect

    SARTORI, ENRICO

    2008-03-17

    Version 00 SMAFS was developed as a part of the study, "Advanced Fuel Cycles and Waste Management", which was performed during 2003-2005 by an ad-hoc expert group under the Nuclear Development Committee in the OECD/NEA. The model was designed for an efficient conduct of nuclear fuel cycle scheme cost analyses. It is simple, transparent and offers users the capability to track down cost analysis results. All the fuel cycle schemes considered in the model are represented in a graphic format and all values related to a fuel cycle step are shown in the graphic interface, i.e., there are no hidden values embedded in the calculations. All data on the fuel cycle schemes considered in the study including mass flows, waste generation, cost data, and other data such as activities, decay heat and neutron sources of spent fuel and high-level waste along time are included in the model and can be displayed. The user can easily modify values of mass flows and/or cost parameters and see corresponding changes in the results. The model calculates: front-end fuel cycle mass flows such as requirements of enrichment and conversion services and natural uranium; mass of waste based on the waste generation parameters and the mass flow; and all costs.

  18. Steady-state Analysis Model for Advanced Fuelcycle Schemes

    SciTech Connect

    2006-05-12

    The model was developed as a part of the study, "Advanced Fuel Cycles and Waste Management", which was performed during 2003—2005 by an ad-hoc expert group under the Nuclear Development Committee in the OECD/NEA. The model was designed for an efficient conduct of nuclear fuel cycle scheme cost analyses. It is simple, transparent and offers users the capability to track down the cost analysis results. All the fuel cycle schemes considered in the model are represented in a graphic format and all values related to a fuel cycle step are shown in the graphic interface, i.e., there are no hidden values embedded in the calculations. All data on the fuel cycle schemes considered in the study including mass flows, waste generation, cost data, and other data such as activities, decay heat and neutron sources of spent fuel and high—level waste along time are included in the model and can be displayed. The user can modify easily the values of mass flows and/or cost parameters and see the corresponding changes in the results. The model calculates: front—end fuel cycle mass flows such as requirements of enrichment and conversion services and natural uranium; mass of waste based on the waste generation parameters and the mass flow; and all costs. It performs Monte Carlo simulations with changing the values of all unit costs within their respective ranges (from lower to upper bounds).

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

    NASA Technical Reports Server (NTRS)

    Jameson, Antony

    1994-01-01

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

  20. 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.

  1. 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.

  2. Positivity-preserving numerical schemes for multidimensional advection

    NASA Technical Reports Server (NTRS)

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

    1993-01-01

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

  3. 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

  4. Towards an unconditionally stable numerical scheme for continuum dislocation transport

    NASA Astrophysics Data System (ADS)

    Hernández, H.; Massart, T. J.; Peerlings, R. H. J.; Geers, M. G. D.

    2015-12-01

    Recent developments in plasticity modeling for crystalline materials are based on dislocations transport models, formulated for computational efficiency in terms of their densities. This leads to sets of coupled partial differential equations in a continuum description involving diffusion and convection-like processes combined with non-linearity. The properties of these equations cause the most traditional numerical methods to fail when applied to solve them. Therefore, dedicated stabilization techniques must be developed in order to obtain physically meaningful and numerically stable approximations. The objective of this paper is to present a dedicated stabilization technique and to apply it to a system of dislocation transport equations in one dimension. This stabilization technique, based on coefficient perturbations, successfully provides unconditional stability with respect to the spatial discretization. Several of its favorable characteristics are discussed, providing evidence of its versatility and effectiveness through a thorough numerical assessment.

  5. Numerical method for boundary layers with blowing - The exponential box scheme

    NASA Technical Reports Server (NTRS)

    El-Mistikawy, T. M.; Werle, M. J.

    1978-01-01

    The paper describes a new numerical scheme based on exponential difference operator concepts combined with Keller's (1968) box scheme approach to produce a stable second-order accurate finite-difference scheme for convection-diffusion problems arising in boundary layer flows in the presence of massive injection through a porous surface. The technique is demonstrated by application to the self-similar boundary layer equations with massive blowing at the surface.

  6. 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

  7. TLC scheme for numerical solution of the transport equation on equilateral triangular meshes

    SciTech Connect

    Walters, W.F.

    1983-01-01

    A new triangular linear characteristic TLC scheme for numerically solving the transport equation on equilateral triangular meshes has been developed. This scheme uses the analytic solution of the transport equation in the triangle as its basis. The data on edges of the triangle are assumed linear as is the source representation. A characteristic approach or nodal approach is used to obtain the analytic solution. Test problems indicate that the new TLC is superior to the widely used DITRI scheme for accuracy.

  8. 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.

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

    NASA Technical Reports Server (NTRS)

    Shu, Chi-Wang

    1990-01-01

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

  10. 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.

  11. 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.

  12. Determination of Solution Accuracy of Numerical Schemes as Part of Code and Calculation Verification

    SciTech Connect

    Blottner, F.G.; Lopez, A.R.

    1998-10-01

    This investigation is concerned with the accuracy of numerical schemes for solving partial differential equations used in science and engineering simulation codes. Richardson extrapolation methods for steady and unsteady problems with structured meshes are presented as part of the verification procedure to determine code and calculation accuracy. The local truncation error de- termination of a numerical difference scheme is shown to be a significant component of the veri- fication procedure as it determines the consistency of the numerical scheme, the order of the numerical scheme, and the restrictions on the mesh variation with a non-uniform mesh. Genera- tion of a series of co-located, refined meshes with the appropriate variation of mesh cell size is in- vestigated and is another important component of the verification procedure. The importance of mesh refinement studies is shown to be more significant than just a procedure to determine solu- tion accuracy. It is suggested that mesh refinement techniques can be developed to determine con- sistency of numerical schemes and to determine if governing equations are well posed. The present investigation provides further insight into the conditions and procedures required to effec- tively use Richardson extrapolation with mesh refinement studies to achieve confidence that sim- ulation codes are producing accurate numerical solutions.

  13. 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

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

    NASA Technical Reports Server (NTRS)

    Yee, H. C.

    1986-01-01

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

  15. 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.

  16. An Improved Mathematical Scheme for LTE-Advanced Coexistence with FM Broadcasting Service.

    PubMed

    Shamsan, Zaid Ahmed; Al-Hetar, Abdulaziz M

    2016-01-01

    Power spectral density (PSD) overlapping analysis is considered the surest approach to evaluate feasibility of compatibility between wireless communication systems. In this paper, a new closed-form for the Interference Signal Power Attenuation (ISPA) is mathematically derived to evaluate interference caused from Orthogonal Frequency Division Multiplexing (OFDM)-based Long Term Evolution (LTE)-Advanced into Frequency Modulation (FM) broadcasting service. In this scheme, ISPA loss due to PSD overlapping of both OFDM-based LTE-Advanced and FM broadcasting service is computed. The proposed model can estimate power attenuation loss more precisely than the Advanced Minimum Coupling Loss (A-MCL) and approximate-ISPA methods. Numerical results demonstrate that the interference power is less than that obtained using the A-MCL and approximate ISPA methods by 2.8 and 1.5 dB at the co-channel and by 5.2 and 2.2 dB at the adjacent channel with null guard band, respectively. The outperformance of this scheme over the other methods leads to more diminishing in the required physical distance between the two systems which ultimately supports efficient use of the radio frequency spectrum.

  17. An Improved Mathematical Scheme for LTE-Advanced Coexistence with FM Broadcasting Service

    PubMed Central

    Al-hetar, Abdulaziz M.

    2016-01-01

    Power spectral density (PSD) overlapping analysis is considered the surest approach to evaluate feasibility of compatibility between wireless communication systems. In this paper, a new closed-form for the Interference Signal Power Attenuation (ISPA) is mathematically derived to evaluate interference caused from Orthogonal Frequency Division Multiplexing (OFDM)-based Long Term Evolution (LTE)-Advanced into Frequency Modulation (FM) broadcasting service. In this scheme, ISPA loss due to PSD overlapping of both OFDM-based LTE-Advanced and FM broadcasting service is computed. The proposed model can estimate power attenuation loss more precisely than the Advanced Minimum Coupling Loss (A-MCL) and approximate-ISPA methods. Numerical results demonstrate that the interference power is less than that obtained using the A-MCL and approximate ISPA methods by 2.8 and 1.5 dB at the co-channel and by 5.2 and 2.2 dB at the adjacent channel with null guard band, respectively. The outperformance of this scheme over the other methods leads to more diminishing in the required physical distance between the two systems which ultimately supports efficient use of the radio frequency spectrum. PMID:27855216

  18. Advanced unrepeatered systems using novel Raman amplification schemes

    NASA Astrophysics Data System (ADS)

    Chang, Do-il; Pelouch, Wayne; Burtsev, Sergey; Perrier, Philippe; Fevrier, Herve

    2015-01-01

    Unrepeatered transmission systems provide a cost-effective solution to transmit high capacity channels in submarine networks to communicate between coastal population centers or in terrestrial networks to connect remote areas where service access is difficult. The main goal of unrepeatered systems has traditionally been to achieve the longest reach, however, increasing traffic demands now require unrepeatered systems to support both longer reach and higher transport capacity. As a result, transmission rate of unrepeatered systems has quickly moved from 10 Gb/s to 40 Gb/s or 100 Gb/s. This paper reviews the key basic technologies, with a specific focus on Raman amplification, required for long-reach, high-capacity unrepeatered optical transmission systems. We will discuss novel Raman amplification schemes, enhanced remote optically pumped amplifiers (ROPA), ultra-low loss / large effective area fibers, and coherent transmission with advanced modulation format and high FEC coding gain. We will also report recent experimental demonstrations that show how these technologies have been combined to achieve industry's leading capacity and reach transmission.

  19. 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.

  20. An efficient numerical scheme for spreading resistance calculations based on the variational method

    NASA Astrophysics Data System (ADS)

    Choo, S. C.; Leong, M. S.; Sim, J. H.

    1983-08-01

    This paper presents a simple and efficient numerical scheme for evaluating the correction factor integrals that arise in the variational method. The scheme is a modification of one recently proposed by Berkowitz and Lux for the uniform flux method. The abscissae and the weights required for the integration are given in a form which allows the numerical scheme to be readily implemented. Using this scheme, it takes, on an average, 0.8 sec to compute one value of correction factor on an Apple II Microcomputer. For a slab of varying thickness, backed by either a perfectly conducting or a high resistivity substrate, the correction factors obtained agree with those derived from the exact constant-potential method to within 1%.

  1. Decoupled time-marching schemes in computational cardiac electrophysiology and ECG numerical simulation.

    PubMed

    Fernández, Miguel A; Zemzemi, Nejib

    2010-07-01

    This work considers the approximation of the cardiac bidomain equations, either isolated or coupled with the torso, via first order semi-implicit time-marching schemes involving a fully decoupled computation of the unknown fields (ionic state, transmembrane potential, extracellular and torso potentials). For the isolated bidomain system, we show that the Gauss-Seidel and Jacobi like splittings do not compromise energy stability; they simply alter the energy norm. Within the framework of the numerical simulation of electrocardiograms (ECG), these bidomain splittings are combined with an explicit Robin-Robin treatment of the heart-torso coupling conditions. We show that the resulting schemes allow a fully decoupled (energy) stable computation of the heart and torso fields, under an additional hyperbolic-CFL like condition. The accuracy and convergence rate of the considered schemes are investigated numerically with a series of numerical experiments.

  2. Advanced Numerical Model for Irradiated Concrete

    SciTech Connect

    Giorla, Alain B.

    2015-03-01

    In this report, we establish a numerical model for concrete exposed to irradiation to address these three critical points. The model accounts for creep in the cement paste and its coupling with damage, temperature and relative humidity. The shift in failure mode with the loading rate is also properly represented. The numerical model for creep has been validated and calibrated against different experiments in the literature [Wittmann, 1970, Le Roy, 1995]. Results from a simplified model are shown to showcase the ability of numerical homogenization to simulate irradiation effects in concrete. In future works, the complete model will be applied to the analysis of the irradiation experiments of Elleuch et al. [1972] and Kelly et al. [1969]. This requires a careful examination of the experimental environmental conditions as in both cases certain critical information are missing, including the relative humidity history. A sensitivity analysis will be conducted to provide lower and upper bounds of the concrete expansion under irradiation, and check if the scatter in the simulated results matches the one found in experiments. The numerical and experimental results will be compared in terms of expansion and loss of mechanical stiffness and strength. Both effects should be captured accordingly by the model to validate it. Once the model has been validated on these two experiments, it can be applied to simulate concrete from nuclear power plants. To do so, the materials used in these concrete must be as well characterized as possible. The main parameters required are the mechanical properties of each constituent in the concrete (aggregates, cement paste), namely the elastic modulus, the creep properties, the tensile and compressive strength, the thermal expansion coefficient, and the drying shrinkage. These can be either measured experimentally, estimated from the initial composition in the case of cement paste, or back-calculated from mechanical tests on concrete. If some

  3. Numerical solution of multiparameter spectral problems by high order finite different schemes

    NASA Astrophysics Data System (ADS)

    Amodio, Pierluigi; Settanni, Giuseppina

    2016-10-01

    We report on the progress achieved in the numerical simulation of self-adjoint multiparameter spectral problems for ordinary differential equations. We describe how to obtain a discrete problem by means of High Order Finite Difference Schemes and discuss its numerical solution. Based on this approach, we also define a recursive algorithm to compute approximations of the parameters by means of the solution of a set of problems converging to the original one.

  4. A quartic B-spline based explicit time integration scheme for structural dynamics with controllable numerical dissipation

    NASA Astrophysics Data System (ADS)

    Wen, W. B.; Duan, S. Y.; Yan, J.; Ma, Y. B.; Wei, K.; Fang, D. N.

    2017-03-01

    An explicit time integration scheme based on quartic B-splines is presented for solving linear structural dynamics problems. The scheme is of a one-parameter family of schemes where free algorithmic parameter controls stability, accuracy and numerical dispersion. The proposed scheme possesses at least second-order accuracy and at most third-order accuracy. A 2D wave problem is analyzed to demonstrate the effectiveness of the proposed scheme in reducing high-frequency modes and retaining low-frequency modes. Except for general structural dynamics, the proposed scheme can be used effectively for wave propagation problems in which numerical dissipation is needed to reduce spurious oscillations.

  5. Advanced Energy Harvesting Control Schemes for Marine Renewable Energy Devices

    SciTech Connect

    McEntee, Jarlath; Polagye, Brian; Fabien, Brian; Thomson, Jim; Kilcher, Levi; Marnagh, Cian; Donegan, James

    2016-03-31

    The Advanced Energy Harvesting Control Schemes for Marine Renewable Energy Devices (Project) investigated, analyzed and modeled advanced turbine control schemes with the objective of increasing the energy harvested by hydrokinetic turbines in turbulent flow. Ocean Renewable Power Company (ORPC) implemented and validated a feedforward controller to increase power capture; and applied and tested the controls on ORPC’s RivGen® Power Systems in Igiugig, Alaska. Assessments of performance improvements were made for the RivGen® in the Igiugig environment and for ORPC’s TidGen® Power System in a reference tidal environment. Annualized Energy Production (AEP) and Levelized Cost of Energy (LCOE) improvements associated with implementation of the recommended control methodology were made for the TidGen® Power System in the DOE reference tidal environment. System Performance Advancement (SPA) goals were selected for the project. SPA targets were to improve Power to Weight Ratio (PWR) and system Availability, with the intention of reducing Levelized Cost of Electricity (LCOE). This project focused primarily reducing in PWR. Reductions in PWR of 25.5% were achieved. Reductions of 20.3% in LCOE were achieved. This project evaluated four types of controllers which were tested in simulation, emulation, a laboratory flume, and the field. The adaptive Kω2 controller performs similarly to the non-adaptive version of the same controller and may be useful in tidal channels where the mean velocity is continually evolving. Trends in simulation were largely verified through experiments, which also provided the opportunity to test assumptions about turbine responsiveness and control resilience to varying scales of turbulence. Laboratory experiments provided an essential stepping stone between simulation and implementation on a field-scale turbine. Experiments also demonstrated that using “energy loss” as a metric to differentiate between well-designed controllers operating at

  6. Development of advanced control schemes for telerobot manipulators

    NASA Technical Reports Server (NTRS)

    Nguyen, Charles C.; Zhou, Zhen-Lei

    1991-01-01

    To study space applications of telerobotics, Goddard Space Flight Center (NASA) has recently built a testbed composed mainly of a pair of redundant slave arms having seven degrees of freedom and a master hand controller system. The mathematical developments required for the computerized simulation study and motion control of the slave arms are presented. The slave arm forward kinematic transformation is presented which is derived using the D-H notation and is then reduced to its most simplified form suitable for real-time control applications. The vector cross product method is then applied to obtain the slave arm Jacobian matrix. Using the developed forward kinematic transformation and quaternions representation of the slave arm end-effector orientation, computer simulation is conducted to evaluate the efficiency of the Jacobian in converting joint velocities into Cartesian velocities and to investigate the accuracy of the Jacobian pseudo-inverse for various sampling times. In addition, the equivalence between Cartesian velocities and quaternion is also verified using computer simulation. The motion control of the slave arm is examined. Three control schemes, the joint-space adaptive control scheme, the Cartesian adaptive control scheme, and the hybrid position/force control scheme are proposed for controlling the motion of the slave arm end-effector. Development of the Cartesian adaptive control scheme is presented and some preliminary results of the remaining control schemes are presented and discussed.

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

    PubMed

    Xu, Zhengfu; Bao, Gang

    2010-11-01

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

  8. Design and simulation of advanced fault tolerant flight control schemes

    NASA Astrophysics Data System (ADS)

    Gururajan, Srikanth

    This research effort describes the design and simulation of a distributed Neural Network (NN) based fault tolerant flight control scheme and the interface of the scheme within a simulation/visualization environment. The goal of the fault tolerant flight control scheme is to recover an aircraft from failures to its sensors or actuators. A commercially available simulation package, Aviator Visual Design Simulator (AVDS), was used for the purpose of simulation and visualization of the aircraft dynamics and the performance of the control schemes. For the purpose of the sensor failure detection, identification and accommodation (SFDIA) task, it is assumed that the pitch, roll and yaw rate gyros onboard are without physical redundancy. The task is accomplished through the use of a Main Neural Network (MNN) and a set of three De-Centralized Neural Networks (DNNs), providing analytical redundancy for the pitch, roll and yaw gyros. The purpose of the MNN is to detect a sensor failure while the purpose of the DNNs is to identify the failed sensor and then to provide failure accommodation. The actuator failure detection, identification and accommodation (AFDIA) scheme also features the MNN, for detection of actuator failures, along with three Neural Network Controllers (NNCs) for providing the compensating control surface deflections to neutralize the failure induced pitching, rolling and yawing moments. All NNs continue to train on-line, in addition to an offline trained baseline network structure, using the Extended Back-Propagation Algorithm (EBPA), with the flight data provided by the AVDS simulation package. The above mentioned adaptive flight control schemes have been traditionally implemented sequentially on a single computer. This research addresses the implementation of these fault tolerant flight control schemes on parallel and distributed computer architectures, using Berkeley Software Distribution (BSD) sockets and Message Passing Interface (MPI) for inter

  9. 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.

  10. Numerical schemes for dynamically orthogonal equations of stochastic fluid and ocean flows

    SciTech Connect

    Ueckermann, M.P.; Lermusiaux, P.F.J.; Sapsis, T.P.

    2013-01-15

    The quantification of uncertainties is critical when systems are nonlinear and have uncertain terms in their governing equations or are constrained by limited knowledge of initial and boundary conditions. Such situations are common in multiscale, intermittent and non-homogeneous fluid and ocean flows. The dynamically orthogonal (DO) field equations provide an adaptive methodology to predict the probability density functions of such flows. The present work derives efficient computational schemes for the DO methodology applied to unsteady stochastic Navier-Stokes and Boussinesq equations, and illustrates and studies the numerical aspects of these schemes. Semi-implicit projection methods are developed for the mean and for the DO modes, and time-marching schemes of first to fourth order are used for the stochastic coefficients. Conservative second-order finite-volumes are employed in physical space with new advection schemes based on total variation diminishing methods. Other results include: (i) the definition of pseudo-stochastic pressures to obtain a number of pressure equations that is linear in the subspace size instead of quadratic; (ii) symmetric advection schemes for the stochastic velocities; (iii) the use of generalized inversion to deal with singular subspace covariances or deterministic modes; and (iv) schemes to maintain orthonormal modes at the numerical level. To verify our implementation and study the properties of our schemes and their variations, a set of stochastic flow benchmarks are defined including asymmetric Dirac and symmetric lock-exchange flows, lid-driven cavity flows, and flows past objects in a confined channel. Different Reynolds number and Grashof number regimes are employed to illustrate robustness. Optimal convergence under both time and space refinements is shown as well as the convergence of the probability density functions with the number of stochastic realizations.

  11. 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.

  12. 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.

  13. 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

  14. 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.

  15. 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.

  16. 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.

  17. Numerical scheme to complete a compressible gas flow in variable porosity media

    NASA Astrophysics Data System (ADS)

    Rochette, D.; Clain, S.; Buffard, T.

    2005-05-01

    We present an approximate Riemann solver coupled with a finite volume method to compute non conservative Euler equations in variable porosity media using ideal gas state law. The non conservative term is numerically taken into account from an original idea of LeRoux (1998) but here Riemann problems at each interface of the mesh are linearized using a VFRoe approach. The main goal is the resolution of the non conservative system even if the porosity is discontinuous. Stationary solutions are determined with continuous and discontinuous porosity in order to test the numerical scheme and computations of gas shock subsonic wave moving in a non continuous porosity medium are presented.

  18. Numerical integration of the stochastic Landau-Lifshitz-Gilbert equation in generic time-discretization schemes.

    PubMed

    Romá, Federico; Cugliandolo, Leticia F; Lozano, Gustavo S

    2014-08-01

    We introduce a numerical method to integrate the stochastic Landau-Lifshitz-Gilbert equation in spherical coordinates for generic discretization schemes. This method conserves the magnetization modulus and ensures the approach to equilibrium under the expected conditions. We test the algorithm on a benchmark problem: the dynamics of a uniformly magnetized ellipsoid. We investigate the influence of various parameters, and in particular, we analyze the efficiency of the numerical integration, in terms of the number of steps needed to reach a chosen long time with a given accuracy.

  19. 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.

  20. Advances in Numerical Boundary Conditions for Computational Aeroacoustics

    NASA Technical Reports Server (NTRS)

    Tam, Christopher K. W.

    1997-01-01

    Advances in Computational Aeroacoustics (CAA) depend critically on the availability of accurate, nondispersive, least dissipative computation algorithm as well as high quality numerical boundary treatments. This paper focuses on the recent developments of numerical boundary conditions. In a typical CAA problem, one often encounters two types of boundaries. Because a finite computation domain is used, there are external boundaries. On the external boundaries, boundary conditions simulating the solution outside the computation domain are to be imposed. Inside the computation domain, there may be internal boundaries. On these internal boundaries, boundary conditions simulating the presence of an object or surface with specific acoustic characteristics are to be applied. Numerical boundary conditions, both external or internal, developed for simple model problems are reviewed and examined. Numerical boundary conditions for real aeroacoustic problems are also discussed through specific examples. The paper concludes with a description of some much needed research in numerical boundary conditions for CAA.

  1. Multidimensional Hall magnetohydrodynamics with isotropic or anisotropic thermal pressure: Numerical scheme and its validation using solitary waves

    NASA Astrophysics Data System (ADS)

    Strumik, Marek; Stasiewicz, Krzysztof

    2017-02-01

    We present a numerical solver for plasma dynamics simulations in Hall magnetohydrodynamic (HMHD) approximation in one, two and three dimensions. We consider both isotropic and anisotropic thermal pressure cases, where a general gyrotropic approximation is used. Both explicit energy conservation equation and general polytropic state equations are considered. The numerical scheme incorporates second-order Runge-Kutta advancing in time and Kurganov-Tadmor scheme with van Leer flux limiter for the approximation of fluxes. A flux-interpolated constrained-transport approach is used to preserve solenoidal magnetic field in the simulations. The implemented code is validated using several test problems previously described in the literature. Additionally, we propose a new validation method for HMHD codes based on solitary waves that provides a possibility of quantitative rigorous testing in nonlinear (large amplitude) regime as an extension to standard tests using small-amplitude whistler waves. Quantitative tests of accuracy and performance of the implemented code show the fidelity of the proposed approach.

  2. Advanced numerical methods and software approaches for semiconductor device simulation

    SciTech Connect

    CAREY,GRAHAM F.; PARDHANANI,A.L.; BOVA,STEVEN W.

    2000-03-23

    In this article the authors concisely present several modern strategies that are applicable to drift-dominated carrier transport in higher-order deterministic models such as the drift-diffusion, hydrodynamic, and quantum hydrodynamic systems. The approaches include extensions of upwind and artificial dissipation schemes, generalization of the traditional Scharfetter-Gummel approach, Petrov-Galerkin and streamline-upwind Petrov Galerkin (SUPG), entropy variables, transformations, least-squares mixed methods and other stabilized Galerkin schemes such as Galerkin least squares and discontinuous Galerkin schemes. The treatment is representative rather than an exhaustive review and several schemes are mentioned only briefly with appropriate reference to the literature. Some of the methods have been applied to the semiconductor device problem while others are still in the early stages of development for this class of applications. They have included numerical examples from the recent research tests with some of the methods. A second aspect of the work deals with algorithms that employ unstructured grids in conjunction with adaptive refinement strategies. The full benefits of such approaches have not yet been developed in this application area and they emphasize the need for further work on analysis, data structures and software to support adaptivity. Finally, they briefly consider some aspects of software frameworks. These include dial-an-operator approaches such as that used in the industrial simulator PROPHET, and object-oriented software support such as those in the SANDIA National Laboratory framework SIERRA.

  3. Advanced Numerical Methods and Software Approaches for Semiconductor Device Simulation

    DOE PAGES

    Carey, Graham F.; Pardhanani, A. L.; Bova, S. W.

    2000-01-01

    In this article we concisely present several modern strategies that are applicable to driftdominated carrier transport in higher-order deterministic models such as the driftdiffusion, hydrodynamic, and quantum hydrodynamic systems. The approaches include extensions of “upwind” and artificial dissipation schemes, generalization of the traditional Scharfetter – Gummel approach, Petrov – Galerkin and streamline-upwind Petrov Galerkin (SUPG), “entropy” variables, transformations, least-squares mixed methods and other stabilized Galerkin schemes such as Galerkin least squares and discontinuous Galerkin schemes. The treatment is representative rather than an exhaustive review and several schemes are mentioned only briefly with appropriate reference to the literature. Some of themore » methods have been applied to the semiconductor device problem while others are still in the early stages of development for this class of applications. We have included numerical examples from our recent research tests with some of the methods. A second aspect of the work deals with algorithms that employ unstructured grids in conjunction with adaptive refinement strategies. The full benefits of such approaches have not yet been developed in this application area and we emphasize the need for further work on analysis, data structures and software to support adaptivity. Finally, we briefly consider some aspects of software frameworks. These include dial-an-operator approaches such as that used in the industrial simulator PROPHET, and object-oriented software support such as those in the SANDIA National Laboratory framework SIERRA.« less

  4. 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.

  5. Application of an efficient hybrid scheme for aeroelastic analysis of advanced propellers

    NASA Technical Reports Server (NTRS)

    Srivastava, R.; Sankar, N. L.; Reddy, T. S. R.; Huff, D. L.

    1989-01-01

    An efficient 3-D hybrid scheme is applied for solving Euler equations to analyze advanced propellers. The scheme treats the spanwise direction semi-explicitly and the other two directions implicitly, without affecting the accuracy, as compared to a fully implicit scheme. This leads to a reduction in computer time and memory requirement. The calculated power coefficients for two advanced propellers, SR3 and SR7L, and various advanced ratios showed good correlation with experiment. Spanwise distribution of elemental power coefficient and steady pressure coefficient differences also showed good agreement with experiment. A study of the effect of structural flexibility on the performance of the advanced propellers showed that structural deformation due to centrifugal and aero loading should be included for better correlation.

  6. An efficient numerical progressive diagonalization scheme for the quantum Rabi model revisited

    NASA Astrophysics Data System (ADS)

    Pan, Feng; Bao, Lina; Dai, Lianrong; Draayer, Jerry P.

    2017-02-01

    An efficient numerical progressive diagonalization scheme for the quantum Rabi model is revisited. The advantage of the scheme lies in the fact that the quantum Rabi model can be solved almost exactly by using the scheme that only involves a finite set of one variable polynomial equations. The scheme is especially efficient for a specified eigenstate of the model, for example, the ground state. Some low-lying level energies of the model for several sets of parameters are calculated, of which one set of the results is compared to that obtained from the Braak’s exact solution proposed recently. It is shown that the derivative of the entanglement measure defined in terms of the reduced von Neumann entropy with respect to the coupling parameter does reach the maximum near the critical point deduced from the classical limit of the Dicke model, which may provide a probe of the critical point of the crossover in finite quantum many-body systems, such as that in the quantum Rabi model.

  7. A chaos detectable and time step-size adaptive numerical scheme for nonlinear dynamical systems

    NASA Astrophysics Data System (ADS)

    Chen, Yung-Wei; Liu, Chein-Shan; Chang, Jiang-Ren

    2007-02-01

    The first step in investigation the dynamics of a continuous time system described by ordinary differential equations is to integrate them to obtain trajectories. In this paper, we convert the group-preserving scheme (GPS) developed by Liu [International Journal of Non-Linear Mechanics 36 (2001) 1047-1068] to a time step-size adaptive scheme, x=x+hf(x,t), where x∈R is the system variables we are concerned with, and f(x,t)∈R is a time-varying vector field. The scheme has the form similar to the Euler scheme, x=x+Δtf(x,t), but our step-size h is adaptive automatically. Very interestingly, the ratio h/Δt, which we call the adaptive factor, can forecast the appearance of chaos if the considered dynamical system becomes chaotical. The numerical examples of the Duffing equation, the Lorenz equation and the Rossler equation, which may exhibit chaotic behaviors under certain parameters values, are used to demonstrate these phenomena. Two other non-chaotic examples are included to compare the performance of the GPS and the adaptive one.

  8. Multiecho scheme advances surface NMR for aquifer characterization

    NASA Astrophysics Data System (ADS)

    Grunewald, Elliot; Walsh, David

    2013-12-01

    nuclear magnetic resonance (NMR) is increasingly used as a method to noninvasively characterize aquifers. This technology follows a successful history of NMR logging, applied over decades to estimate hydrocarbon reservoir properties. In contrast to logging, however, surface methods have utilized relatively simple acquisition sequences, from which pore-scale properties may not be reliably and efficiently estimated. We demonstrate for the first time the capability of sophisticated multiecho measurements to rapidly record a surface NMR response that more directly reflects aquifer characteristics. Specifically, we develop an adaptation of the multipulse Carr-Purcell-Meiboom-Gill (CPMG) sequence, widely used in logging, to measure the T2 relaxation response in a single scan. We validate this approach in a field surface NMR data set and by direct comparison with an NMR log. Adoption of the CPMG marked a landmark advancement in the history of logging NMR; we have now realized this same advancement in the surface NMR method.

  9. Preface to advances in numerical simulation of plasmas

    NASA Astrophysics Data System (ADS)

    Parker, Scott E.; Chacon, Luis

    2016-10-01

    This Journal of Computational Physics Special Issue, titled "Advances in Numerical Simulation of Plasmas," presents a snapshot of the international state of the art in the field of computational plasma physics. The articles herein are a subset of the topics presented as invited talks at the 24th International Conference on the Numerical Simulation of Plasmas (ICNSP), August 12-14, 2015 in Golden, Colorado. The choice of papers was highly selective. The ICNSP is held every other year and is the premier scientific meeting in the field of computational plasma physics.

  10. 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.

  11. 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

  12. Advanced scheme for high-yield laser driven nuclear reactions

    NASA Astrophysics Data System (ADS)

    Margarone, D.; Picciotto, A.; Velyhan, A.; Krasa, J.; Kucharik, M.; Mangione, A.; Szydlowsky, A.; Malinowska, A.; Bertuccio, G.; Shi, Y.; Crivellari, M.; Ullschmied, J.; Bellutti, P.; Korn, G.

    2015-01-01

    The use of a low contrast nanosecond laser pulse with a relatively low intensity (3  ×  1016 W cm-2) allowed the enhancing of the yield of induced nuclear reactions in advanced solid targets. In particular the ‘ultraclean’ proton-boron fusion reaction, producing energetic alpha particles without neutron generation, was chosen. A spatially well-defined layer of boron dopants in a hydrogen-enriched silicon substrate was used as a target. A combination of the specific target composition and the laser pulse temporal shape allowed the enhancing of the yield of alpha particles up to 109 per steradian. This result can be ascribed to the interaction of the long-laser pre-pulse with the target and to the optimal target geometry and composition.

  13. Some considerations on numerical schemes for treating hyperbolicity issues in two-layer models

    NASA Astrophysics Data System (ADS)

    Sarno, L.; Carravetta, A.; Martino, R.; Papa, M. N.; Tai, Y.-C.

    2017-02-01

    Multi-layer depth-averaged models are widely employed in various hydraulic engineering applications. Yet, such models are not strictly hyperbolic. Their equation systems typically lose hyperbolicity when the relative velocities between layers become too large, which is associated with Kelvin-Helmholtz instabilities involving turbulent momentum exchanges between the layers. Focusing on the two-layer case, we present a numerical improvement that locally avoids the loss of hyperbolicity. The proposed modification introduces an additional momentum exchange between layers, whose value is iteratively calculated to be strictly sufficient to keep the system hyperbolic. The approach can be easily implemented in any finite volume scheme and there is no limitation concerning the density ratio between layers. Numerical examples, employing both HLL-type and Roe-type approximate Riemann solvers, are reported to validate the method and its key features.

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

    NASA Astrophysics Data System (ADS)

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

    2016-12-01

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

  15. 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.

  16. 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.

  17. Numerical simulation of transonic limit cycle oscillations using high-order low-diffusion schemes

    NASA Astrophysics Data System (ADS)

    Wang, Baoyuan; Zha, Ge-Cheng

    2010-05-01

    This paper simulates the NLR7301 airfoil limit cycle oscillation (LCO) caused by fluid-structure interaction (FSI) using Reynolds averaged Navier-Stokes equations (RANS) coupled with Spalart-Allmaras (S-A) one-equation turbulence model. A low diffusion E-CUSP (LDE) scheme with 5th order weighted essentially nonoscillatory scheme (WENO) is employed to calculate the inviscid fluxes. A fully conservative 4th order central differencing is used for the viscous terms. A fully coupled fluid-structural interaction model is employed. For the case computed in this paper, the predicted LCO frequency, amplitudes, averaged lift and moment, all agree excellently with the experiment performed by Schewe et al. The solutions appear to have bifurcation and are dependent on the initial fields or initial perturbation. The developed computational fluid dynamics (CFD)/computational structure dynamics (CSD) simulation is able to capture the LCO with very small amplitudes measured in the experiment. This is attributed to the high order low diffusion schemes, fully coupled FSI model, and the turbulence model used. This research appears to be the first time that a numerical simulation of LCO matches the experiment. The simulation confirms several observations of the experiment.

  18. 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.

  19. A well-balanced numerical scheme for shallow water simulation on adaptive grids

    NASA Astrophysics Data System (ADS)

    Zhang, H. J.; Zhou, J. Z.; Bi, S.; Li, Q. Q.; Fan, Y.

    2014-04-01

    The efficiency of solving two-dimensional shallow-water equations (SWEs) is vital for simulation of large-scale flood inundation. For flood flows over real topography, local high-resolution method, which uses adaptable grids, is required in order to prevent the loss of accuracy of the flow pattern while saving computational cost. This paper introduces an adaptive grid model, which uses an adaptive criterion calculated on the basis of the water lever. The grid adaption is performed by manipulating subdivision levels of the computation grids. As the flow feature varies during the shallow wave propagation, the local grid density changes adaptively and the stored information of neighbor relationship updates correspondingly, achieving a balance between the model accuracy and running efficiency. In this work, a well-balanced (WB) scheme for solving SWEs is introduced. In reconstructions of Riemann state, the definition of the unique bottom elevation on grid interfaces is modified, and the numerical scheme is pre-balanced automatically. By the validation against two idealist test cases, the proposed model is applied to simulate flood inundation due to a dam-break of Zhanghe Reservoir, Hubei province, China. The results show that the presented model is robust and well-balanced, has nice computational efficiency and numerical stability, and thus has bright application prospects.

  20. Numerical Simulation of Compressible Multi-phase flows using HLLC extension of AUSM +-up Scheme

    NASA Astrophysics Data System (ADS)

    Dhir, Gaurav; Bodi, Kowsik

    2016-11-01

    Solving Multi-fluid equations has always required an onerous effort from researchers with regards to implementing an appropriate numerical scheme which could capture the various facets of such type of flows along with the interaction between the various phases present. Additionally, multi-phase flows bring with them peculiar mathematical properties such as non-hyperbolicity and non-conservativeness which further increases the complexity involved. Our presentation shall present an insight into the advantages and limitations of several numerical schemes proposed in the past and propose to use the HLLC extension of AUSM +-up approach to model such type of flows. We use the single pressure based stratified flow concept and by presenting several test cases, we prove that our method robustly computes multi-phase flow involving discontinuities, such as shock waves and fluid interfaces. Additionally, we present a formulation to incorporate phase transition within multi-fluid equations and establish the validity of this method by presenting several two dimensional test cases such as the Shock-Water Column Interaction problem, the Water-Shock/Air Bubble Interaction problem and the 2D Underwater Explosion problem. Industrial Research and Consultancy Centre, IIT Bombay.

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

    SciTech Connect

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

    2016-06-15

    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.

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

    SciTech Connect

    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.

  3. Orthogonal Metal Cutting Simulation Using Advanced Constitutive Equations with Damage and Fully Adaptive Numerical Procedure

    NASA Astrophysics Data System (ADS)

    Saanouni, Kkemais; Labergère, Carl; Issa, Mazen; Rassineux, Alain

    2010-06-01

    This work proposes a complete adaptive numerical methodology which uses `advanced' elastoplastic constitutive equations coupling: thermal effects, large elasto-viscoplasticity with mixed non linear hardening, ductile damage and contact with friction, for 2D machining simulation. Fully coupled (strong coupling) thermo-elasto-visco-plastic-damage constitutive equations based on the state variables under large plastic deformation developed for metal forming simulation are presented. The relevant numerical aspects concerning the local integration scheme as well as the global resolution strategy and the adaptive remeshing facility are briefly discussed. Applications are made to the orthogonal metal cutting by chip formation and segmentation under high velocity. The interactions between hardening, plasticity, ductile damage and thermal effects and their effects on the adiabatic shear band formation including the formation of cracks are investigated.

  4. Numerical Design of Drawbeads for Advanced High Strength Steel Sheets

    NASA Astrophysics Data System (ADS)

    Keum, Y. T.; Kim, D. J.; Kim, G. S.

    2010-06-01

    The map for designing the drawbeads used in the stamping dies for advanced high strength steel (AHSS) sheets is numerically investigated and its application is introduced. The bending limit of AHSS sheet is determined from the extreme R/t's obtained simulating numerically the plane-strain process formed by the cylindrical punches and dies with various radii. In addition, the forming allowance defined by the difference between FLC0 and the strain after passing the drawbead, which is observed by the numerical simulation of drawbead pulling test, is computed. Based on the bending limit and forming allowance, the design map for determining the height, width, and shoulder radius of the drawbead which are key parameters in the drawbead design and depend on the restraining force is constructed by aid of the equivalent drawbead model. A drawbead of the stamping die for forming a channel-typed panel is designed by using the design map, and the formability and springback of the panel to be formed are numerically evaluated, from which the availability of the design map is demonstrated.

  5. Recent advances to NEC (Numerical Electromagnetics Code): Applications and validation

    SciTech Connect

    Burke, G.J. )

    1989-03-03

    Capabilities of the antenna modeling code NEC are reviewed and results are presented to illustrate typical applications. Recent developments are discussed that will improve accuracy in modeling electrically small antennas, stepped-radius wires and junctions of tightly coupled wires, and also a new capability for modeling insulated wires in air or earth is described. These advances will be included in a future release of NEC, while for now the results serve to illustrate limitations of the present code. NEC results are compared with independent analytical and numerical solutions and measurements to validate the model for wires near ground and for insulated wires. 41 refs., 26 figs., 1 tab.

  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. BTTB-based numerical schemes for three-dimensional gravity field inversion

    NASA Astrophysics Data System (ADS)

    Zhang, Yile; Wong, Yau Shu

    2015-10-01

    This paper presents efficient numerical schemes for 3-D gravity field inversion. We propose a 2-D multilayer model to approximate a 3-D density distribution, and prove that the solution of the multilayer model will converge to the discretized 3-D solution. Differed from the conventional fast Fourier transform (FFT) based methods in which FFT is applied to the kernel, the proposed approach directly generates the Block-Toeplitz Toeplitz-Block (BTTB) structure by discretizing the multilayer model and the BTTB matrix is embedded into a Block-Circulant Circulant-Block (BCCB) matrix such that FFT can be utilized. In this approach, both regularization and optimal pre-conditioning operator can be constructed in the form of BTTB matrix. Consequently, very efficient solvers can be developed, and tremendous reduction in storage requirement and computing time can be achieved. To validate the new approach, numerical simulations using synthetic and real field data are reported, and numerical analysis is carried out for the inversion problems. Based on this study, we conclude that the proposed methods are capable of performing large-scale 3-D density inversions with a modest computing resource.

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

    NASA Technical Reports Server (NTRS)

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

    1989-01-01

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

  9. A benchmark for numerical scheme validation of airborne particle exposure in street canyons.

    PubMed

    Marini, S; Buonanno, G; Stabile, L; Avino, P

    2015-02-01

    Measurements of particle concentrations and distributions in terms of number, surface area, and mass were performed simultaneously at eight sampling points within a symmetric street canyon of an Italian city. The aim was to obtain a useful benchmark for validation of wind tunnel experiments and numerical schemes: to this purpose, the influence of wind directions and speeds was considered. Particle number concentrations (PNCs) were higher on the leeward side than the windward side of the street canyon due to the wind vortex effect. Different vertical PNC profiles were observed between the two canyon sides depending on the wind direction and speed at roof level. A decrease in particle concentrations was observed with increasing rooftop wind speed, except for the coarse fraction indicating a possible particle resuspension due to the traffic and wind motion. This study confirms that particle concentration fields in urban street canyons are strongly influenced by traffic emissions and meteorological parameters, especially wind direction and speed.

  10. 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.

  11. ADI FD schemes for the numerical solution of the three-dimensional Heston-Cox-Ingersoll-Ross PDE

    NASA Astrophysics Data System (ADS)

    Haentjens, Tinne

    2012-09-01

    This paper deals with the numerical solution of the time-dependent, three-dimensional Heston-Cox-Ingersoll- Ross PDE, with all correlations nonzero, for the fair pricing of European call options. We apply a finite difference dis-cretization on non-uniform spatial grids and then numerically solve the semi-discrete system in time by using an Alternating Direction Implicit scheme. We show that this leads to a highly efficient and stable numerical solution method.

  12. Numerical analysis of the V-Y shaped advancement flap.

    PubMed

    Remache, D; Chambert, J; Pauchot, J; Jacquet, E

    2015-10-01

    The V-Y advancement flap is a usual technique for the closure of skin defects. A triangular flap is incised adjacent to a skin defect of rectangular shape. As the flap is advanced to close the initial defect, two smaller defects in the shape of a parallelogram are formed with respect to a reflection symmetry. The height of the defects depends on the apex angle of the flap and the closure efforts are related to the defects height. Andrades et al. 2005 have performed a geometrical analysis of the V-Y flap technique in order to reach a compromise between the flap size and the defects width. However, the geometrical approach does not consider the mechanical properties of the skin. The present analysis based on the finite element method is proposed as a complement to the geometrical one. This analysis aims to highlight the major role of the skin elasticity for a full analysis of the V-Y advancement flap. Furthermore, the study of this technique shows that closing at the flap apex seems mechanically the most interesting step. Thus different strategies of defect closure at the flap apex stemming from surgeon's know-how have been tested by numerical simulations.

  13. 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.

  14. 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).

  15. 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.

  16. Optimal Numerical Schemes for Time Accurate Compressible Large Eddy Simulations: Comparison of Artificial Dissipation and Filtering Schemes

    DTIC Science & Technology

    2014-11-01

    content (ie: low- pass response) 1) compare damping character of Artificial Dissipation and Filtering 2) formulate filter as an equivalent...Artificial Dissipation scheme - consequence of filter damping for stiff problems 3) insight on achieving “ideal” low- pass response for general...require very high order for low- pass response –  overly dissipative for small time-steps •  Implicit filters can be efficiently designed for low- pass

  17. Advanced numerical methods in mesh generation and mesh adaptation

    SciTech Connect

    Lipnikov, Konstantine; Danilov, A; Vassilevski, Y; Agonzal, A

    2010-01-01

    Numerical solution of partial differential equations requires appropriate meshes, efficient solvers and robust and reliable error estimates. Generation of high-quality meshes for complex engineering models is a non-trivial task. This task is made more difficult when the mesh has to be adapted to a problem solution. This article is focused on a synergistic approach to the mesh generation and mesh adaptation, where best properties of various mesh generation methods are combined to build efficiently simplicial meshes. First, the advancing front technique (AFT) is combined with the incremental Delaunay triangulation (DT) to build an initial mesh. Second, the metric-based mesh adaptation (MBA) method is employed to improve quality of the generated mesh and/or to adapt it to a problem solution. We demonstrate with numerical experiments that combination of all three methods is required for robust meshing of complex engineering models. The key to successful mesh generation is the high-quality of the triangles in the initial front. We use a black-box technique to improve surface meshes exported from an unattainable CAD system. The initial surface mesh is refined into a shape-regular triangulation which approximates the boundary with the same accuracy as the CAD mesh. The DT method adds robustness to the AFT. The resulting mesh is topologically correct but may contain a few slivers. The MBA uses seven local operations to modify the mesh topology. It improves significantly the mesh quality. The MBA method is also used to adapt the mesh to a problem solution to minimize computational resources required for solving the problem. The MBA has a solid theoretical background. In the first two experiments, we consider the convection-diffusion and elasticity problems. We demonstrate the optimal reduction rate of the discretization error on a sequence of adaptive strongly anisotropic meshes. The key element of the MBA method is construction of a tensor metric from hierarchical edge

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

    SciTech Connect

    Angstmann, C.N.; Donnelly, I.C.; Henry, B.I.; Jacobs, B.A.; Langlands, T.A.M.; Nichols, J.A.

    2016-02-15

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

  19. NUMERICAL COMPUTATIONS OF CO-EXISTING SUPER-CRITICAL AND SUB-CRITICAL FLOWS BASED UPON CRD SCHEMES

    NASA Astrophysics Data System (ADS)

    Horie, Katsuya; Okamura, Seiji; Kobayashi, Yusuke; Hyodo, Makoto; Hida, Yoshihisa; Nishimoto, Naoshi; Mori, Akio

    Stream flows in steep gradient bed form complicating flow configurations, where co-exist super-critical and sub-critical flows. Computing numerically such flows are the key to successful river management. This study applied CRD schemes to 1D and 2D stream flow computations and proposed genuine ways to eliminate expansion shock waves. Through various cases of computing stream flows conducted, CRD schemes showed that i) conservativeness of discharge and accuracy of four significant figures are ensured, ii) artificial viscosity is not explicitly used for computational stabilization, and thus iii) 1D and 2D computations based upon CRD schemes are applicable to evaluating complicating stream flows for river management.

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

    SciTech Connect

    Dai, William W. Scannapieco, Anthony J.

    2015-11-01

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

  2. 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.

  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. 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.

  5. 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

  6. Linear, first and second-order, unconditionally energy stable numerical schemes for the phase field model of homopolymer blends

    NASA Astrophysics Data System (ADS)

    Yang, Xiaofeng

    2016-12-01

    In this paper, we develop a series of efficient numerical schemes to solve the phase field model for homopolymer blends. The governing system is derived from the energetic variational approach of a total free energy, that consists of a nonlinear logarithmic Flory-Huggins potential, and a gradient entropy with a concentration-dependent de-Gennes type coefficient. The main challenging issue to solve this kind of models numerically is about the time marching problem, i.e., how to develop suitable temporal discretizations for the nonlinear terms in order to preserve the energy stability at the discrete level. We solve this issue in this paper, by developing the first and second order temporal approximation schemes based on the "Invariant Energy Quadratization" method, where all nonlinear terms are treated semi-explicitly. Consequently, the resulting numerical schemes lead to a symmetric positive definite linear system to be solved at each time step. The unconditional energy stabilities are further proved. Various numerical simulations of 2D and 3D are presented to demonstrate the stability and the accuracy of the proposed schemes.

  7. Assessment of the weather research and forecasting model generalized parameterization schemes for advancement of precipitation forecasting in monsoon-driven river basins

    NASA Astrophysics Data System (ADS)

    Sikder, Safat; Hossain, Faisal

    2016-09-01

    Some of the world's largest and flood-prone river basins experience a seasonal flood regime driven by the monsoon weather system. Highly populated river basins with extensive rain-fed agricultural productivity such as the Ganges, Indus, Brahmaputra, Irrawaddy, and Mekong are examples of monsoon-driven river basins. It is therefore appropriate to investigate how precipitation forecasts from numerical models can advance flood forecasting in these basins. In this study, the Weather Research and Forecasting model was used to evaluate downscaling of coarse-resolution global precipitation forecasts from a numerical weather prediction model. Sensitivity studies were conducted using the TOPSIS analysis to identify the likely best set of microphysics and cumulus parameterization schemes, and spatial resolution from a total set of 15 combinations. This identified best set can pinpoint specific parameterizations needing further development to advance flood forecasting in monsoon-dominated regimes. It was found that the Betts-Miller-Janjic cumulus parameterization scheme with WRF Single-Moment 5-class, WRF Single-Moment 6-class, and Thompson microphysics schemes exhibited the most skill in the Ganges-Brahmaputra-Meghna basins. Finer spatial resolution (3 km) without cumulus parameterization schemes did not yield significant improvements. The short-listed set of the likely best microphysics-cumulus parameterization configurations was found to also hold true for the Indus basin. The lesson learned from this study is that a common set of model parameterization and spatial resolution exists for monsoon-driven seasonal flood regimes at least in South Asian river basins.

  8. A hybrid numerical technique for predicting the aerodynamic and acoustic fields of advanced turboprops

    NASA Technical Reports Server (NTRS)

    Homicz, G. F.; Moselle, J. R.

    1985-01-01

    A hybrid numerical procedure is presented for the prediction of the aerodynamic and acoustic performance of advanced turboprops. A hybrid scheme is proposed which in principle leads to a consistent simultaneous prediction of both fields. In the inner flow a finite difference method, the Approximate-Factorization Alternating-Direction-Implicit (ADI) scheme, is used to solve the nonlinear Euler equations. In the outer flow the linearized acoustic equations are solved via a Boundary-Integral Equation (BIE) method. The two solutions are iteratively matched across a fictitious interface in the flow so as to maintain continuity. At convergence the resulting aerodynamic load prediction will automatically satisfy the appropriate free-field boundary conditions at the edge of the finite difference grid, while the acoustic predictions will reflect the back-reaction of the radiated field on the magnitude of the loading source terms, as well as refractive effects in the inner flow. The equations and logic needed to match the two solutions are developed and the computer program implementing the procedure is described. Unfortunately, no converged solutions were obtained, due to unexpectedly large running times. The reasons for this are discussed and several means to alleviate the situation are suggested.

  9. 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.

  10. 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.

  11. Nonstandard Finite Difference Schemes: Relations Between Time and Space Step-Sizes in Numerical Schemes for PDE's That Follow from Positivity Condition

    NASA Technical Reports Server (NTRS)

    Mickens, Ronald E.

    1996-01-01

    A large class of physical phenomena can be modeled by evolution and wave type Partial Differential Equations (PDE). Few of these equations have known explicit exact solutions. Finite-difference techniques are a popular method for constructing discrete representations of these equations for the purpose of numerical integration. However, the solutions to the difference equations often contain so called numerical instabilities; these are solutions to the difference equations that do not correspond to any solution of the PDE's. For explicit schemes, the elimination of this behavior requires functional relations to exist between the time and space steps-sizes. We show that such functional relations can be obtained for certain PDE's by use of a positivity condition. The PDE's studied are the Burgers, Fisher, and linearized Euler equations.

  12. 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.

  13. An Examination of Stability Criteria for Iterative Numerical Schemes Used in Solving Differential Equations

    DTIC Science & Technology

    1981-07-01

    of Defence Farnborough, Hants ""� 31 024 -L~~caJLj UDC 517.956.224 : 517.962.2 519.6 : 518.1 : 517.933 ROYAL AIRCRAFT ESTABLISHMENT Technical...row, H is diagonally dominant. 26 Scheme III If Igj > 2N Scheme II will not be satisfactory. However, now write equation (3-9) in the form 4 + gtx

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

    NASA Astrophysics Data System (ADS)

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

    2015-12-01

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

  15. Recent advances in two-phase flow numerics

    SciTech Connect

    Mahaffy, J.H.; Macian, R.

    1997-07-01

    The authors review three topics in the broad field of numerical methods that may be of interest to individuals modeling two-phase flow in nuclear power plants. The first topic is iterative solution of linear equations created during the solution of finite volume equations. The second is numerical tracking of macroscopic liquid interfaces. The final area surveyed is the use of higher spatial difference techniques.

  16. 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.

  17. Advances in the numerical investigation of the immersion quenching process

    NASA Astrophysics Data System (ADS)

    Zhang, D. S.; Kopun, R.; Kosir, N.; Edelbauer, W.

    2017-01-01

    A numerical investigation of the immersion quenching process is presented in this paper. Immersion quenching is recognized as one of the common ways to achieve the desirable microstructure, and to improve the mechanical properties after thermal treatment. Furthermore it is important to prevent distortion and cracking of the cast parts. Accurate prediction of all three boiling regimes and the heat transfer inside the structure during quenching are important to finally evaluate the residual stresses and deformations of thermally treated parts. Numerical details focus on the handling of the enthalpy with variable specific heat capacity in the solid. For two application cases, comparison between measured and simulated temperatures at different monitoring positions shows very good agreement. The study demonstrates the capability of the present model to overcome the numerical challenges occurring during immersion quenching and it is capable of predicting the complex physics with good accuracy.

  18. 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.

  19. Role of numerical scheme choice on the results of mathematical modeling of combustion and detonation

    NASA Astrophysics Data System (ADS)

    Yakovenko, I. S.; Kiverin, A. D.; Pinevich, S. G.; Ivanov, M. F.

    2016-11-01

    The present study discusses capabilities of dissipation-free CABARET numerical method application to unsteady reactive gasdynamic flows modeling. In framework of present research the method was adopted for reactive flows governed by real gas equation of state and applied for several typical problems of unsteady gas dynamics and combustion modeling such as ignition and detonation initiation by localized energy sources. Solutions were thoroughly analyzed and compared with that derived by using of the modified Euler-Lagrange method of “coarse” particles. Obtained results allowed us to distinguish range of phenomena where artificial effects of numerical approach may counterfeit their physical nature and to develop guidelines for numerical approach selection appropriate for unsteady reactive gasdynamic flows numerical modeling.

  20. Numerical simulation of turbomachinery flows with advanced turbulence models

    NASA Technical Reports Server (NTRS)

    Lakshminarayana, B.; Kunz, R.; Luo, J.; Fan, S.

    1992-01-01

    A three dimensional full Navier-Stokes (FNS) code is used to simulate complex turbomachinery flows. The code incorporates an explicit multistep scheme and solves a conservative form of the density averaged continuity, momentum, and energy equations. A compressible low Reynolds number form of the k-epsilon turbulence model, and a q-omega model and an algebraic Reynolds stress model have been incorporated in a fully coupled manner to approximate Reynolds stresses. The code is used to predict the viscous flow field in a backswept transonic centrifugal compressor for which laser two focus data is available. The code is also used to simulate the tip clearance flow in a cascade. The code has been extended to include unsteady Euler solutions for predicting the unsteady flow through a cascade due to incoming wakes, simulating rotor-stator interactions.

  1. Recent advances in numerical analysis of structural eigenvalue problems

    NASA Technical Reports Server (NTRS)

    Gupta, K. K.

    1973-01-01

    A wide range of eigenvalue problems encountered in practical structural engineering analyses is defined, in which the structures are assumed to be discretized by any suitable technique such as the finite-element method. A review of the usual numerical procedures for the solution of such eigenvalue problems is presented and is followed by an extensive account of recently developed eigenproblem solution procedures. Particular emphasis is placed on the new numerical algorithms and associated computer programs based on the Sturm sequence method. Eigenvalue algorithms developed for efficient solution of natural frequency and buckling problems of structures are presented, as well as some eigenvalue procedures formulated in connection with the solution of quadratic matrix equations associated with free vibration analysis of structures. A new algorithm is described for natural frequency analysis of damped structural systems.

  2. Validation Testing and Numerical Modeling of Advanced Armor Materials

    DTIC Science & Technology

    2012-11-01

    constitutive material strength response with an appropriate yield surface model. The research is sub-divided into three areas: engineering design...and specimen preparation for Taylor impact testing, analytical solution for the dynamic yield strength of the materials used, and numerical modeling...aluminum alloy only. We perform a detailed analysis of the deformed specimen shapes to determine the dynamic yield strength . Additionally, hydrocode

  3. 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.

  4. A Numerical Scheme for Computing Stable and Unstable Manifolds in Nonautonomous Flows

    NASA Astrophysics Data System (ADS)

    Balasuriya, Sanjeeva

    2016-12-01

    There are many methods for computing stable and unstable manifolds in autonomous flows. When the flow is nonautonomous, however, difficulties arise since the hyperbolic trajectory to which these manifolds are anchored, and the local manifold emanation directions, are changing with time. This article utilizes recent results which approximate the time-variation of both these quantities to design a numerical algorithm which can obtain high resolution in global nonautonomous stable and unstable manifolds. In particular, good numerical approximation is possible locally near the anchor trajectory. Nonautonomous manifolds are computed for two examples: a Rossby wave situation which is highly chaotic, and a nonautonomus (time-aperiodic) Duffing oscillator model in which the manifold emanation directions are rapidly changing. The numerical method is validated and analyzed in these cases using finite-time Lyapunov exponent fields and exactly known nonautonomous manifolds.

  5. Advanced Physical Models and Numerical Methods for High Enthalpy and Plasma Flows Applied to Hypersonics

    DTIC Science & Technology

    2011-07-28

    nonequilibrium. For example, the plasma transport may transition between rarefied and continuum flow , requiring appropriate models for each case through...AFRL-AFOSR-UK-TR-2011-0023 Advanced Physical Models and Numerical Methods for High Enthalpy and Plasma Flows Applied to Hypersonics...2010 4. TITLE AND SUBTITLE Advanced Physical Models and Numerical Methods for High Enthalpy and Plasma Flows Applied to Hypersonics 5a

  6. Numerical study of a finite volume scheme for incompressible Navier-Stokes equations based on SIMPLE-family algorithms

    NASA Astrophysics Data System (ADS)

    Alahyane, M.; Hakim, A.; Raghay, S.

    2017-01-01

    In this work, we present a numerical study of a finite volume scheme based on SIMPLE algorithm for incompressible Navier-Stokes problem. However, this algorithm still not applicable to a large category of problems this could be understood from its stability and convergence, which depends strongly on the parameter of relaxation, in some cases this algorithm could have an unexpected behavior. Therefore, in our work we focus on this particular point to overcome this respected choice of relaxation parameter and to find a sufficient condition for the convergence of the algorithm in general cases. This will be followed by numerical applications in image processing variety of fluid flow problems described by incompressible Navier-Stokes equations.

  7. Generation of a composite grid for turbine flows and consideration of a numerical scheme

    NASA Technical Reports Server (NTRS)

    Choo, Y.; Yoon, S.; Reno, C.

    1986-01-01

    A composite grid was generated for flows in turbines. It consisted of the C-grid (or O-grid) in the immediate vicinity of the blade and the H-grid in the middle of the blade passage between the C-grids and in the upstream region. This new composite grid provides better smoothness, resolution, and orthogonality than any single grid for a typical turbine blade with a large camber and rounded leading and trailing edges. The C-H (or O-H) composite grid has an unusual grid point that is connected to more than four neighboring nodes in two dimensions (more than six neighboring nodes in three dimensions). A finite-volume lower-upper (LU) implicit scheme to be used on this grid poses no problem and requires no special treatment because each interior cell of this composite grid has only four neighboring cells in two dimensions (six cells in three dimensions). The LU implicit scheme was demonstrated to be efficient and robust for external flows in a broad flow regime and can be easily applied to internal flows and extended from two to three dimensions.

  8. Numerical simulation of a Richtmyer-Meshkov instability with an adaptive central-upwind sixth-order WENO scheme

    NASA Astrophysics Data System (ADS)

    Tritschler, V. K.; Hu, X. Y.; Hickel, S.; Adams, N. A.

    2013-07-01

    Two-dimensional simulations of the single-mode Richtmyer-Meshkov instability (RMI) are conducted and compared to experimental results of Jacobs and Krivets (2005 Phys. Fluids 17 034105). The employed adaptive central-upwind sixth-order weighted essentially non-oscillatory (WENO) scheme (Hu et al 2010 J. Comput. Phys. 229 8952-65) introduces only very small numerical dissipation while preserving the good shock-capturing properties of other standard WENO schemes. Hence, it is well suited for simulations with both small-scale features and strong gradients. A generalized Roe average is proposed to make the multicomponent model of Shyue (1998 J. Comput. Phys. 142 208-42) suitable for high-order accurate reconstruction schemes. A first sequence of single-fluid simulations is conducted and compared to the experiment. We find that the WENO-CU6 method better resolves small-scale structures, leading to earlier symmetry breaking and increased mixing. The first simulation, however, fails to correctly predict the global characteristic structures of the RMI. This is due to a mismatch of the post-shock parameters in single-fluid simulations when the pre-shock states are matched with the experiment. When the post-shock parameters are matched, much better agreement with the experimental data is achieved. In a sequence of multifluid simulations, the uncertainty in the density gradient associated with transition between the fluids is assessed. Thereby the multifluid simulations show a considerable improvement over the single-fluid simulations.

  9. Advances and Challenges in Numerical Weather and Climate Prediction

    NASA Astrophysics Data System (ADS)

    Yu, Tsann-Wang

    2010-10-01

    In this review article, the dispersive nature of various waves that exist in the atmosphere is first reviewed. These waves include Rossby waves, Kelvin wave, acoustic wave, internal and external gravity waves and many others, whose intrinsic nature and great relevancy to weather and climate forecasts are described. This paper then describes the latest development in global observations and data analysis and assimilation methodologies. These include three-dimensional and four dimensional variational data assimilation systems that are being used in the world's major operational weather and climate forecasting centers. Some of the recent results in using novel atmospheric satellite and chemical observation data applied to these data assimilation systems and those from the latest development in high resolution modeling and the ensemble forecasting approach in the operational numerical weather forecasting centers are also presented. Finally, problems of inherent errors associated with initial conditions, and those associated with the coupling of dynamics and physics and their related numerical issues in variational data assimilation systems are discussed.

  10. Basic and advanced numerical performances relate to mathematical expertise but are fully mediated by visuospatial skills.

    PubMed

    Sella, Francesco; Sader, Elie; Lolliot, Simon; Cohen Kadosh, Roi

    2016-09-01

    Recent studies have highlighted the potential role of basic numerical processing in the acquisition of numerical and mathematical competences. However, it is debated whether high-level numerical skills and mathematics depends specifically on basic numerical representations. In this study mathematicians and nonmathematicians performed a basic number line task, which required mapping positive and negative numbers on a physical horizontal line, and has been shown to correlate with more advanced numerical abilities and mathematical achievement. We found that mathematicians were more accurate compared with nonmathematicians when mapping positive, but not negative numbers, which are considered numerical primitives and cultural artifacts, respectively. Moreover, performance on positive number mapping could predict whether one is a mathematician or not, and was mediated by more advanced mathematical skills. This finding might suggest a link between basic and advanced mathematical skills. However, when we included visuospatial skills, as measured by block design subtest, the mediation analysis revealed that the relation between the performance in the number line task and the group membership was explained by non-numerical visuospatial skills. These results demonstrate that relation between basic, even specific, numerical skills and advanced mathematical achievement can be artifactual and explained by visuospatial processing. (PsycINFO Database Record

  11. Basic and Advanced Numerical Performances Relate to Mathematical Expertise but Are Fully Mediated by Visuospatial Skills

    PubMed Central

    2016-01-01

    Recent studies have highlighted the potential role of basic numerical processing in the acquisition of numerical and mathematical competences. However, it is debated whether high-level numerical skills and mathematics depends specifically on basic numerical representations. In this study mathematicians and nonmathematicians performed a basic number line task, which required mapping positive and negative numbers on a physical horizontal line, and has been shown to correlate with more advanced numerical abilities and mathematical achievement. We found that mathematicians were more accurate compared with nonmathematicians when mapping positive, but not negative numbers, which are considered numerical primitives and cultural artifacts, respectively. Moreover, performance on positive number mapping could predict whether one is a mathematician or not, and was mediated by more advanced mathematical skills. This finding might suggest a link between basic and advanced mathematical skills. However, when we included visuospatial skills, as measured by block design subtest, the mediation analysis revealed that the relation between the performance in the number line task and the group membership was explained by non-numerical visuospatial skills. These results demonstrate that relation between basic, even specific, numerical skills and advanced mathematical achievement can be artifactual and explained by visuospatial processing. PMID:26913930

  12. Numerical simulations of non-equilibrium shock layers with efficient implicit schemes

    NASA Technical Reports Server (NTRS)

    Cambier, Jean-Luc; Prabhu, Dinesh K.

    1992-01-01

    Current and future calculations of nonequilibrium shock layers require the use of a very large number of equations, due to a multiplicity of chemical species, excited states, and internal energy modes. The computational cost associated with the use of standard implicit methods becomes prohibitive; it is therefore desirable to examine the potential of several methods and determine if any can be projected to be more efficient and accurate for large systems of equations. Here, the performance of several implicit schemes on several simple practical examples of reacting flows is examined. The Euler equations are solved by three different implicit methods, and two methods of coupling between the fluid dynamics and the chemistry are studied. Several cases of stiffness are considered and both 1D and 2D examples are computed.

  13. 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.

  14. A one-parameter family of difference schemes for the numerical solution of the Keplerian problem

    NASA Astrophysics Data System (ADS)

    Elenin, G. G.; Elenina, T. G.

    2015-08-01

    A family of numerical methods for solving the Keplerian problem is proposed. All the methods in this family are symplectic. They preserve the angular momentum, the total energy, the components of the Laplace-Runge-Lenz vector, and the phase volume. The underlying idea is an exact linearization of the problem based on the Levi-Civita transformation and two-stage symmetricsymplectic Runge-Kutta methods.

  15. 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.

  16. Numerical modeling of spray combustion with an advanced VOF method

    NASA Technical Reports Server (NTRS)

    Chen, Yen-Sen; Shang, Huan-Min; Shih, Ming-Hsin; Liaw, Paul

    1995-01-01

    This paper summarizes the technical development and validation of a multiphase computational fluid dynamics (CFD) numerical method using the volume-of-fluid (VOF) model and a Lagrangian tracking model which can be employed to analyze general multiphase flow problems with free surface mechanism. The gas-liquid interface mass, momentum and energy conservation relationships are modeled by continuum surface mechanisms. A new solution method is developed such that the present VOF model can be applied for all-speed flow regimes. The objectives of the present study are to develop and verify the fractional volume-of-fluid cell partitioning approach into a predictor-corrector algorithm and to demonstrate the effectiveness of the present approach by simulating benchmark problems including laminar impinging jets, shear coaxial jet atomization and shear coaxial spray combustion flows.

  17. Advances in numerical solutions to integral equations in liquid state theory

    NASA Astrophysics Data System (ADS)

    Howard, Jesse J.

    Solvent effects play a vital role in the accurate description of the free energy profile for solution phase chemical and structural processes. The inclusion of solvent effects in any meaningful theoretical model however, has proven to be a formidable task. Generally, methods involving Poisson-Boltzmann (PB) theory and molecular dynamic (MD) simulations are used, but they either fail to accurately describe the solvent effects or require an exhaustive computation effort to overcome sampling problems. An alternative to these methods are the integral equations (IEs) of liquid state theory which have become more widely applicable due to recent advancements in the theory of interaction site fluids and the numerical methods to solve the equations. In this work a new numerical method is developed based on a Newton-type scheme coupled with Picard/MDIIS routines. To extend the range of these numerical methods to large-scale data systems, the size of the Jacobian is reduced using basis functions, and the Newton steps are calculated using a GMRes solver. The method is then applied to calculate solutions to the 3D reference interaction site model (RISM) IEs of statistical mechanics, which are derived from first principles, for a solute model of a pair of parallel graphene plates at various separations in pure water. The 3D IEs are then extended to electrostatic models using an exact treatment of the long-range Coulomb interactions for negatively charged walls and DNA duplexes in aqueous electrolyte solutions to calculate the density profiles and solution thermodynamics. It is found that the 3D-IEs provide a qualitative description of the density distributions of the solvent species when compared to MD results, but at a much reduced computational effort in comparison to MD simulations. The thermodynamics of the solvated systems are also qualitatively reproduced by the IE results. The findings of this work show the IEs to be a valuable tool for the study and prediction of

  18. 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.

  19. Plasma evolution regulations with the change of initial conditions of femtosecond laser and an optical detecting scheme is verified numerically

    NASA Astrophysics Data System (ADS)

    Hu, Yuze; Nie, Jinsong; Wang, Haitao; Wang, Lei; Dou, Xianan

    2016-10-01

    The plasma channel evolution tendencies are studied numerically with the change of initial conditions based on the Nonlinear Schrödinger Equation. Then, the accuracy of an optical scheme to detect the plasma density inside the filaments is certified numerically. A Gaussian beam with pulse width 50fs, radius 2.5mm ranging energy from 10mJ to 50mJ at interval of 10mJ are simulated to yield plasma channel. With the augment of energy, firstly, the beginning position of plasma channel tend to be drew back gradually whereas the end position of the channel can be putted forward in a gradient form instead of continuously. Secondly, the number of peaks add one each time when the energy increase 10mJ. Lastly, the radius of plasma channel barely changes with initial energy up from 10mJ to 50mJ. On the other hand, plasma channel produced by a Gaussian beam with pulse width 50fs, energy 50mJ ranging the radius from 2.5mm to 10mm at interval of 2.5mm are simulated. With the increase of initial beam waist, the plasma channel length becomes shorter. The channel becomes broader and broader whereas the length of the channel becomes shorter. In order to verify the rationality of the approximation, Nornaraki detecting scheme through interference of the probe laser has been tested with the numerical simulation. As a consequence, the integral of refractive index along the radius direction can be replaced by the product of average refractive index and plasma channel diameter.

  20. 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.

  1. High security chaotic multiple access scheme for visible light communication systems with advanced encryption standard interleaving

    NASA Astrophysics Data System (ADS)

    Qiu, Junchao; Zhang, Lin; Li, Diyang; Liu, Xingcheng

    2016-06-01

    Chaotic sequences can be applied to realize multiple user access and improve the system security for a visible light communication (VLC) system. However, since the map patterns of chaotic sequences are usually well known, eavesdroppers can possibly derive the key parameters of chaotic sequences and subsequently retrieve the information. We design an advanced encryption standard (AES) interleaving aided multiple user access scheme to enhance the security of a chaotic code division multiple access-based visible light communication (C-CDMA-VLC) system. We propose to spread the information with chaotic sequences, and then the spread information is interleaved by an AES algorithm and transmitted over VLC channels. Since the computation complexity of performing inverse operations to deinterleave the information is high, the eavesdroppers in a high speed VLC system cannot retrieve the information in real time; thus, the system security will be enhanced. Moreover, we build a mathematical model for the AES-aided VLC system and derive the theoretical information leakage to analyze the system security. The simulations are performed over VLC channels, and the results demonstrate the effectiveness and high security of our presented AES interleaving aided chaotic CDMA-VLC system.

  2. A discontinuous wave-in-cell numerical scheme for hyperbolic conservation laws

    NASA Astrophysics Data System (ADS)

    Thompson, Richard J.; Moeller, Trevor

    2015-10-01

    A new Riemann solver scheme for hyperbolic systems is introduced. The method consists of a discretization of the initial data into an approximate representation by discrete, discontinuous waves. Instead of calculating an intercell flux based on these waves, the discontinuous waves are propagated directly. Since the sum total of all discontinuous waves represents an extension of the linear Riemann problem, the solution is determined straightforwardly. For nonlinear systems, each timestep is considered a separate linear Riemann problem, and the projected waves are weighted to a background grid. This method is strikingly similar to the particle-in-cell approach, except that discontinuous waves are pushed around instead of macroparticles. The method is applied to Maxwell's equations and the equations of inviscid gasdynamics. For linear systems, exact solutions can be achieved without dissipation, and exact transmissive boundary condition treatments are trivial to implement. For inviscid gasdynamics, the nonlinear method tended to resolve discontinuities more sharply than the Roe, HLL or HLLC methods while requiring only between 30% and 50% of the execution time under identical conditions. The approach is also extremely robust, as it works for any Courant number. In the limit that the Courant number becomes infinite, the nonlinear solution approaches the linearized solution.

  3. Improved computational schemes for the numerical modeling of hydrothermal resources in Wyoming

    SciTech Connect

    Heasler, H.P.; George, J.H.; Allen, M.B.

    1990-05-01

    A new method, the Conjugate Gradient Squared (CGS) solution technique, is shown to be extremely effective when applied to the finite-difference solution of conductive and convective heat transfer in geologic systems. The CGS method is compared to the Successive Over/Under Relaxation schemes, a version of the Gaussian elimination method, and the Generalized Minimum Residual (GMRES) approach. The CGS procedure converges at least ten times faster than the nearest competitor. The model is applied to the Thermopolis hydrothermal system, located in northwestern Wyoming. Modeled results are compared with measured temperature-depth profiles and results from other studies. The temperature decrease from 72{degree}C to 54{degrees}C along the crest of the Thermopolis anticline is shown to result from cooling of the geothermal fluid as it moves to the southeast. Modeled results show correct general trends, however, a time-varying three-dimensional model will be needed to fully explain the effects of mixing within the aquifers along the crest of the anticline and thermal affects of surface surface topography. 29 refs., 18 figs., 2 tabs.

  4. Q-S (lag or anticipated) synchronization backstepping scheme in a class of continuous-time hyperchaotic systems--a symbolic-numeric computation approach.

    PubMed

    Yan, Zhenya

    2005-06-01

    First, a Q-S (lag or anticipated) synchronization of continuous-time dynamical systems is defined. Second, based on a backstepping design with one controller, a systematic, concrete, and automatic scheme is developed to investigate the Q-S (lag or anticipated) synchronization between the drive system and response system with a strict-feedback form. Two identical hyperchaotic Tamasevicius-Namajunas-Cenys(TNC) systems as well as the hyperchaotic TNC system and hyperchaotic Rossler system are chosen to illustrate the proposed scheme. Numerical simulations are used to verify the effectiveness of the proposed scheme. The scheme can also be extended to study Q-S (lag or anticipated) synchronization between other dynamical systems with strict-feedback forms. With the aid of symbolic-numeric computation, the scheme can be performed to yield automatically the scalar controller in computer.

  5. Numerical optimization design of advanced transonic wing configurations

    NASA Technical Reports Server (NTRS)

    Cosentino, G. B.; Holst, T. L.

    1985-01-01

    A computationally efficient and versatile technique for use in the design of advanced transonic wing configurations has been developed. A reliable and fast transonic wing flow-field analysis program, TWING, has been coupled with a modified quasi-Newton method, unconstrained optimization algorithm, QNMDIF, to create a new design tool. Fully three-dimensional wing designs utilizing both specified wing pressure disributions and drag-to-lift ratio minimization as design objectives are demonstrated. Because of the high computational efficiency of each of the components of the design code, in particular the vectorization of TWING and the high speed of the Cray X-MP vector computer, the computer time required for a typical wing design is reduced by approximately an order of magnitude over previous methods. In the results presented here, this computed wave drag has been used as the quantity to be optimized (minimized) with great success, yielding wing designs with nearly shock-free (zero wave drag) pressure distributions and very reasonable wing section shapes.

  6. Numerical optimization design of advanced transonic wing configurations

    NASA Technical Reports Server (NTRS)

    Cosentino, G. B.; Holst, T. L.

    1984-01-01

    A computationally efficient and versatile technique for use in the design of advanced transonic wing configurations has been developed. A reliable and fast transonic wing flow-field analysis program, TWING, has been coupled with a modified quasi-Newton method, unconstrained optimization algorithm, QNMDIF, to create a new design tool. Fully three-dimensional wing designs utilizing both specified wing pressure distributions and drag-to-lift ration minimization as design objectives are demonstrated. Because of the high computational efficiency of each of the components of the design code, in particular the vectorization of TWING and the high speed of the Cray X-MP vector computer, the computer time required for a typical wing design is reduced by approximately an order of magnitude over previous methods. In the results presented here, this computed wave drag has been used as the quantity to be optimized (minimized) with great success, yielding wing designs with nearly shock-free (zero wave drag) pressure distributions and very reasonable wing section shapes.

  7. The grid-based fast multipole method--a massively parallel numerical scheme for calculating two-electron interaction energies.

    PubMed

    Toivanen, Elias A; Losilla, Sergio A; Sundholm, Dage

    2015-12-21

    Algorithms and working expressions for a grid-based fast multipole method (GB-FMM) have been developed and implemented. The computational domain is divided into cubic subdomains, organized in a hierarchical tree. The contribution to the electrostatic interaction energies from pairs of neighboring subdomains is computed using numerical integration, whereas the contributions from further apart subdomains are obtained using multipole expansions. The multipole moments of the subdomains are obtained by numerical integration. Linear scaling is achieved by translating and summing the multipoles according to the tree structure, such that each subdomain interacts with a number of subdomains that are almost independent of the size of the system. To compute electrostatic interaction energies of neighboring subdomains, we employ an algorithm which performs efficiently on general purpose graphics processing units (GPGPU). Calculations using one CPU for the FMM part and 20 GPGPUs consisting of tens of thousands of execution threads for the numerical integration algorithm show the scalability and parallel performance of the scheme. For calculations on systems consisting of Gaussian functions (α = 1) distributed as fullerenes from C20 to C720, the total computation time and relative accuracy (ppb) are independent of the system size.

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

    SciTech Connect

    Ohsuga, Ken; Takahashi, Hiroyuki R.

    2016-02-20

    We develop a numerical scheme for solving the equations of fully special relativistic, radiation magnetohydrodynamics (MHDs), in which the frequency-integrated, time-dependent radiation transfer equation is solved to calculate the specific intensity. The radiation energy density, the radiation flux, and the radiation stress tensor are obtained by the angular quadrature of the intensity. In the present method, conservation of total mass, momentum, and energy of the radiation magnetofluids is guaranteed. We treat not only the isotropic scattering but also the Thomson scattering. The numerical method of MHDs is the same as that of our previous work. The advection terms are 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.

  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. 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.

  11. 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.

  12. Hybrid Semi-numerical Simulation Scheme to Predict Transducer Outputs of Acoustic Microscopes.

    PubMed

    Nierla, Michael; Rupitsch, Stefan

    2015-12-18

    We present a semi-numerical simulation method called SIRFEM, which enables the efficient prediction of high frequency transducer outputs. In particular, this is important for acoustic microscopy where the specimen under investigation is immersed in a coupling fluid. Conventional Finite Element (FE) simulations for such applications would consume too much computational power due to the required spatial and temporal discretization, especially for the coupling fluid between ultrasonic transducer and specimen. However, FE simulations are in most cases essential to consider the mode conversion at and inside the solid specimen as well as the wave propagation in its interior. SIRFEM reduces the computational effort of pure FE simulations by treating only the solid specimen and a small part of the fluid layer with FE. The propagation in the coupling fluid from transducer to specimen and back is processed by the so-called spatial impulse response (SIR). Through this hybrid approach, the number of elements as well as the number of time steps for the FE simulation can be reduced significantly, as it is presented for an axis-symmetric setup. Three B-mode images of a plane 2-D setup - computed at a transducer center frequency of 20 MHz - show that SIRFEM is, furthermore, able to predict reflections at inner structures as well as multiple reflections between those structures and the specimen's surface. For the purpose of a pure 2-D setup, the spatial impulse response of a curved-line transducer is derived and compared to the response function of a cylindrically focused aperture of negligible extend in the third spatial dimension.

  13. Modeling Small Exoplanets Interiors: a Numerical Scheme to Explore Possible Compositions

    NASA Astrophysics Data System (ADS)

    Brugger, B.; Mousis, O.; Deleuil, M.

    2016-12-01

    Despite the huge number of discovered exoplanets, our knowledge of their compositions remains extremely limited. Modeling the interiors of such bodies is necessary to go further than the first approximation given by their mean density. Here we present a numerical model aiming at computing the internal structure of a given exoplanet from its measured mass and radius, and providing a range of compositions compatible with these data. Our model assumes the presence of a metal core surrounded by a silicate mantle and a water layer. Depending on their respective proportions, we can model various compositions, typically from terrestrial planets to ocean or Mercury-like planets. We apply this model to the case of CoRoT-7b, whose mass and radius values have recently been updated to 4.73 ± 0.95% mearth and 1.585 ± 0.064 rearth, respectively. We show that these values are fully compatible with a solid composition, and find that CoRoT-7b may present a core mass fraction of 80% at maximum, or on the opposite, a maximum water mass fraction of 51%. If this latter composition is compatible with that of several icy moons in the solar system, a 80% core in mass is less conceivable and a lower limit can be placed from solar system formation conditions. These results confirm the Super-Earth status of CoRoT-7b, and show that an Earth-like composition may be obtained more easily compared to previous conclusions.

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

    NASA Astrophysics Data System (ADS)

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

    2014-07-01

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

  15. Technical note: Improving the AWAT filter with interpolation schemes for advanced processing of high resolution data

    NASA Astrophysics Data System (ADS)

    Peters, Andre; Nehls, Thomas; Wessolek, Gerd

    2016-06-01

    Weighing lysimeters with appropriate data filtering yield the most precise and unbiased information for precipitation (P) and evapotranspiration (ET). A recently introduced filter scheme for such data is the AWAT (Adaptive Window and Adaptive Threshold) filter (Peters et al., 2014). The filter applies an adaptive threshold to separate significant from insignificant mass changes, guaranteeing that P and ET are not overestimated, and uses a step interpolation between the significant mass changes. In this contribution we show that the step interpolation scheme, which reflects the resolution of the measuring system, can lead to unrealistic prediction of P and ET, especially if they are required in high temporal resolution. We introduce linear and spline interpolation schemes to overcome these problems. To guarantee that medium to strong precipitation events abruptly following low or zero fluxes are not smoothed in an unfavourable way, a simple heuristic selection criterion is used, which attributes such precipitations to the step interpolation. The three interpolation schemes (step, linear and spline) are tested and compared using a data set from a grass-reference lysimeter with 1 min resolution, ranging from 1 January to 5 August 2014. The selected output resolutions for P and ET prediction are 1 day, 1 h and 10 min. As expected, the step scheme yielded reasonable flux rates only for a resolution of 1 day, whereas the other two schemes are well able to yield reasonable results for any resolution. The spline scheme returned slightly better results than the linear scheme concerning the differences between filtered values and raw data. Moreover, this scheme allows continuous differentiability of filtered data so that any output resolution for the fluxes is sound. Since computational burden is not problematic for any of the interpolation schemes, we suggest always using the spline scheme.

  16. Numerical scheme for non-linear model of supercritical fluid extraction from polydisperse ground plant material: single transport system

    NASA Astrophysics Data System (ADS)

    Salamatin, A.

    2016-11-01

    Numerical algorithm is developed for modelling non-linear mass transfer process in supercritical fluid extraction (SFE). The ground raw material is considered as polydisperse, characterized by discrete number of effective particle fractions. Two continuous interacting counterparts separated by permeable membrane are distinguished in plant material build-up. The apoplast plays role of transport channels during extraction, and symplast contains extractable oil. The complete SFE model is non-linear as a result of non-linearity of oil dissolution kinetics. The computational scheme is based on the finite-volume approximation method and Thomas elimination procedure. The resulting system of algebraic equations is solved iteratively. Special attention is paid to polydisperse substrates, when particle scale characteristics of all fractions interact with each other through pore phase concentration on the vessel scale. Stability of the developed algorithm is demonstrated in numerical tests. Special iterative procedure guarantees a monotonic decrease of oil content in individual particles of substrate. It is also shown that in the limit of the so-called shrinking core approach the number of mesh nodes on a particle scale should be increased.

  17. BOOK REVIEW: Advanced Topics in Computational Partial Differential Equations: Numerical Methods and Diffpack Programming

    NASA Astrophysics Data System (ADS)

    Katsaounis, T. D.

    2005-02-01

    The scope of this book is to present well known simple and advanced numerical methods for solving partial differential equations (PDEs) and how to implement these methods using the programming environment of the software package Diffpack. A basic background in PDEs and numerical methods is required by the potential reader. Further, a basic knowledge of the finite element method and its implementation in one and two space dimensions is required. The authors claim that no prior knowledge of the package Diffpack is required, which is true, but the reader should be at least familiar with an object oriented programming language like C++ in order to better comprehend the programming environment of Diffpack. Certainly, a prior knowledge or usage of Diffpack would be a great advantage to the reader. The book consists of 15 chapters, each one written by one or more authors. Each chapter is basically divided into two parts: the first part is about mathematical models described by PDEs and numerical methods to solve these models and the second part describes how to implement the numerical methods using the programming environment of Diffpack. Each chapter closes with a list of references on its subject. The first nine chapters cover well known numerical methods for solving the basic types of PDEs. Further, programming techniques on the serial as well as on the parallel implementation of numerical methods are also included in these chapters. The last five chapters are dedicated to applications, modelled by PDEs, in a variety of fields. The first chapter is an introduction to parallel processing. It covers fundamentals of parallel processing in a simple and concrete way and no prior knowledge of the subject is required. Examples of parallel implementation of basic linear algebra operations are presented using the Message Passing Interface (MPI) programming environment. Here, some knowledge of MPI routines is required by the reader. Examples solving in parallel simple PDEs using

  18. 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.

  19. 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.

  20. Physical control oriented model of large scale refrigerators to synthesize advanced control schemes. Design, validation, and first control results

    NASA Astrophysics Data System (ADS)

    Bonne, François; Alamir, Mazen; Bonnay, Patrick

    2014-01-01

    In this paper, a physical method to obtain control-oriented dynamical models of large scale cryogenic refrigerators is proposed, in order to synthesize model-based advanced control schemes. These schemes aim to replace classical user experience designed approaches usually based on many independent PI controllers. This is particularly useful in the case where cryoplants are submitted to large pulsed thermal loads, expected to take place in the cryogenic cooling systems of future fusion reactors such as the International Thermonuclear Experimental Reactor (ITER) or the Japan Torus-60 Super Advanced Fusion Experiment (JT-60SA). Advanced control schemes lead to a better perturbation immunity and rejection, to offer a safer utilization of cryoplants. The paper gives details on how basic components used in the field of large scale helium refrigeration (especially those present on the 400W @1.8K helium test facility at CEA-Grenoble) are modeled and assembled to obtain the complete dynamic description of controllable subsystems of the refrigerator (controllable subsystems are namely the Joule-Thompson Cycle, the Brayton Cycle, the Liquid Nitrogen Precooling Unit and the Warm Compression Station). The complete 400W @1.8K (in the 400W @4.4K configuration) helium test facility model is then validated against experimental data and the optimal control of both the Joule-Thompson valve and the turbine valve is proposed, to stabilize the plant under highly variable thermals loads. This work is partially supported through the European Fusion Development Agreement (EFDA) Goal Oriented Training Program, task agreement WP10-GOT-GIRO.

  1. Physical control oriented model of large scale refrigerators to synthesize advanced control schemes. Design, validation, and first control results

    SciTech Connect

    Bonne, François; Bonnay, Patrick

    2014-01-29

    In this paper, a physical method to obtain control-oriented dynamical models of large scale cryogenic refrigerators is proposed, in order to synthesize model-based advanced control schemes. These schemes aim to replace classical user experience designed approaches usually based on many independent PI controllers. This is particularly useful in the case where cryoplants are submitted to large pulsed thermal loads, expected to take place in the cryogenic cooling systems of future fusion reactors such as the International Thermonuclear Experimental Reactor (ITER) or the Japan Torus-60 Super Advanced Fusion Experiment (JT-60SA). Advanced control schemes lead to a better perturbation immunity and rejection, to offer a safer utilization of cryoplants. The paper gives details on how basic components used in the field of large scale helium refrigeration (especially those present on the 400W @1.8K helium test facility at CEA-Grenoble) are modeled and assembled to obtain the complete dynamic description of controllable subsystems of the refrigerator (controllable subsystems are namely the Joule-Thompson Cycle, the Brayton Cycle, the Liquid Nitrogen Precooling Unit and the Warm Compression Station). The complete 400W @1.8K (in the 400W @4.4K configuration) helium test facility model is then validated against experimental data and the optimal control of both the Joule-Thompson valve and the turbine valve is proposed, to stabilize the plant under highly variable thermals loads. This work is partially supported through the European Fusion Development Agreement (EFDA) Goal Oriented Training Program, task agreement WP10-GOT-GIRO.

  2. Advanced numerical analyses for complex thermal-hydraulics in nuclear engineering

    SciTech Connect

    Seiichi Koshizuka; Yoshiaki Oka

    2002-07-01

    Complex thermal-hydraulic phenomena in the nuclear engineering have been solved by advanced numerical analyses based on fundamental governing equations excluding experimental correlations. A new method, called Moving Particle Semi-implicit (MPS) method, is developed as one of the advanced methods. Governing equations are discretized to particle dynamics using particle interaction models. Grids are not necessary. Therefore, complex motion of interfaces can be calculated without grid tangling or numerical diffusion. This is advantageous to multi-fluid and multi-phase thermal-hydraulic problems which emerge in the nuclear engineering. The analyzed problems are vapor explosions, molten core-concrete interaction, fluid-structure interaction, nucleate boiling, transient boiling at reactivity initiated accidents, and the critical Weber number for droplet breakup. These examples show that the MPS method is being useful for direct simulation of complex thermal-hydraulics, particularly multi-phase flows, in the nuclear engineering. (authors)

  3. Left ventricular flow analysis: recent advances in numerical methods and applications in cardiac ultrasound.

    PubMed

    Borazjani, Iman; Westerdale, John; McMahon, Eileen M; Rajaraman, Prathish K; Heys, Jeffrey J; Belohlavek, Marek

    2013-01-01

    The left ventricle (LV) pumps oxygenated blood from the lungs to the rest of the body through systemic circulation. The efficiency of such a pumping function is dependent on blood flow within the LV chamber. It is therefore crucial to accurately characterize LV hemodynamics. Improved understanding of LV hemodynamics is expected to provide important clinical diagnostic and prognostic information. We review the recent advances in numerical and experimental methods for characterizing LV flows and focus on analysis of intraventricular flow fields by echocardiographic particle image velocimetry (echo-PIV), due to its potential for broad and practical utility. Future research directions to advance patient-specific LV simulations include development of methods capable of resolving heart valves, higher temporal resolution, automated generation of three-dimensional (3D) geometry, and incorporating actual flow measurements into the numerical solution of the 3D cardiovascular fluid dynamics.

  4. Left Ventricular Flow Analysis: Recent Advances in Numerical Methods and Applications in Cardiac Ultrasound

    PubMed Central

    Borazjani, Iman; Westerdale, John; McMahon, Eileen M.; Rajaraman, Prathish K.; Heys, Jeffrey J.

    2013-01-01

    The left ventricle (LV) pumps oxygenated blood from the lungs to the rest of the body through systemic circulation. The efficiency of such a pumping function is dependent on blood flow within the LV chamber. It is therefore crucial to accurately characterize LV hemodynamics. Improved understanding of LV hemodynamics is expected to provide important clinical diagnostic and prognostic information. We review the recent advances in numerical and experimental methods for characterizing LV flows and focus on analysis of intraventricular flow fields by echocardiographic particle image velocimetry (echo-PIV), due to its potential for broad and practical utility. Future research directions to advance patient-specific LV simulations include development of methods capable of resolving heart valves, higher temporal resolution, automated generation of three-dimensional (3D) geometry, and incorporating actual flow measurements into the numerical solution of the 3D cardiovascular fluid dynamics. PMID:23690874

  5. Advanced numerical study of the three-axis magnetic attitude control and determination with uncertainties

    NASA Astrophysics Data System (ADS)

    Ivanov, D. S.; Ovchinnikov, M. Yu.; Penkov, V. I.; Roldugin, D. S.; Doronin, D. M.; Ovchinnikov, A. V.

    2017-03-01

    Attitude motion of a satellite equipped with magnetic control system is considered. System comprises of three magnetorquers and one three-axis magnetometer. Satellite is stabilized in orbital reference frame using PD controller and extended Kalman filter. Three-axis attitude is analyzed numerically with advanced assumptions: inertia tensor uncertainty, disturbances of unknown nature, magnetometer errors are taken into account. Stabilization and determination accuracy dependence on orbit inclination is studied.

  6. The effect of a sub-grid statistical cloud-cover scheme applied to the COSMO local numerical weather prediction model over the wider geographical domain of Greece

    NASA Astrophysics Data System (ADS)

    Avgoustoglou, Euripides; Tzeferi, Theodora

    2015-01-01

    The COSMO model uses operationally two sub-grid schemes for the evaluation of stratus clouds. A semi-empirical scheme based on relative humidity is used in the radiation module while a statistical scheme is used in the turbulence module. The objective is to investigate the possibility of the implementation of the statistical scheme also in the radiation module. The relative impact is presented in reference to a spring test case with synoptic conditions that favor stratiform clouds. The domain considered is the wider Balkan region around the Hellenic geographical area and is characterized by comparable sea and land partitions. This particular domain choice gives rise to a strong coexistence of continental as well as marine clouds which is one of the most challenging features regarding the operational use of numerical weather prediction models by the Hellenic Meteorological Service. The results are evaluated through direct comparisons with satellite data as well as the observed 2-m temperatures for an approximate total of fifty Greek synoptic meteorological stations. The implementation of the statistical scheme led to an underestimation of low cloud-cover by the model in contrast to the implementation of the default relative-humidity scheme, while regarding medium cloud-cover the situation was reversed. Also, the daily 2-meter minimum and maximum temperatures were slightly better simulated, but not conclusively, when the statistical scheme was implemented in the radiation module. Although the statistical scheme cannot in its present form replace operationally the relative-humidity scheme in the radiation module, it is an important asset to COSMO model invoking valuable insight to the physics of the model and can be used as a basis to support the ongoing research in this crucial area of atmospheric sciences.

  7. Q-S (complete or anticipated) synchronization backstepping scheme in a class of discrete-time chaotic (hyperchaotic) systems: a symbolic-numeric computation approach.

    PubMed

    Yan, Zhenya

    2006-03-01

    First, a type of Q-S (complete or anticipated) synchronization is defined in discrete-time dynamical systems. Second, based on backstepping design with a scalar controller, a systematic, concrete and automatic scheme is presented to investigate Q-S (complete or anticipated) synchronization between the discrete-time drive system and response system with strict-feedback form. Finally, the proposed scheme is used to illustrate Q-S (complete or anticipated) synchronization between the two-dimensional discrete-time Lorenz system and Fold system, as well as the three-dimensional hyperchaotic discrete-time Rossler system and generalized discrete-time Rossler system. Moreover numerical simulations are used to verify the effectiveness of the proposed scheme. Our scheme can be also extended to investigate Q-S (complete or anticipated) synchronization between other discrete-time dynamical systems with strict-feedback forms. With the aid of symbolic-numeric computation, the scheme can be performed to yield automatically the scalar controller and to verify its effectiveness in computer.

  8. 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.

  9. Advanced Numerical Prediction and Modeling of Tropical Cyclones Using WRF-NMM modeling system

    NASA Astrophysics Data System (ADS)

    Gopalakrishnan, S. G.; Rogers, R. F.; Marks, F. D.; Atlas, R.

    2007-12-01

    Dramatic improvement in tropical cyclone track forecasts have occurred through advancements in high quality observations, high speed computers and improvements in dynamical models. Similar advancements now need to be made for tropical cyclone intensity, structure and rainfall prediction. The Weather Research Forecasting Model (WRF) is a general purpose, multi-institutional mesoscale modeling system. A version of the WRF model called the HWRF/WRF-NMM modeling system, developed at the National Center for Environmental Protection (NCEP) was recently adopted for hurricane forecasting (Gopalakrishnan et al, 2006) by the National Hurricane Center (NHC). At the Hurricane Research Division (HRD/AOML/OAR) we are developing and further advancing a research version of this modeling system. This work is done in collaboration with the Developmental Test bed Center (DTC), Boulder, CO, Global Systems division (GSD/ESRL/OAR), Boulder, CO, The Air Resources Laboratory (ARL/OAR), Washington, D.C., the U.S. university community, the Indian Institute of Technology, IIT.Delhi, India, and the India Meteorological Department, New Delhi, India Our modeling effort includes advancing the WRF system for Ensemble Hurricane Forecasting, advancing our understanding of Ensemble-vs- High Resolution Forecasting of Hurricanes, advancing WRF/WRF-NMM with better analysis techniques (e.g. Four Dimensional Data Assimilation) for improving forecasts and above all, advancing our understanding of hurricane processes using a high resolution numerical modeling approach. Examples of some of these applications will be shown here. Reference: NCEP's Two-way-Interactive-Moving-Nest NMM-WRF modeling system for Hurricane Forecasting, S.G. Gopalakrishnan, N. Surgi, R. Tuleya, and Z. Janjic 27th Conference on Hurricanes and Tropical Meteorology, 24- 28 April 2006, Monterey, California.

  10. Advanced control schemes and kinematic analysis for a kinematically redundant 7 DOF manipulator

    NASA Technical Reports Server (NTRS)

    Nguyen, Charles C.; Zhou, Zhen-Lei

    1990-01-01

    The kinematic analysis and control of a kinematically redundant manipulator is addressed. The manipulator is the slave arm of a telerobot system recently built at Goddard Space Flight Center (GSFC) to serve as a testbed for investigating research issues in telerobotics. A forward kinematic transformation is developed in its most simplified form, suitable for real-time control applications, and the manipulator Jacobian is derived using the vector cross product method. Using the developed forward kinematic transformation and quaternion representation of orientation matrices, we perform computer simulation to evaluate the efficiency of the Jacobian in converting joint velocities into Cartesian velocities and to investigate the accuracy of Jacobian pseudo-inverse for various sampling times. The equivalence between Cartesian velocities and quaternion is also verified using computer simulation. Three control schemes are proposed and discussed for controlling the motion of the slave arm end-effector.

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

    DTIC Science & Technology

    2011-08-01

    and Computational Studies for Dynamically Orthogonal Equations by Mattheus P. Ueckermann Pierre F. J. Lermusiaux Themis P. Sapsis...COVERED 00-00-2011 to 00-00-2011 4. TITLE AND SUBTITLE Numerical Schemes and Computational Studies for Dynamically Orthogonal Equations 5a...ocean ows, and other non-linear dynamical systems. The Dynamically Orthogonal (DO) eld equations provide an e cient time- dependent adaptive methodology

  12. Theoretical analysis of advanced schemes for free electron laser with a large {mu}{sub c}

    SciTech Connect

    Zhulin, V.I.; Zanadvorov, N.P.

    1995-12-31

    The possibility to operate with a short pulse FEL (electron pulse length a {sigma} {approx_equal} 1mm) in far infrared region (with the radiation wavelength 10{mu}m {le}{lambda}{le}300{mu}m) gives rise to many new applications. The parameter {mu}{sub c} = N{lambda}/{sigma}, which characterises the interaction time between the electron and radiation pulses in the undulator with N periods, becomes rather large ({mu}{sub c}{approximately}10) even for {lambda}{approximately}100{mu}m. An increase in {lambda} leads to the reduction in output power owing to an increase in both the diffraction losses and {mu}{sub c}. We consider two options capable to improve the situation in the FEL with planar undulator geometry: I. Reduction of the diffraction losses by use of circular or rectangular hollow waveguides in the cavity. II. Effective reduction of {mu}{sub c} factor by increasing the FEL-interaction time by means of the optical klystron undulator scheme. We demonstrate that; I. Introduction of a waveguide into the cavity causes additional difficulties. In both circular and rectangular cases the waveguide dispersion leads to the undesirable variation of radiation pulse shape. For the circular case the effect of depolarization becomes important and leads to the additional losses (up to 30%) due to the violation of the axial symmetry and linear polarization. II. The optical klystron scheme consisting of several separated undulators, can indeed increase the FEL-interaction time. The right choice of electron bunch delay between these undulators gives the possibility to couple several successive electron pulses with one radiation pulse during one passage through the cavity. This results in considerable increase in FEL-interaction time and corresponding increase in gain.

  13. Numerical simulation of the reactive flow in advanced (HSR) combustors using KIVA-2

    NASA Technical Reports Server (NTRS)

    Winowich, Nicholas S.

    1991-01-01

    Recent work has been done with the goal of establishing ultralow emission aircraft gas turbine combustors. A significant portion of the effort is the development of three dimensional computational combustor models. The KIVA-II computer code which is based on the Implicit Continuous Eulerian Difference mesh Arbitrary Lagrangian Eulerian (ICED-ALE) numerical scheme is one of the codes selected by NASA to achieve these goals. This report involves a simulation of jet injection through slanted slots within the Rich burn/Quick quench/Lean burn (RQL) baseline experimental rig. The RQL combustor distinguishes three regions of combustion. This work specifically focuses on modeling the quick quench mixer region in which secondary injection air is introduced radially through 12 equally spaced slots around the mixer circumference. Steady state solutions are achieved with modifications to the KIVA-II program. Work currently underway will evaluate thermal mixing as a function of injection air velocity and angle of inclination of the slots.

  14. Recent numerical and algorithmic advances within the volume tracking framework for modeling interfacial flows

    DOE PAGES

    François, Marianne M.

    2015-05-28

    A review of recent advances made in numerical methods and algorithms within the volume tracking framework is presented. The volume tracking method, also known as the volume-of-fluid method has become an established numerical approach to model and simulate interfacial flows. Its advantage is its strict mass conservation. However, because the interface is not explicitly tracked but captured via the material volume fraction on a fixed mesh, accurate estimation of the interface position, its geometric properties and modeling of interfacial physics in the volume tracking framework remain difficult. Several improvements have been made over the last decade to address these challenges.more » In this study, the multimaterial interface reconstruction method via power diagram, curvature estimation via heights and mean values and the balanced-force algorithm for surface tension are highlighted.« less

  15. Application of numerical optimization to the design of advanced supercritical airfoils

    NASA Technical Reports Server (NTRS)

    Johnson, R. R.; Hicks, R. M.

    1979-01-01

    An application of numerical optimization to the design of advanced airfoils for transonic aircraft showed that low-drag sections can be developed for a given design Mach number without an accompanying drag increase at lower Mach numbers. This is achieved by imposing a constraint on the drag coefficient at an off-design Mach number while minimizing the drag coefficient at the design Mach number. This multiple design-point numerical optimization has been implemented with the use of airfoil shape functions which permit a wide range of attainable profiles during the optimization process. Analytical data for the starting airfoil shape, a single design-point optimized shape, and a double design-point optimized shape are presented. Experimental data obtained in the NASA Ames two-by two-foot wind tunnel are also presented and discussed.

  16. Numerical study of Alfvén eigenmodes in the Experimental Advanced Superconducting Tokamak

    SciTech Connect

    Hu, Youjun; Li, Guoqiang; Yang, Wenjun; Zhou, Deng; Ren, Qilong; Gorelenkov, N. N.; Cai, Huishan

    2014-05-15

    Alfvén eigenmodes in up-down asymmetric tokamak equilibria are studied by a new magnetohydrodynamic eigenvalue code. The code is verified with the NOVA code for the Solovév equilibrium and then is used to study Alfvén eigenmodes in a up-down asymmetric equilibrium of the Experimental Advanced Superconducting Tokamak. The frequency and mode structure of toroidicity-induced Alfvén eigenmodes are calculated. It is demonstrated numerically that up-down asymmetry induces phase variation in the eigenfunction across the major radius on the midplane.

  17. Advanced Numerical methods for F. E. Simulation of Metal Forming Processes

    NASA Astrophysics Data System (ADS)

    Chenot, Jean-Loup; Bernacki, Marc; Fourment, Lionel; Ducloux, Richard

    2010-06-01

    The classical scientific basis for finite element modeling of metal forming processes is first recalled. Several developments in advanced topics are summarized: adaptive and anisotropic remeshing, parallel solving, multi material deformation. More recent researches in numerical analysis are outlined, including multi grid and multi mesh methods, mainly devoted to decrease computation time, automatic optimization method for faster and more effective design of forming processes. The link of forming simulation and structural computations is considered with emphasis on the necessity to predict the final mechanical properties. Finally a brief account of computation at the micro scale level is given.

  18. 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.

  19. Advanced scheme for high-yield laser driven proton-boron fusion reaction

    NASA Astrophysics Data System (ADS)

    Margarone, D.; Picciotto, A.; Velyhan, A.; Krasa, J.; Kucharik, M.; Morrissey, M.; Mangione, A.; Szydlowsky, A.; Malinowska, A.; Bertuccio, G.; Shi, Y.; Crivellari, M.; Ullschmied, J.; Bellutti, P.; Korn, G.

    2015-02-01

    A low contrast nanosecond laser pulse with relatively low intensity (3 × 1016 W cm-2) was used to enhance the yield of induced nuclear reactions in advanced solid targets. In particular the "ultraclean" proton-boron fusion reaction, producing energetic alpha-particles without neutron generation, was chosen. A spatially well-defined layer of boron dopants in a hydrogen-enriched silicon substrate was used as target. The combination of the specific target geometry and the laser pulse temporal shape allowed enhancing the yield of alpha-particles up to 109 per steradian, i.e 100 times higher than previous experimental achievements. Moreover the alpha particle stream presented a clearly peaked angular and energy distribution, which make this secondary source attractive for potential applications. This result can be ascribed to the interaction of the long laser pre-pulse with the target and to the optimal target geometry and composition.

  20. 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...

  1. Comparison of hybrid schemes for the combination of shallow approximations in numerical simulations of the Antarctic Ice Sheet

    NASA Astrophysics Data System (ADS)

    Bernales, Jorge; Rogozhina, Irina; Greve, Ralf; Thomas, Maik

    2017-01-01

    The shallow ice approximation (SIA) is commonly used in ice-sheet models to simplify the force balance equations within the ice. However, the SIA cannot adequately reproduce the dynamics of the fast flowing ice streams usually found at the margins of ice sheets. To overcome this limitation, recent studies have introduced heuristic hybrid combinations of the SIA and the shelfy stream approximation. Here, we implement four different hybrid schemes into a model of the Antarctic Ice Sheet in order to compare their performance under present-day conditions. For each scheme, the model is calibrated using an iterative technique to infer the spatial variability in basal sliding parameters. Model results are validated against topographic and velocity data. Our analysis shows that the iterative technique compensates for the differences between the schemes, producing similar ice-sheet configurations through quantitatively different results of the sliding coefficient calibration. Despite this we observe a robust agreement in the reconstructed patterns of basal sliding parameters. We exchange the calibrated sliding parameter distributions between the schemes to demonstrate that the results of the model calibration cannot be straightforwardly transferred to models based on different approximations of ice dynamics. However, easily adaptable calibration techniques for the potential distribution of basal sliding coefficients can be implemented into ice models to overcome such incompatibility, as shown in this study.

  2. 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.

  3. Advanced Numerical-Algebraic Thinking: Constructing the Concept of Covariation as a Prelude to the Concept of Function

    ERIC Educational Resources Information Center

    Hitt, Fernando; Morasse, Christian

    2009-01-01

    Introduction: In this document we stress the importance of developing in children a structure for advanced numerical-algebraic thinking that can provide an element of control when solving mathematical situations. We analyze pupils' conceptions that induce errors in algebra due to a lack of control in connection with their numerical thinking. We…

  4. 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.

  5. A membrane-integrated advanced scheme for treatment of industrial wastewater: dynamic modeling towards scale up.

    PubMed

    Kumar, Ramesh; Pal, Parimal

    2013-08-01

    Modeling and simulation was carried out for an advanced membrane-integrated hybrid treatment process that ensures reuse of water with conversion and recovery of ammoniacal nitrogen as value-added struvite fertilizer from coke wastewater. While toxic cyanide was largely removed in a pre-chemical treatment unit using Fenton's reagents under optimized conditions, more than 95% of NH4(+)-N could be recovered as a valuable by-product called struvite through addition of appropriate doses of magnesium and phosphate salts. Water could be turned reusable through a polishing treatment by nanofiltration membranes in a largely fouling free membrane module following a biodegradation step. Mathematical modeling of such an integrated process was done with Haldane-Andrew approach for the associated microbial degradation of phenol by Pseudomonas putida. Residual NH4(+) was degraded by nitrification and denitrification following the modified Monod kinetics. The model could successfully predict the plant performance as reflected in reasonably low relative error (0.03-0.18) and high Willmott d-index (>0.98).

  6. 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

  7. 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.

  8. Numerical approach for the voloxidation process of an advanced spent fuel conditioning process (ACP)

    SciTech Connect

    Park, Byung Heung; Jeong, Sang Mun; Seo, Chung-Seok

    2007-07-01

    A voloxidation process is adopted as the first step of an advanced spent fuel conditioning process in order to prepare the SF oxide to be reduced in the following electrolytic reduction process. A semi-batch type voloxidizer was devised to transform a SF pellet into powder. In this work, a simple reactor model was developed for the purpose of correlating a gas phase flow rate with an operation time as a numerical approach. With an assumption that a solid phase and a gas phase are homogeneous in a reactor, a reaction rate for an oxidation was introduced into a mass balance equation. The developed equation can describe a change of an outlet's oxygen concentration including such a case that a gas flow is not sufficient enough to continue a reaction at its maximum reaction rate. (authors)

  9. 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.

  10. The role of numerical simulation for the development of an advanced HIFU system

    NASA Astrophysics Data System (ADS)

    Okita, Kohei; Narumi, Ryuta; Azuma, Takashi; Takagi, Shu; Matumoto, Yoichiro

    2014-10-01

    High-intensity focused ultrasound (HIFU) has been used clinically and is under clinical trials to treat various diseases. An advanced HIFU system employs ultrasound techniques for guidance during HIFU treatment instead of magnetic resonance imaging in current HIFU systems. A HIFU beam imaging for monitoring the HIFU beam and a localized motion imaging for treatment validation of tissue are introduced briefly as the real-time ultrasound monitoring techniques. Numerical simulations have a great impact on the development of real-time ultrasound monitoring as well as the improvement of the safety and efficacy of treatment in advanced HIFU systems. A HIFU simulator was developed to reproduce ultrasound propagation through the body in consideration of the elasticity of tissue, and was validated by comparison with in vitro experiments in which the ultrasound emitted from the phased-array transducer propagates through the acrylic plate acting as a bone phantom. As the result, the defocus and distortion of the ultrasound propagating through the acrylic plate in the simulation quantitatively agree with that in the experimental results. Therefore, the HIFU simulator accurately reproduces the ultrasound propagation through the medium whose shape and physical properties are well known. In addition, it is experimentally confirmed that simulation-assisted focus control of the phased-array transducer enables efficient assignment of the focus to the target. Simulation-assisted focus control can contribute to design of transducers and treatment planning.

  11. Numerical solution of the equation of neutrons transport on plane geometry by analytical schemes using acceleration by synthetic diffusion

    NASA Astrophysics Data System (ADS)

    Alonso-Vargas, G.

    A computer program has been developed which uses a technique of synthetic acceleration by diffusion by analytical schemes. Both in the diffusion equation as in that of transport, analytical schemes were used which allowed a substantial time saving in the number of iterations required by source iteration method to obtain the K(sub e)ff. The program developed ASD (Synthetic Diffusion Acceleration) by diffusion was written in FORTRAN and can be executed on a personal computer with a hard disc and mathematical O-processor. The program is unlimited as to the number of regions and energy groups. The results obtained by the ASD program for K(sub e)ff is nearly completely concordant with those obtained by utilizing the ANISN-PC code for different analytical type problems in this work. The ASD program allowed obtention of an approximate solution of the neutron transport equation with a relatively low number of internal reiterations with good precision. One of its applications would be in the direct determinations of axial distribution neutronic flow in a fuel assembly as well as in the obtention of the effective multiplication factor.

  12. A Low-order Coupled Chemistry Meteorology Model for Testing Online and Offline Advanced Data Assimilation Schemes

    NASA Astrophysics Data System (ADS)

    Bocquet, M.; Haussaire, J. M.

    2015-12-01

    Bocquet and Sakov have recently introduced a low-order model based on the coupling of thechaotic Lorenz-95 model which simulates winds along a mid-latitude circle, with thetransport of a tracer species advected by this wind field. It has been used to testadvanced data assimilation methods with an online model that couples meteorology andtracer transport. In the present study, the tracer subsystem of the model is replacedwith a reduced photochemistry module meant to emulate reactive air pollution. Thiscoupled chemistry meteorology model, the L95-GRS model, mimics continental andtranscontinental transport and photochemistry of ozone, volatile organic compounds andnitrogen dioxides.The L95-GRS is specially useful in testing advanced data assimilation schemes, such as theiterative ensemble Kalman smoother (IEnKS) that combines the best of ensemble andvariational methods. The model provides useful insights prior to any implementation ofthe data assimilation method on larger models. For instance, online and offline dataassimilation strategies based on the ensemble Kalman filter or the IEnKS can easily beevaluated with it. It allows to document the impact of species concentration observationson the wind estimation. The model also illustrates a long standing issue in atmosphericchemistry forecasting: the impact of the wind chaotic dynamics and of the chemical speciesnon-chaotic but highly nonlinear dynamics on the selected data assimilation approach.

  13. 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.

  14. Numerical Hydrodynamics in General Relativity.

    PubMed

    Font, José A

    2000-01-01

    The current status of numerical solutions for the equations of ideal general relativistic hydrodynamics is reviewed. Different formulations of the equations are presented, with special mention of conservative and hyperbolic formulations well-adapted to advanced numerical methods. A representative sample of available numerical schemes is discussed and particular emphasis is paid to solution procedures based on schemes exploiting the characteristic structure of the equations through linearized Riemann solvers. A comprehensive summary of relevant astrophysical simulations in strong gravitational fields, including gravitational collapse, accretion onto black holes and evolution of neutron stars, is also presented.

  15. 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

  16. Numerical Simulations of Optical Turbulence Using an Advanced Atmospheric Prediction Model: Implications for Adaptive Optics Design

    NASA Astrophysics Data System (ADS)

    Alliss, R.

    2014-09-01

    Optical turbulence (OT) acts to distort light in the atmosphere, degrading imagery from astronomical telescopes and reducing the data quality of optical imaging and communication links. Some of the degradation due to turbulence can be corrected by adaptive optics. However, the severity of optical turbulence, and thus the amount of correction required, is largely dependent upon the turbulence at the location of interest. Therefore, it is vital to understand the climatology of optical turbulence at such locations. In many cases, it is impractical and expensive to setup instrumentation to characterize the climatology of OT, so numerical simulations become a less expensive and convenient alternative. The strength of OT is characterized by the refractive index structure function Cn2, which in turn is used to calculate atmospheric seeing parameters. While attempts have been made to characterize Cn2 using empirical models, Cn2 can be calculated more directly from Numerical Weather Prediction (NWP) simulations using pressure, temperature, thermal stability, vertical wind shear, turbulent Prandtl number, and turbulence kinetic energy (TKE). In this work we use the Weather Research and Forecast (WRF) NWP model to generate Cn2 climatologies in the planetary boundary layer and free atmosphere, allowing for both point-to-point and ground-to-space seeing estimates of the Fried Coherence length (ro) and other seeing parameters. Simulations are performed using a multi-node linux cluster using the Intel chip architecture. The WRF model is configured to run at 1km horizontal resolution and centered on the Mauna Loa Observatory (MLO) of the Big Island. The vertical resolution varies from 25 meters in the boundary layer to 500 meters in the stratosphere. The model top is 20 km. The Mellor-Yamada-Janjic (MYJ) TKE scheme has been modified to diagnose the turbulent Prandtl number as a function of the Richardson number, following observations by Kondo and others. This modification

  17. Numerical Evaluation of Fluid Mixing Phenomena in Boiling Water Reactor Using Advanced Interface Tracking Method

    NASA Astrophysics Data System (ADS)

    Yoshida, Hiroyuki; Takase, Kazuyuki

    Thermal-hydraulic design of the current boiling water reactor (BWR) is performed with the subchannel analysis codes which incorporated the correlations based on empirical results including actual-size tests. Then, for the Innovative Water Reactor for Flexible Fuel Cycle (FLWR) core, an actual size test of an embodiment of its design is required to confirm or modify such correlations. In this situation, development of a method that enables the thermal-hydraulic design of nuclear reactors without these actual size tests is desired, because these tests take a long time and entail great cost. For this reason, we developed an advanced thermal-hydraulic design method for FLWRs using innovative two-phase flow simulation technology. In this study, a detailed Two-Phase Flow simulation code using advanced Interface Tracking method: TPFIT is developed to calculate the detailed information of the two-phase flow. In this paper, firstly, we tried to verify the TPFIT code by comparing it with the existing 2-channel air-water mixing experimental results. Secondary, the TPFIT code was applied to simulation of steam-water two-phase flow in a model of two subchannels of a current BWRs and FLWRs rod bundle. The fluid mixing was observed at a gap between the subchannels. The existing two-phase flow correlation for fluid mixing is evaluated using detailed numerical simulation data. This data indicates that pressure difference between fluid channels is responsible for the fluid mixing, and thus the effects of the time average pressure difference and fluctuations must be incorporated in the two-phase flow correlation for fluid mixing. When inlet quality ratio of subchannels is relatively large, it is understood that evaluation precision of the existing two-phase flow correlations for fluid mixing are relatively low.

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

    NASA Astrophysics Data System (ADS)

    Deetz, K.; Klose, M.; Kirchner, I.; Cubasch, U.

    2016-02-01

    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 to be relatively high in the model during the investigation period and has been reduced by different degree to investigate the resulting changes in dust emissions. Two different vegetation datasets have been tested as model input: the climatological vegetation cover data of COSMO-ART (ECOCLIMAP) and the SPOT5 remote sensing vegetation cover data for the time of the event. By varying soil moisture, vegetation cover and by restricting the potential emission area, a set of eleven simulations was generated. Vegetation cover during the event was about 24% lower on average compared to the climatological mean. Thus, dust emissions modeled with SPOT5 vegetation exceeded that modeled with climatological data by a factor of about 5. The modeled dust concentrations were compared with in-situ measurements of aerosol concentration. The temporal evolutions of simulations and observations have significant correlations (0.42-0.85) especially in rural backgrounds. The lower correlations at urban sites are attributed to anthropogenic PM10 sources, which are not included in the model. However, a verification of the magnitude of modeled dust concentrations is not possible due to the uncertainty in soil moisture and emission area.

  19. Basic and Advanced Numerical Performances Relate to Mathematical Expertise but Are Fully Mediated by Visuospatial Skills

    ERIC Educational Resources Information Center

    Sella, Francesco; Sader, Elie; Lolliot, Simon; Cohen Kadosh, Roi

    2016-01-01

    Recent studies have highlighted the potential role of basic numerical processing in the acquisition of numerical and mathematical competences. However, it is debated whether high-level numerical skills and mathematics depends specifically on basic numerical representations. In this study mathematicians and nonmathematicians performed a basic…

  20. 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

  1. A numerical scheme for the identification of hybrid systems describing the vibration of flexible beams with tip bodies

    NASA Technical Reports Server (NTRS)

    Rosen, I. G.

    1984-01-01

    A cubic spline based Galerkin-like method is developed for the identification of a class of hybrid systems which describe the transverse vibration to flexible beams with attached tip bodies. The identification problem is formulated as a least squares fit to data subject to the system dynamics given by a coupled system of ordnary and partial differential equations recast as an abstract evolution equation (AEE) in an appropriate infinite dimensional Hilbert space. Projecting the AEE into spline-based subspaces leads naturally to a sequence of approximating finite dimensional identification problems. The solutions to these problems are shown to exist, are relatively easily computed, and are shown to, in some sense, converge to solutions to the original identification problem. Numerical results for a variety of examples are discussed.

  2. 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.

  3. 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

  4. 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.

  5. Advanced Numerical Imaging Procedure Accounting for Non-Ideal Effects in GPR Scenarios

    NASA Astrophysics Data System (ADS)

    Comite, Davide; Galli, Alessandro; Catapano, Ilaria; Soldovieri, Francesco

    2015-04-01

    advanced implementation have also been tested by introducing 'errors' on the knowledge of the background medium permittivity, by simulating the presence of one or more layers, and by choosing different models of the surface roughness. The impact of these issues on the performance of both the conventional procedure and the advanced one will be extensively highlighted and discussed at the conference. [1] G. Valerio et al., "GPR detectability of rocks in a Martian-like shallow subsoil: A numerical approach," Plan. Sp. Sci., vol. 62, pp. 31-40, 2012. [2] A. Galli et al., "3D imaging of buried dielectric targets with a tomographic microwave approach applied to GPR synthetic data," Int. J. Antennas Propag., art. ID 610389, 10 pp., 2013 [3] F. Soldovieri et al., "A linear inverse scattering algorithm for realistic GPR applications," Near Surface Geophysics, 5 (1), pp. 29-42, 2007.

  6. Investigation of upwind, multigrid, multiblock numerical schemes for three dimensional flows. Volume 1: Runge-Kutta methods for a thin layer Navier-Stokes solver

    NASA Technical Reports Server (NTRS)

    Cannizzaro, Frank E.; Ash, Robert L.

    1992-01-01

    A state-of-the-art computer code has been developed that incorporates a modified Runge-Kutta time integration scheme, upwind numerical techniques, multigrid acceleration, and multi-block capabilities (RUMM). A three-dimensional thin-layer formulation of the Navier-Stokes equations is employed. For turbulent flow cases, the Baldwin-Lomax algebraic turbulence model is used. Two different upwind techniques are available: van Leer's flux-vector splitting and Roe's flux-difference splitting. Full approximation multi-grid plus implicit residual and corrector smoothing were implemented to enhance the rate of convergence. Multi-block capabilities were developed to provide geometric flexibility. This feature allows the developed computer code to accommodate any grid topology or grid configuration with multiple topologies. The results shown in this dissertation were chosen to validate the computer code and display its geometric flexibility, which is provided by the multi-block structure.

  7. 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.

  8. Recent advances in theoretical and numerical studies of wire array Z-pinch in the IAPCM

    SciTech Connect

    Ding, Ning Zhang, Yang Xiao, Delong Wu, Jiming Huang, Jun Yin, Li Sun, Shunkai Xue, Chuang Dai, Zihuan Ning, Cheng Shu, Xiaojian Wang, Jianguo Li, Hua

    2014-12-15

    Fast Z-pinch has produced the most powerful X-ray radiation source in laboratory and also shows the possibility to drive inertial confinement fusion (ICF). Recent advances in wire-array Z-pinch researches at the Institute of Applied Physics and Computational Mathematics are presented in this paper. A typical wire array Z-pinch process has three phases: wire plasma formation and ablation, implosion and the MRT instability development, stagnation and radiation. A mass injection model with azimuthal modulation coefficient is used to describe the wire initiation, and the dynamics of ablated plasmas of wire-array Z-pinches in (r, θ) geometry is numerically studied. In the implosion phase, a two-dimensional(r, z) three temperature radiation MHD code MARED has been developed to investigate the development of the Magneto-Rayleigh-Taylor(MRT) instability. We also analyze the implosion modes of nested wire-array and find that the inner wire-array is hardly affected before the impaction of the outer wire-array. While the plasma accelerated to high speed in the implosion stage stagnates on the axis, abundant x-ray radiation is produced. The energy spectrum of the radiation and the production mechanism are investigated. The computational x-ray pulse shows a reasonable agreement with the experimental result. We also suggest that using alloyed wire-arrays can increase multi-keV K-shell yield by decreasing the opacity of K-shell lines. In addition, we use a detailed circuit model to study the energy coupling between the generator and the Z-pinch implosion. Recently, we are concentrating on the problems of Z-pinch driven ICF, such as dynamic hohlraum and capsule implosions. Our numerical investigations on the interaction of wire-array Z-pinches on foam convertors show qualitative agreements with experimental results on the “Qiangguang I” facility. An integrated two-dimensional simulation of dynamic hohlraum driven capsule implosion provides us the physical insights of wire

  9. Recent advances in theoretical and numerical studies of wire array Z-pinch in the IAPCM

    NASA Astrophysics Data System (ADS)

    Ding, Ning; Zhang, Yang; Xiao, Delong; Wu, Jiming; Huang, Jun; Yin, Li; Sun, Shunkai; Xue, Chuang; Dai, Zihuan; Ning, Cheng; Shu, Xiaojian; Wang, Jianguo; Li, Hua

    2014-12-01

    Fast Z-pinch has produced the most powerful X-ray radiation source in laboratory and also shows the possibility to drive inertial confinement fusion (ICF). Recent advances in wire-array Z-pinch researches at the Institute of Applied Physics and Computational Mathematics are presented in this paper. A typical wire array Z-pinch process has three phases: wire plasma formation and ablation, implosion and the MRT instability development, stagnation and radiation. A mass injection model with azimuthal modulation coefficient is used to describe the wire initiation, and the dynamics of ablated plasmas of wire-array Z-pinches in (r, θ) geometry is numerically studied. In the implosion phase, a two-dimensional(r, z) three temperature radiation MHD code MARED has been developed to investigate the development of the Magneto-Rayleigh-Taylor(MRT) instability. We also analyze the implosion modes of nested wire-array and find that the inner wire-array is hardly affected before the impaction of the outer wire-array. While the plasma accelerated to high speed in the implosion stage stagnates on the axis, abundant x-ray radiation is produced. The energy spectrum of the radiation and the production mechanism are investigated. The computational x-ray pulse shows a reasonable agreement with the experimental result. We also suggest that using alloyed wire-arrays can increase multi-keV K-shell yield by decreasing the opacity of K-shell lines. In addition, we use a detailed circuit model to study the energy coupling between the generator and the Z-pinch implosion. Recently, we are concentrating on the problems of Z-pinch driven ICF, such as dynamic hohlraum and capsule implosions. Our numerical investigations on the interaction of wire-array Z-pinches on foam convertors show qualitative agreements with experimental results on the "Qiangguang I" facility. An integrated two-dimensional simulation of dynamic hohlraum driven capsule implosion provides us the physical insights of wire

  10. An Advanced Temporal Credential-Based Security Scheme with Mutual Authentication and Key Agreement for Wireless Sensor Networks

    PubMed Central

    Li, Chun-Ta; Weng, Chi-Yao; Lee, Cheng-Chi

    2013-01-01

    Wireless sensor networks (WSNs) can be quickly and randomly deployed in any harsh and unattended environment and only authorized users are allowed to access reliable sensor nodes in WSNs with the aid of gateways (GWNs). Secure authentication models among the users, the sensor nodes and GWN are important research issues for ensuring communication security and data privacy in WSNs. In 2013, Xue et al. proposed a temporal-credential-based mutual authentication and key agreement scheme for WSNs. However, in this paper, we point out that Xue et al.'s scheme cannot resist stolen-verifier, insider, off-line password guessing, smart card lost problem and many logged-in users' attacks and these security weaknesses make the scheme inapplicable to practical WSN applications. To tackle these problems, we suggest a simple countermeasure to prevent proposed attacks while the other merits of Xue et al.'s authentication scheme are left unchanged. PMID:23887085

  11. An advanced temporal credential-based security scheme with mutual authentication and key agreement for wireless sensor networks.

    PubMed

    Li, Chun-Ta; Weng, Chi-Yao; Lee, Cheng-Chi

    2013-07-24

    Wireless sensor networks (WSNs) can be quickly and randomly deployed in any harsh and unattended environment and only authorized users are allowed to access reliable sensor nodes in WSNs with the aid of gateways (GWNs). Secure authentication models among the users, the sensor nodes and GWN are important research issues for ensuring communication security and data privacy in WSNs. In 2013, Xue et al. proposed a temporal-credential-based mutual authentication and key agreement scheme for WSNs. However, in this paper, we point out that Xue et al.'s scheme cannot resist stolen-verifier, insider, off-line password guessing, smart card lost problem and many logged-in users' attacks and these security weaknesses make the scheme inapplicable to practical WSN applications. To tackle these problems, we suggest a simple countermeasure to prevent proposed attacks while the other merits of Xue et al.'s authentication scheme are left unchanged.

  12. Comparison of the lattice Boltzmann equation and discrete unified gas-kinetic scheme methods for direct numerical simulation of decaying turbulent flows.

    PubMed

    Wang, Peng; Wang, Lian-Ping; Guo, Zhaoli

    2016-10-01

    The main objective of this work is to perform a detailed comparison of the lattice Boltzmann equation (LBE) and the recently developed discrete unified gas-kinetic scheme (DUGKS) methods for direct numerical simulation (DNS) of the decaying homogeneous isotropic turbulence and the Kida vortex flow in a periodic box. The flow fields and key statistical quantities computed by both methods are compared with those from the pseudospectral method at both low and moderate Reynolds numbers. The results show that the LBE is more accurate and efficient than the DUGKS, but the latter has a superior numerical stability, particularly for high Reynolds number flows. In addition, we conclude that the DUGKS can adequately resolve the flow when the minimum spatial resolution parameter k_{max}η>3, where k_{max} is the maximum resolved wave number and η is the flow Kolmogorov length. This resolution requirement can be contrasted with the requirements of k_{max}η>1 for the pseudospectral method and k_{max}η>2 for the LBE. It should be emphasized that although more validations should be conducted before the DUGKS can be called a viable tool for DNS of turbulent flows, the present work contributes to the overall assessment of the DUGKS, and it provides a basis for further applications of DUGKS in studying the physics of turbulent flows.

  13. Finding the best combination of numerical schemes for 2-D SPH simulation of wedge water entry for a wide range of deadrise angles

    NASA Astrophysics Data System (ADS)

    Farsi, Mohammad; Ghadimi, Parviz

    2014-09-01

    Main aim of this paper is to find the best combination of numerical schemes for 2-D SPH simulation of wedge water entry. Diffusion term is considered as laminar, turbulent, and artificial viscosity. Density filter that seriously affects the pressure distribution is investigated by adopting no filter, first order filter, and second order filter. Validation of the results indicates that turbulent model and first order density filter can lead to more reasonable solutions. This simulation was then conducted for wedge water entry with wide range of deadrise angles including 10 degrees, 20 degrees, 30 degrees, 45 degrees, 60 degrees and 81 degrees, with extreme deadrise angles of 10 degrees, 60 degrees and 81 degrees being considered. Comparison of SPH results with BEM solutions has displayed favorable agreement. In two particular cases where experimental data are available, the SPH results are shown to be closer to the experiments than BEM solution. While, accuracy of the obtained results for moderate deadrise angles is desirable, numerical findings for very small or very large deadrise angles are also very reasonable

  14. Development and validation of burnup dependent computational schemes for the analysis of assemblies with advanced lattice codes

    NASA Astrophysics Data System (ADS)

    Ramamoorthy, Karthikeyan

    The main aim of this research is the development and validation of computational schemes for advanced lattice codes. The advanced lattice code which forms the primary part of this research is "DRAGON Version4". The code has unique features like self shielding calculation with capabilities to represent distributed and mutual resonance shielding effects, leakage models with space-dependent isotropic or anisotropic streaming effect, availability of the method of characteristics (MOC), burnup calculation with reaction-detailed energy production etc. Qualified reactor physics codes are essential for the study of all existing and envisaged designs of nuclear reactors. Any new design would require a thorough analysis of all the safety parameters and burnup dependent behaviour. Any reactor physics calculation requires the estimation of neutron fluxes in various regions of the problem domain. The calculation goes through several levels before the desired solution is obtained. Each level of the lattice calculation has its own significance and any compromise at any step will lead to poor final result. The various levels include choice of nuclear data library and energy group boundaries into which the multigroup library is cast; self shielding of nuclear data depending on the heterogeneous geometry and composition; tracking of geometry, keeping error in volume and surface to an acceptable minimum; generation of regionwise and groupwise collision probabilities or MOC-related information and their subsequent normalization thereof, solution of transport equation using the previously generated groupwise information and obtaining the fluxes and reaction rates in various regions of the lattice; depletion of fuel and of other materials based on normalization with constant power or constant flux. Of the above mentioned levels, the present research will mainly focus on two aspects, namely self shielding and depletion. The behaviour of the system is determined by composition of resonant

  15. Advances in Analytical and Numerical Dispersion Modeling of Pollutants Releasing from an Area-source

    NASA Astrophysics Data System (ADS)

    Nimmatoori, Praneeth

    The air quality near agricultural activities such as tilling, plowing, harvesting, and manure application is of main concern because they release fine particulate matter into the atmosphere. These releases are modeled as area-sources in the air quality modeling research. None of the currently available dispersion models relate and incorporate physical characteristics and meteorological conditions for modeling the dispersion and deposition of particulates emitting from such area-sources. This knowledge gap was addressed by developing the advanced analytical and numerical methods for modeling the dispersion of particulate matter. The development, application, and evaluation of new dispersion modeling methods are discussed in detail in this dissertation. In the analytical modeling, a ground-level area source analytical dispersion model known as particulate matter deposition -- PMD was developed for predicting the concentrations of different particle sizes. Both the particle dynamics (particle physical characteristics) and meteorological conditions which have significant effect on the dispersion of particulates were related and incorporated in the PMD model using the formulations of particle gravitational settling and dry deposition velocities. The modeled particle size concentrations of the PMD model were evaluated statistically after applying it to particulates released from a biosolid applied agricultural field. The evaluation of the PMD model using the statistical criteria concluded effective and successful inclusion of dry deposition theory for modeling particulate matter concentrations. A comprehensive review of analytical area-source dispersion models, which do not account for dry deposition and treat pollutants as gases, was conducted and determined three models -- the Shear, the Parker, and the Smith. A statistical evaluation of these dispersion models was conducted after applying them to two different field data sets and the statistical results concluded that

  16. Simultaneous detection of multiple debris via a cascade of numerical evaluations and a voting scheme for lines in an image sequence

    NASA Astrophysics Data System (ADS)

    Fujita, Koki; Ichimura, Naoyuki; Hanada, Toshiya

    2017-04-01

    This paper presents a novel method to simultaneously detect multiple trajectories of space debris in an observation image sequence to establish a reliable model for space debris environment in Geosynchronous Earth Orbit (GEO). The debris in GEO often appear faintly in image sequences due to the high altitude. A simple but steady way to detect such faint debris is to decrease a threshold value of binarization applied to an image sequence during preprocessing. However, a low threshold value of binarization leads to extracting a large number of objects other than debris that become obstacles to detect debris trajectories. In order to detect debris from binarized image frames with massive obstacles, this work proposes a method that utilizes a cascade of numerical evaluations and a voting scheme to evaluate characteristics of the line segments obtained by connecting two image objects in different image frames, which are the candidates of debris trajectories. In the proposed method, the line segments corresponding to objects other than debris are filtered out using three types of characteristics, namely displacement, direction, and continuity. First, the displacement and direction of debris motion are evaluated to remove irrelevant trajectories. Then, the continuity of the remaining line segments is checked to find debris by counting the number of image objects appearing on or close to the line segments. Since checking the continuity can be regarded as a voting scheme, the proposed cascade algorithm can take advantage of the properties of voting method such as the Hough transform, i.e., the robustness against heavy noises and clutters, and ability of detecting multiple trajectories simultaneously. The experimental tests using real image sequences obtained in a past observation campaign demonstrate the effectiveness of the proposed method.

  17. Free Radical Addition Polymerization Kinetics without Steady-State Approximations: A Numerical Analysis for the Polymer, Physical, or Advanced Organic Chemistry Course

    ERIC Educational Resources Information Center

    Iler, H. Darrell; Brown, Amber; Landis, Amanda; Schimke, Greg; Peters, George

    2014-01-01

    A numerical analysis of the free radical addition polymerization system is described that provides those teaching polymer, physical, or advanced organic chemistry courses the opportunity to introduce students to numerical methods in the context of a simple but mathematically stiff chemical kinetic system. Numerical analysis can lead students to an…

  18. A Simple Scheme for Estimating Turbulent Heat Flux over Landfast Arctic Sea Ice from Dry Snow to Advanced Melt

    NASA Astrophysics Data System (ADS)

    Raddatz, R. L.; Papakyriakou, T. N.; Else, B. G.; Swystun, K.; Barber, D. G.

    2015-05-01

    We describe a dynamic-parameter aggregation scheme to estimate hourly turbulent heat fluxes over landfast sea ice during the transition from winter to spring. Hourly albedo measurements are used to track the morphology of the surface as it evolved from a fairly smooth homogeneous dry snow surface to a rougher heterogeneous surface with spatially differential melting and melt ponds. The estimates of turbulent heat fluxes for 928 h are compared with eddy-covariance measurements. The model performance metrics (W m) for sensible heat flux were found to be: mean bias , root-mean-square error 6 and absolute accuracy 4, and for latent heat flux near zero, 3 and 2, respectively. The correlation coefficient between modelled and measured sensible heat fluxes was 0.82, and for latent heat fluxes 0.88. The turbulent heat fluxes were estimated more accurately without adjustments than with adjustments for atmospheric stability based on the bulk Richardson number. Overall, and across all metrics for both sensible and latent heat fluxes, the dynamic-parameter aggregation scheme outperformed the static Community Ice (C-ICE) scheme, part of the Community Climate System model, applied to the same winter-to-spring transition period.

  19. A review of recent advances in numerical simulations of microscale fuel processor for hydrogen production

    NASA Astrophysics Data System (ADS)

    Holladay, J. D.; Wang, Y.

    2015-05-01

    Microscale (<5 W) reformers for hydrogen production have been investigated for over a decade. These devices are intended to provide hydrogen for small fuel cells. Due to the reformer's small size, numerical simulations are critical to understand heat and mass transfer phenomena occurring in the systems and help guide the further improvements. This paper reviews the development of the numerical codes and details the reaction equations used. The majority of the devices utilized methanol as the fuel due to methanol's low reforming temperature and high conversion, although, there are several methane fueled systems. The increased computational power and more complex codes have led to improved accuracy of numerical simulations. Initial models focused on the reformer, while more recently, the simulations began including other unit operations such as vaporizers, inlet manifolds, and combustors. These codes are critical for developing the next generation systems. The systems reviewed included plate reactors, microchannel reactors, and annulus reactors for both wash-coated and packed bed systems.

  20. CNC Turning Center Advanced Operations. Computer Numerical Control Operator/Programmer. 444-332.

    ERIC Educational Resources Information Center

    Skowronski, Steven D.; Tatum, Kenneth

    This student guide provides materials for a course designed to introduce the student to the operations and functions of a two-axis computer numerical control (CNC) turning center. The course consists of seven units. Unit 1 presents course expectations and syllabus, covers safety precautions, and describes the CNC turning center components, CNC…

  1. An advanced scheme for wet scavenging and liquid-phase chemistry in a regional online-coupled chemistry transport model

    NASA Astrophysics Data System (ADS)

    Knote, C.; Brunner, D.

    2012-10-01

    Clouds are reaction chambers for atmospheric trace gases and aerosols, and the associated precipitation is a major sink for atmospheric constituents. The regional chemistry-climate model COSMO-ART has been lacking a description of wet scavenging of gases and aqueous-phase chemistry. In this work we present a coupling of COSMO-ART with a wet scavenging and aqueous-phase chemistry scheme. The coupling is made consistent with the cloud microphysics scheme of the underlying meteorological model COSMO. While the choice of the aqueous-chemistry mechanism is flexible, the effects of a simple sulfur oxidation scheme are shown in the application of the coupled system in this work. We give details explaining the coupling and extensions made, then present results from idealized flow-over-hill experiments in a 2-D model setup and finally results from a full 3-D simulation. Comparison against measurement data shows that the scheme efficiently reduces SO2 trace gas concentrations by 0.3 ppbv (-30%) on average, while leaving O3 and NOx unchanged. PM10 aerosol mass, which has been overestimated previously, is now in much better agreement with measured values due to a stronger scavenging of coarse particles. While total PM2.5 changes only little, chemical composition is improved notably. Overestimations of nitrate aerosols are reduced by typically 0.5-1 μg m-3 (up to -2 μg m-3 in the Po Valley) while sulfate mass is increased by 1-1.5 μg m-3 on average (up to 2.5 μg m-3 in Eastern Europe). The effect of cloud processing of aerosols on its size distribution, i. e. a shift towards larger diameters, is observed. Compared against wet deposition measurements the system underestimates the total wet deposited mass for the simulated case study. We find that while evaporation of cloud droplets dominates in higher altitudes, evaporation of precipitation can contribute up to 50% of total evaporated mass near the surface.

  2. Investigation of advanced pre- and post-equalization schemes in high-order CAP modulation based high-speed indoor VLC transmission system

    NASA Astrophysics Data System (ADS)

    Wang, Yiguang; Chi, Nan

    2016-10-01

    Light emitting diodes (LEDs) based visible light communication (VLC) has been considered as a promising technology for indoor high-speed wireless access, due to its unique advantages, such as low cost, license free and high security. To achieve high-speed VLC transmission, carrierless amplitude and phase (CAP) modulation has been utilized for its lower complexity and high spectral efficiency. Moreover, to compensate the linear and nonlinear distortions such as frequency attenuation, sampling time offset, LED nonlinearity etc., series of pre- and post-equalization schemes should be employed in high-speed VLC systems. In this paper, we make an investigation on several advanced pre- and postequalization schemes for high-order CAP modulation based VLC systems. We propose to use a weighted preequalization technique to compensate the LED frequency attenuation. In post-equalization, a hybrid post equalizer is proposed, which consists of a linear equalizer, a Volterra series based nonlinear equalizer, and a decision-directed least mean square (DD-LMS) equalizer. Modified cascaded multi-modulus algorithm (M-CMMA) is employed to update the weights of the linear and the nonlinear equalizer, while DD-LMS can further improve the performance after the preconvergence. Based on high-order CAP modulation and these equalization schemes, we have experimentally demonstrated a 1.35-Gb/s, a 4.5-Gb/s and a 8-Gb/s high-speed indoor VLC transmission systems. The results show the benefit and feasibility of the proposed equalization schemes for high-speed VLC systems.

  3. A review of recent advances of numerical simulations of microscale fuel processors for hydrogen production

    SciTech Connect

    Holladay, Jamelyn D.; Wang, Yong

    2015-05-01

    Microscale (<5W) reformers for hydrogen production have been investigated for over a decade. These devices are intended to provide hydrogen for small fuel cells. Due to the reformer’s small size, numerical simulations are critical to understand heat and mass transfer phenomena occurring in the systems. This paper reviews the development of the numerical codes and details the reaction equations used. The majority of the devices utilized methanol as the fuel due to methanol’s low reforming temperature and high conversion, although, there are several methane fueled systems. As computational power has decreased in cost and increased in availability, the codes increased in complexity and accuracy. Initial models focused on the reformer, while more recently, the simulations began including other unit operations such as vaporizers, inlet manifolds, and combustors. These codes are critical for developing the next generation systems. The systems reviewed included, plate reactors, microchannel reactors, annulus reactors, wash-coated, packed bed systems.

  4. Advanced Techniques for Seismic Protection of Historical Buildings: Experimental and Numerical Approach

    SciTech Connect

    Mazzolani, Federico M.

    2008-07-08

    The seismic protection of historical and monumental buildings, namely dating back from the ancient age up to the 20th Century, is being looked at with greater and greater interest, above all in the Euro-Mediterranean area, its cultural heritage being strongly susceptible to undergo severe damage or even collapse due to earthquake. The cultural importance of historical and monumental constructions limits, in many cases, the possibility to upgrade them from the seismic point of view, due to the fear of using intervention techniques which could have detrimental effects on their cultural value. Consequently, a great interest is growing in the development of sustainable methodologies for the use of Reversible Mixed Technologies (RMTs) in the seismic protection of the existing constructions. RMTs, in fact, are conceived for exploiting the peculiarities of innovative materials and special devices, and they allow ease of removal when necessary. This paper deals with the experimental and numerical studies, framed within the EC PROHITECH research project, on the application of RMTs to the historical and monumental constructions mainly belonging to the cultural heritage of the Euro-Mediterranean area. The experimental tests and the numerical analyses are carried out at five different levels, namely full scale models, large scale models, sub-systems, devices, materials and elements.

  5. Numerical Study of Equilibrium, Stability, and Advanced Resistive Wall Mode Feedback Algorithms on KSTAR

    NASA Astrophysics Data System (ADS)

    Katsuro-Hopkins, Oksana; Sabbagh, S. A.; Bialek, J. M.; Park, H. K.; Kim, J. Y.; You, K.-I.; Glasser, A. H.; Lao, L. L.

    2007-11-01

    Stability to ideal MHD kink/ballooning modes and the resistive wall mode (RWM) is investigated for the KSTAR tokamak. Free-boundary equilibria that comply with magnetic field coil current constraints are computed for monotonic and reversed shear safety factor profiles and H-mode tokamak pressure profiles. Advanced tokamak operation at moderate to low plasma internal inductance shows that a factor of two improvement in the plasma beta limit over the no-wall beta limit is possible for toroidal mode number of unity. The KSTAR conducting structure, passive stabilizers, and in-vessel control coils are modeled by the VALEN-3D code and the active RWM stabilization performance of the device is evaluated using both standard and advanced feedback algorithms. Steady-state power and voltage requirements for the system are estimated based on the expected noise on the RWM sensor signals. Using NSTX experimental RWM sensors noise data as input, a reduced VALEN state-space LQG controller is designed to realistically assess KSTAR stabilization system performance.

  6. Investigation of the Hot-Stamping Process for Advanced High-Strength Steel Sheet by Numerical Simulation

    NASA Astrophysics Data System (ADS)

    Liu, H. S.; Xing, Z. W.; Bao, J.; Song, B. Y.

    2010-04-01

    Hot forming is a new way to manufacture complex-shaped components of advanced high-strength steel (AHSS) sheet with a minimum of spring-back. Numerical simulation is an effective way to examine the hot-forming process, particularly to determine thermal and thermo-mechanical characteristics and their dependencies on temperature, strain and strain rate. The flow behavior of the 22MnB5 AHSS is investigated through hot tensile tests. A 3D finite element (FE) model of hot-stamping process for the [InlineMediaObject not available: see fulltext.] shaped part is built under the ABAQUS/Explicit environment based on the solutions of several key problems, such as treatment of contact between blank and tools, determination of material characteristics and meshing, etc. Numerical simulation is carried out to investigate the influence of blank holder force (BHF) and die gap on the hot-forming process for the [InlineMediaObject not available: see fulltext.] shaped part. Numerical results show the FE model is effective in simulation of hot-forming process. Large BHF reduces the amount of spring-back and improves the contact of flange with tools while avoiding cracking of stamped part. Die gap has a considerable influence on the distribution of temperature on side walls; the larger the die gap, higher is the temperature on the sidewall of [InlineMediaObject not available: see fulltext.] shaped part.

  7. Numerical simulation of fine blanking process using fully coupled advanced constitutive equations with ductile damage

    NASA Astrophysics Data System (ADS)

    Labergere, C.; Saanouni, K.; Benafia, S.; Galmiche, J.; Sulaiman, H.

    2013-05-01

    This paper presents the modelling and adaptive numerical simulation of the fine blanking process. Thermodynamically-consistent constitutive equations, strongly coupled with ductile damage, together with specific boundary conditions (particular command of forces on blank holder and counterpunch) are presented. This model is implemented into ABAQUS/EXPLICIT using the Vumat user subroutine and connected with an adaptive 2D remeshing procedure. The different material parameters are identified for the steel S600MC using experimental tensile tests conducted until the final fracture. A parametric study aiming to examine the sensitivity of the process parameters (die radius, clearance die/punch) to the punch force and fracture surfaces topology (convex zone, sheared zone, fracture zone and the burr).

  8. Evaluation of Temperature Gradient in Advanced Automated Directional Solidification Furnace (AADSF) by Numerical Simulation

    NASA Technical Reports Server (NTRS)

    Bune, Andris V.; Gillies, Donald C.; Lehoczky, Sandor L.

    1996-01-01

    A numerical model of heat transfer using combined conduction, radiation and convection in AADSF was used to evaluate temperature gradients in the vicinity of the crystal/melt interface for variety of hot and cold zone set point temperatures specifically for the growth of mercury cadmium telluride (MCT). Reverse usage of hot and cold zones was simulated to aid the choice of proper orientation of crystal/melt interface regarding residual acceleration vector without actual change of furnace location on board the orbiter. It appears that an additional booster heater will be extremely helpful to ensure desired temperature gradient when hot and cold zones are reversed. Further efforts are required to investigate advantages/disadvantages of symmetrical furnace design (i.e. with similar length of hot and cold zones).

  9. Recent advances in methods for numerical solution of O.D.E. initial value problems

    NASA Technical Reports Server (NTRS)

    Bui, T. D.; Oppenheim, A. K.; Pratt, D. T.

    1984-01-01

    In the mathematical modeling of physical systems, it is often necessary to solve an initial value problem (IVP), consisting of a system of ordinary differential equations (ODE). A typical program produces approximate solutions at certain mesh points. Almost all existing codes try to control the local truncation error, while the user is really interested in controlling the true or global error. The present investigation provides a review of recent advances regarding the solution of the IVP, giving particular attention to stiff systems. Stiff phenomena are customarily defined in terms of the eigenvalues of the Jacobian. There are, however, some difficulties connected with this approach. It is pointed out that an estimate of the Lipschitz constant proves to be a very practical way to determine the stiffness of a problem.

  10. The validation of various schemes for parameterizing evaporation from bare soil for use in meteorological models: A numerical study using in situ data

    NASA Astrophysics Data System (ADS)

    Mihailović, Dragutin T.; Rajković, Borivoj; Dekić, Ljiljana; Pielke, Roger A.; Lee, Tsengdar J.; Ye, Zhuojia

    1995-11-01

    Parameterization of evaporation from a non-plant-covered surface is very important in the hierarchy strategy of modelling land surface processes. One of the representations frequently used in its computation is the resistance formulation. The performance of the evaporation schemes using the “α”, “β”, and their combination resistance approaches to parameterize evaporation from bare soil surfaces is discussed. For that purpose, the nine schemes, based on a different dependence of α and β on volumetric soil moisture content and its saturated value, are used. The tests of performances of the considered schemes are based on time integrations by the land surface module (BARESOIL) using observed data. The 23 data sets at a bare surface experimental site in Rimski Šančevi, Yugoslavia on chernozem soil, were used for the resistance algorithm evaluation. The quality of the schemes was compared with the observed values of the latent heat flux using several statistical parameters.

  11. Numerical solution of axisymmetric, unsteady free-boundary problems at finite Reynolds number. I - Finite-difference scheme and its application to the deformation of a bubble in a uniaxial straining flow

    NASA Astrophysics Data System (ADS)

    Kang, I. S.; Leal, L. G.

    1987-07-01

    A numerical technique for solving axisymmetric, unsteady free-boundary problems in fluid mechanics is presented. This finite-difference method is a generalization of the steady algorithm reported by Ryskin and Leal (1984). In this scheme, all boundary surfaces of the solution domain at any time coincide exactly with a coordinate line of a numerically generated orthogonal coordinate system. Thus, unreasonable grid deformation during calculation is not a problem. A transient algorithm for applying the orthogonal mapping technique to unsteady free-boundary problems is developed. The unsteady deformation of a bubble in a uniaxial extensional flow for Reynolds numbers between 0.1 and 100 is considered as an example.

  12. Numerical Modelling of Subduction Plate Interface, Technical Advances for Outstanding Questions

    NASA Astrophysics Data System (ADS)

    Le Pourhiet, L.; Ruh, J.; Pranger, C. C.; Zheng, L.; van Dinther, Y.; May, D.; Gerya, T.; Burov, E. B.

    2015-12-01

    and fluids pathways together with adaptative time stepping schemes permitting to switch from static long term-tectonic approach to seismic cycle modelling within the same frame work and discuss how the results of these forward models can be used to better assess coupling at the subduction zone interface from geodetic, seismologic and geologic record.

  13. Advancing predictive models for particulate formation in turbulent flames via massively parallel direct numerical simulations

    PubMed Central

    Bisetti, Fabrizio; Attili, Antonio; Pitsch, Heinz

    2014-01-01

    Combustion of fossil fuels is likely to continue for the near future due to the growing trends in energy consumption worldwide. The increase in efficiency and the reduction of pollutant emissions from combustion devices are pivotal to achieving meaningful levels of carbon abatement as part of the ongoing climate change efforts. Computational fluid dynamics featuring adequate combustion models will play an increasingly important role in the design of more efficient and cleaner industrial burners, internal combustion engines, and combustors for stationary power generation and aircraft propulsion. Today, turbulent combustion modelling is hindered severely by the lack of data that are accurate and sufficiently complete to assess and remedy model deficiencies effectively. In particular, the formation of pollutants is a complex, nonlinear and multi-scale process characterized by the interaction of molecular and turbulent mixing with a multitude of chemical reactions with disparate time scales. The use of direct numerical simulation (DNS) featuring a state of the art description of the underlying chemistry and physical processes has contributed greatly to combustion model development in recent years. In this paper, the analysis of the intricate evolution of soot formation in turbulent flames demonstrates how DNS databases are used to illuminate relevant physico-chemical mechanisms and to identify modelling needs. PMID:25024412

  14. A review on recent advances in numerical modelling of bone cutting.

    PubMed

    Marco, Miguel; Rodríguez-Millán, Marcos; Santiuste, Carlos; Giner, Eugenio; Henar Miguélez, María

    2015-04-01

    Common practice of surgical treatments in orthopaedics and traumatology involves cutting processes of bone. These operations introduce risk of thermo-mechanical damage, since the threshold of critical temperature producing thermal osteonecrosis is very low. Therefore, it is important to develop predictive tools capable of simulating accurately the increase of temperature during bone cutting, being the modelling of these processes still a challenge. In addition, the prediction of cutting forces and mechanical damage is also important during machining operations. As the accuracy of simulations depends greatly on the proper choice of the thermo-mechanical properties, an essential part of the numerical model is the constitutive behaviour of the bone tissue, which is considered in different ways in the literature. This paper focuses on the review of the main contributions in modelling of bone cutting with special attention to the bone mechanical behaviour. The aim is to give the reader a complete vision of the approaches commonly presented in the literature in order to help in the development of accurate models for bone cutting.

  15. Advanced numerical techniques for accurate unsteady simulations of a wingtip vortex

    NASA Astrophysics Data System (ADS)

    Ahmad, Shakeel

    A numerical technique is developed to simulate the vortices associated with stationary and flapping wings. The Unsteady Reynolds-Averaged Navier-Stokes (URANS) equations are used over an unstructured grid. The present work assesses the locations of the origins of vortex generation, models those locations and develops a systematic mesh refinement strategy to simulate vortices more accurately using the URANS model. The vortex center plays a key role in the analysis of the simulation data. A novel approach to locating a vortex center is also developed referred to as the Max-Max criterion. Experimental validation of the simulated vortex from a stationary NACA0012 wing is achieved. The tangential velocity along the core of the vortex falls within five percent of the experimental data in the case of the stationary NACA0012 simulation. The wing surface pressure coefficient also matches with the experimental data. The refinement techniques are then focused on unsteady simulations of pitching and dual-mode wing flapping. Tip vortex strength, location, and wing surface pressure are analyzed. Links to vortex behavior and wing motion are inferred. Key words: vortex, tangential velocity, Cp, vortical flow, unsteady vortices, URANS, Max-Max, Vortex center

  16. Advancing predictive models for particulate formation in turbulent flames via massively parallel direct numerical simulations.

    PubMed

    Bisetti, Fabrizio; Attili, Antonio; Pitsch, Heinz

    2014-08-13

    Combustion of fossil fuels is likely to continue for the near future due to the growing trends in energy consumption worldwide. The increase in efficiency and the reduction of pollutant emissions from combustion devices are pivotal to achieving meaningful levels of carbon abatement as part of the ongoing climate change efforts. Computational fluid dynamics featuring adequate combustion models will play an increasingly important role in the design of more efficient and cleaner industrial burners, internal combustion engines, and combustors for stationary power generation and aircraft propulsion. Today, turbulent combustion modelling is hindered severely by the lack of data that are accurate and sufficiently complete to assess and remedy model deficiencies effectively. In particular, the formation of pollutants is a complex, nonlinear and multi-scale process characterized by the interaction of molecular and turbulent mixing with a multitude of chemical reactions with disparate time scales. The use of direct numerical simulation (DNS) featuring a state of the art description of the underlying chemistry and physical processes has contributed greatly to combustion model development in recent years. In this paper, the analysis of the intricate evolution of soot formation in turbulent flames demonstrates how DNS databases are used to illuminate relevant physico-chemical mechanisms and to identify modelling needs.

  17. 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.

  18. 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.

  19. Numerical Investigation of a Cascaded Longitudinal Space-Charge Amplifier at the Fermilab's Advanced Superconducting Test Accelerator

    SciTech Connect

    Halavanau, A.; Piot, P.

    2015-06-01

    In a cascaded longitudinal space-charge amplifier (LSCA), initial density noise in a relativistic e-beam is amplified via the interplay of longitudinal space charge forces and properly located dispersive sections. This type of amplification process was shown to potentially result in large final density modulations [1] compatible with the production of broadband electromagnetic radiation. The technique was recently demonstrated in the optical domain [2]. In this paper we investigate, via numerical simulations, the performances of a cascaded LSCA beamline at the Fermilab’s Advanced Superconducting Test Accelerator (ASTA). We especially explore the properties of the produced broadband radiation. Our studies have been conducted with a grid-less three-dimensional space-charge algorithm.

  20. Optimised prefactored compact schemes for linear wave propagation phenomena

    NASA Astrophysics Data System (ADS)

    Rona, A.; Spisso, I.; Hall, E.; Bernardini, M.; Pirozzoli, S.

    2017-01-01

    A family of space- and time-optimised prefactored compact schemes are developed that minimise the computational cost for given levels of numerical error in wave propagation phenomena, with special reference to aerodynamic sound. This work extends the approach of Pirozzoli [1] to the MacCormack type prefactored compact high-order schemes developed by Hixon [2], in which their shorter Padé stencil from the prefactorisation leads to a simpler enforcement of numerical boundary conditions. An explicit low-storage multi-step Runge-Kutta integration advances the states in time. Theoretical predictions for spatial and temporal error bounds are derived for the cost-optimised schemes and compared against benchmark schemes of current use in computational aeroacoustic applications in terms of computational cost for a given relative numerical error value. One- and two-dimensional test cases are presented to examine the effectiveness of the cost-optimised schemes for practical flow computations. An effectiveness up to about 50% higher than the standard schemes is verified for the linear one-dimensional advection solver, which is a popular baseline solver kernel for computational physics problems. A substantial error reduction for a given cost is also obtained in the more complex case of a two-dimensional acoustic pulse propagation, provided the optimised schemes are made to operate close to their nominal design points.

  1. 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.

  2. Advancing Efficient All-Electron Electronic Structure Methods Based on Numeric Atom-Centered Orbitals for Energy Related Materials

    NASA Astrophysics Data System (ADS)

    Blum, Volker

    This talk describes recent advances of a general, efficient, accurate all-electron electronic theory approach based on numeric atom-centered orbitals; emphasis is placed on developments related to materials for energy conversion and their discovery. For total energies and electron band structures, we show that the overall accuracy is on par with the best benchmark quality codes for materials, but scalable to large system sizes (1,000s of atoms) and amenable to both periodic and non-periodic simulations. A recent localized resolution-of-identity approach for the Coulomb operator enables O (N) hybrid functional based descriptions of the electronic structure of non-periodic and periodic systems, shown for supercell sizes up to 1,000 atoms; the same approach yields accurate results for many-body perturbation theory as well. For molecular systems, we also show how many-body perturbation theory for charged and neutral quasiparticle excitation energies can be efficiently yet accurately applied using basis sets of computationally manageable size. Finally, the talk highlights applications to the electronic structure of hybrid organic-inorganic perovskite materials, as well as to graphene-based substrates for possible future transition metal compound based electrocatalyst materials. All methods described here are part of the FHI-aims code. VB gratefully acknowledges contributions by numerous collaborators at Duke University, Fritz Haber Institute Berlin, TU Munich, USTC Hefei, Aalto University, and many others around the globe.

  3. Numerical and experimental evaluation of the impact performance of advanced high-strength steel sheets based on a damage model

    NASA Astrophysics Data System (ADS)

    Ma, Ning; Park, Taejoon; Kim, Dongun; Kim, Chongmin; Chung, Kwansoo

    2010-06-01

    The impact performance in a Charpy impact test was experimentally and numerically studied for the advanced high-strength steel sheets (AHSS) TWIP940 and TRIP590 as well as the high-strength grade known as 340R. To characterize the mechanical properties, uni-axial simple tension tests were conducted to determine the anisotropic properties and strain rate sensitivities of these materials. In particular, the high-speed strain-rate sensitivity of TRIP590 and 340R (rate sensitive) was also characterized to account for the high strain rates involved in the Charpy impact test. To evaluate fracture behavior in the Charpy impact test, a new damage model including a triaxiality-dependent fracture criterion and hardening behavior with stiffness deterioration was introduced. The model was calibrated via numerical simulations and experiments involving simple tension and V-notch tests. The new damage model along with the anisotropic yield function Hill 1948 was incorporated into the ABAQUS/Explicit FEM code, which performed reasonably well to predict the impact energy absorbed during the Charpy impact test.

  4. Numerical solution of the gross-pitaevskii equation using an explicit finite-difference scheme: An application to trapped bose-einstein condensates

    PubMed

    Cerimele; Chiofalo; Pistella; Succi; Tosi

    2000-07-01

    We present the application of a fast, explicit time-marching scheme for the solution of the Gross-Pitaevskii equation in cylindrical geometry. The scheme is validated on simple analytical tests and demonstrated for two situations of physical interest in experiments on the Bose-Einstein condensation (BEC) of trapped alkali-metal vapors. It is tested by reproducing known results on the free expansion of a BEC after removing a cylindrical trap, and it is then used to address the formation of matter-wave pulses that result from gravity-induced transport of a condensate in an optical potential.

  5. Numerical Viscous Flow Analysis of an Advanced Semispan Diamond-Wing Model at High-Life Conditions

    NASA Technical Reports Server (NTRS)

    Ghaffari, F.; Biedron, R. T.; Luckring, J. M.

    2002-01-01

    Turbulent Navier-Stokes computational results are presented for an advanced diamond wing semispan model at low speed, high-lift conditions. The numerical results are obtained in support of a wind-tunnel test that was conducted in the National Transonic Facility (NTF) at the NASA Langley Research Center. The model incorporated a generic fuselage and was mounted on the tunnel sidewall using a constant width standoff. The analyses include: (1) the numerical simulation of the NTF empty, tunnel flow characteristics; (2) semispan high-lift model with the standoff in the tunnel environment; (3) semispan high-lift model with the standoff and viscous sidewall in free air; and (4) semispan high-lift model without the standoff in free air. The computations were performed at conditions that correspond to a nominal approach and landing configuration. The wing surface pressure distributions computed for the model in both the tunnel and in free air agreed well with the corresponding experimental data and they both indicated small increments due to the wall interference effects. However, the wall interference effects were found to be more pronounced in the total measured and the computed lift, drag and pitching moment due to standard induced up-flow effects. Although the magnitudes of the computed forces and moment were slightly off compared to the measured data, the increments due the wall interference effects were predicted well. The numerical predictions are also presented on the combined effects of the tunnel sidewall boundary layer and the standoff geometry on the fuselage fore-body pressure distributions and the resulting impact on the overall configuration longitudinal aerodynamic characteristics.

  6. 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.

  7. Incorporating an advanced aerosol activation parameterization into WRF-CAM5: Model evaluation and parameterization intercomparison: An Advanced Aerosol Activation Scheme

    SciTech Connect

    Zhang, Yang; Zhang, Xin; Wang, Kai; He, Jian; Leung, L. Ruby; Fan, Jiwen; Nenes, Athanasios

    2015-07-22

    Aerosol activation into cloud droplets is an important process that governs aerosol indirect effects. The advanced treatment of aerosol activation by Fountoukis and Nenes (2005) and its recent updates, collectively called the FN series, have been incorporated into a newly developed regional coupled climate-air quality model based on the Weather Research and Forecasting model with the physics package of the Community Atmosphere Model version 5 (WRF-CAM5) to simulate aerosol-cloud interactions in both resolved and convective clouds. The model is applied to East Asia for two full years of 2005 and 2010. A comprehensive model evaluation is performed for model predictions of meteorological, radiative, and cloud variables, chemical concentrations, and column mass abundances against satellite data and surface observations from air quality monitoring sites across East Asia. The model performs overall well for major meteorological variables including near-surface temperature, specific humidity, wind speed, precipitation, cloud fraction, precipitable water, downward shortwave and longwave radiation, and column mass abundances of CO, SO2, NO2, HCHO, and O3 in terms of both magnitudes and spatial distributions. Larger biases exist in the predictions of surface concentrations of CO and NOx at all sites and SO2, O3, PM2.5, and PM10 concentrations at some sites, aerosol optical depth, cloud condensation nuclei over ocean, cloud droplet number concentration (CDNC), cloud liquid and ice water path, and cloud optical thickness. Compared with the default Abdul-Razzack Ghan (2000) parameterization, simulations with the FN series produce ~107–113% higher CDNC, with half of the difference attributable to the higher aerosol activation fraction by the FN series and the remaining half due to feedbacks in subsequent cloud microphysical processes. With the higher CDNC, the FN series are more skillful in simulating cloud water path, cloud optical thickness, downward shortwave radiation

  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. 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.

  10. Upwind schemes and bifurcating solutions in real gas computations

    NASA Technical Reports Server (NTRS)

    Suresh, Ambady; Liou, Meng-Sing

    1992-01-01

    The area of high speed flow is seeing a renewed interest due to advanced propulsion concepts such as the National Aerospace Plane (NASP), Space Shuttle, and future civil transport concepts. Upwind schemes to solve such flows have become increasingly popular in the last decade due to their excellent shock capturing properties. In the first part of this paper the authors present the extension of the Osher scheme to equilibrium and non-equilibrium gases. For simplicity, the source terms are treated explicitly. Computations based on the above scheme are presented to demonstrate the feasibility, accuracy and efficiency of the proposed scheme. One of the test problems is a Chapman-Jouguet detonation problem for which numerical solutions have been known to bifurcate into spurious weak detonation solutions on coarse grids. Results indicate that the numerical solution obtained depends both on the upwinding scheme used and the limiter employed to obtain second order accuracy. For example, the Osher scheme gives the correct CJ solution when the super-bee limiter is used, but gives the spurious solution when the Van Leer limiter is used. With the Roe scheme the spurious solution is obtained for all limiters.

  11. Numerical Investigation of Cross Flow Phenomena in a Tight-Lattice Rod Bundle Using Advanced Interface Tracking Method

    NASA Astrophysics Data System (ADS)

    Zhang, Weizhong; Yoshida, Hiroyuki; Ose, Yasuo; Ohnuki, Akira; Akimoto, Hajime; Hotta, Akitoshi; Fujimura, Ken

    In relation to the design of an innovative FLexible-fuel-cycle Water Reactor (FLWR), investigation of thermal-hydraulic performance in tight-lattice rod bundles of the FLWR is being carried out at Japan Atomic Energy Agency (JAEA). The FLWR core adopts a tight triangular lattice arrangement with about 1 mm gap clearance between adjacent fuel rods. In view of importance of accurate prediction of cross flow between subchannels in the evaluation of the boiling transition (BT) in the FLWR core, this study presents a statistical evaluation of numerical simulation results obtained by a detailed two-phase flow simulation code, TPFIT, which employs an advanced interface tracking method. In order to clarify mechanisms of cross flow in such tight lattice rod bundles, the TPFIT is applied to simulate water-steam two-phase flow in two modeled subchannels. Attention is focused on instantaneous fluctuation characteristics of cross flow. With the calculation of correlation coefficients between differential pressure and gas/liquid mixing coefficients, time scales of cross flow are evaluated, and effects of mixing section length, flow pattern and gap spacing on correlation coefficients are investigated. Differences in mechanism between gas and liquid cross flows are pointed out.

  12. A joint numerical and experimental study of the jet of an aircraft engine installation with advanced techniques

    NASA Astrophysics Data System (ADS)

    Brunet, V.; Molton, P.; Bézard, H.; Deck, S.; Jacquin, L.

    2012-01-01

    This paper describes the results obtained during the European Union JEDI (JEt Development Investigations) project carried out in cooperation between ONERA and Airbus. The aim of these studies was first to acquire a complete database of a modern-type engine jet installation set under a wall-to-wall swept wing in various transonic flow conditions. Interactions between the engine jet, the pylon, and the wing were studied thanks to ¤advanced¥ measurement techniques. In parallel, accurate Reynolds-averaged Navier Stokes (RANS) simulations were carried out from simple ones with the Spalart Allmaras model to more complex ones like the DRSM-SSG (Differential Reynolds Stress Modef of Speziale Sarkar Gatski) turbulence model. In the end, Zonal-Detached Eddy Simulations (Z-DES) were also performed to compare different simulation techniques. All numerical results are accurately validated thanks to the experimental database acquired in parallel. This complete and complex study of modern civil aircraft engine installation allowed many upgrades in understanding and simulation methods to be obtained. Furthermore, a setup for engine jet installation studies has been validated for possible future works in the S3Ch transonic research wind-tunnel. The main conclusions are summed up in this paper.

  13. Numerical and structural aberrations in advanced neuroblastoma tumours by CGH analysis; survival correlates with chromosome 17 status

    PubMed Central

    Cunsolo, C Lo; Bicocchi, M P; Petti, A R; Tonini, G P

    2000-01-01

    Rapid tumour progression in neuroblastoma is associated with MYCN amplification, deletion of the short arm of chromosome 1 and gain of 17q. However, patients with advanced disease without MYCN amplification and/or 1p deletion have a very poor outcome too, which suggests other genetic defects may predict an unfavourable prognosis. We employed CGH to study 22 tumours of patients at stages 3 and 4 over one year of age (6 and 16 cases respectively). Patients were divided in groups (A) long-term survivors and (B) short-term survivors. CGH showed a total of 226 chromosome imbalances (110 in group A and 116 in group B). The neuroblastoma cells of long-term survivors showed a preponderance of numerical aberrations (54%vs 43%); particularly gains of entire chromosomes 1 (P< 0.03), 7 (P< 0.04) and 19 (P< 0.05). An extra copy of 17 was detected in 6/8 (75%) samples of group A and only 1/14 (7%) samples of group B (P< 0.002). Conversely, tumours of patients who died from disease progression displayed a higher frequency of structural abnormalities (43%vs 35%), including loss of 1p, 9p, 11q, 15q and 18q and gain of 12q, although the difference was not significant (P= 0.24). Unbalanced gain of 17q was detected in 8/14 (57%) tumours of group B and only 1/8 (13%) tumours of group A (P< 0.05). The peculiar genetic difference observed in the tumours of long and short-term survivors may have prognostic relevance. © 2000 Cancer Research Campaign PMID:11044353

  14. 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.

  15. Advancing Clouds Lifecycle Representation in Numerical Models Using Innovative Analysis Methods that Bridge ARM Observations and Models Over a Breadth of Scales

    SciTech Connect

    Kollias, Pavlos

    2016-09-06

    This the final report for the DE-SC0007096 - Advancing Clouds Lifecycle Representation in Numerical Models Using Innovative Analysis Methods that Bridge ARM Observations and Models Over a Breadth of Scales - PI: Pavlos Kollias. The final report outline the main findings of the research conducted using the aforementioned award in the area of cloud research from the cloud scale (10-100 m) to the mesoscale (20-50 km).

  16. INTERACTION OF LASER RADIATION WITH MATTER: Numerical simulation of the quasi-resonance regime of a transient double resonance in a scheme with a common upper level at a large inhomogeneous broadening of quantum transitions

    NASA Astrophysics Data System (ADS)

    Dmitriev, A. E.; Parshkov, O. M.

    2005-08-01

    The transient double resonance in the Λ scheme is numerically investigated in the case of a strong inhomogeneous spectral broadening of a medium and nonzero detunings of the frequencies of interacting pulses from the central frequencies of corresponding quantum transitions. It is shown that the signal pulse efficiently interacts with the pump pulse only when a certain condition imposed on the nonzero detunings is satisfied. If this condition is strongly violated at the input to the resonance medium, only a weak field of the rear edge of the input signal pulse mainly interacts with the pump field. In this case, two pulses with different frequencies are formed in the signal channel. This is explained by the specific interaction of radiation with Doppler-broadened quantum transitions.

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

    NASA Technical Reports Server (NTRS)

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

    2007-01-01

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

  18. Numerical Relativity

    NASA Technical Reports Server (NTRS)

    Baker, John G.

    2009-01-01

    Recent advances in numerical relativity have fueled an explosion of progress in understanding the predictions of Einstein's theory of gravity, General Relativity, for the strong field dynamics, the gravitational radiation wave forms, and consequently the state of the remnant produced from the merger of compact binary objects. I will review recent results from the field, focusing on mergers of two black holes.

  19. Numerical Modeling for Hole-Edge Cracking of Advanced High-Strength Steels (AHSS) Components in the Static Bend Test

    NASA Astrophysics Data System (ADS)

    Kim, Hyunok; Mohr, William; Yang, Yu-Ping; Zelenak, Paul; Kimchi, Menachem

    2011-08-01

    Numerical modeling of local formability, such as hole-edge cracking and shear fracture in bending of AHSS, is one of the challenging issues for simulation engineers for prediction and evaluation of stamping and crash performance of materials. This is because continuum-mechanics-based finite element method (FEM) modeling requires additional input data, "failure criteria" to predict the local formability limit of materials, in addition to the material flow stress data input for simulation. This paper presents a numerical modeling approach for predicting hole-edge failures during static bend tests of AHSS structures. A local-strain-based failure criterion and a stress-triaxiality-based failure criterion were developed and implemented in LS-DYNA simulation code to predict hole-edge failures in component bend tests. The holes were prepared using two different methods: mechanical punching and water-jet cutting. In the component bend tests, the water-jet trimmed hole showed delayed fracture at the hole-edges, while the mechanical punched hole showed early fracture as the bending angle increased. In comparing the numerical modeling and test results, the load-displacement curve, the displacement at the onset of cracking, and the final crack shape/length were used. Both failure criteria also enable the numerical model to differentiate between the local formability limit of mechanical-punched and water-jet-trimmed holes. The failure criteria and static bend test developed here are useful to evaluate the local formability limit at a structural component level for automotive crash tests.

  20. Modified symplectic schemes with nearly-analytic discrete operators for acoustic wave simulations

    NASA Astrophysics Data System (ADS)

    Liu, Shaolin; Yang, Dinghui; Lang, Chao; Wang, Wenshuai; Pan, Zhide

    2017-04-01

    Using a structure-preserving algorithm significantly increases the computational efficiency of solving wave equations. However, only a few explicit symplectic schemes are available in the literature, and the capabilities of these symplectic schemes have not been sufficiently exploited. Here, we propose a modified strategy to construct explicit symplectic schemes for time advance. The acoustic wave equation is transformed into a Hamiltonian system. The classical symplectic partitioned Runge-Kutta (PRK) method is used for the temporal discretization. Additional spatial differential terms are added to the PRK schemes to form the modified symplectic methods and then two modified time-advancing symplectic methods with all of positive symplectic coefficients are then constructed. The spatial differential operators are approximated by nearly-analytic discrete (NAD) operators, and we call the fully discretized scheme modified symplectic nearly analytic discrete (MSNAD) method. Theoretical analyses show that the MSNAD methods exhibit less numerical dispersion and higher stability limits than conventional methods. Three numerical experiments are conducted to verify the advantages of the MSNAD methods, such as their numerical accuracy, computational cost, stability, and long-term calculation capability.

  1. 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.

  2. Multi-resolution analysis for ENO schemes

    NASA Technical Reports Server (NTRS)

    Harten, Ami

    1993-01-01

    Given a function u(x) which is represented by its cell-averages in cells which are formed by some unstructured grid, we show how to decompose the function into various scales of variation. This is done by considering a set of nested grids in which the given grid is the finest, and identifying in each locality the coarsest grid in the set from which u(x) can be recovered to a prescribed accuracy. We apply this multi-resolution analysis to Essentially Non-oscillatory Schemes (ENO) schemes in order to reduce the number of numerical flux computations which is needed in order to advance the solution by one time-step. This is accomplished by decomposing the numerical solution at the beginning of each time-step into levels of resolution, and performing the computation in each locality at the appropriate coarser grid. We present an efficient algorithm for implementing this program in the one-dimensional case; this algorithm can be extended to the multi-dimensional case with cartesian grids.

  3. Nonlinearly stable compact schemes for shock calculations

    NASA Technical Reports Server (NTRS)

    Cockburn, Bernardo; Shu, Chi-Wang

    1992-01-01

    The applications of high-order, compact finite difference methods in shock calculations are discussed. The main concern is to define a local mean which will serve as a reference for introducing a local nonlinear limiting to control spurious numerical oscillations while maintaining the formal accuracy of the scheme. For scalar conservation laws, the resulting schemes can be proven total-variation stable in one space dimension and maximum-norm stable in multiple space dimensions. Numerical examples are shown to verify accuracy and stability of such schemes for problems containing shocks. These ideas can also be applied to other implicit schemes such as the continuous Galerkin finite element methods.

  4. Numerical Study of the Impact of Resonant Magnetic Perturbations on Recycling Sources In Advanced Divertor Configurations of NSTX-U

    NASA Astrophysics Data System (ADS)

    Waters, Ian; Flesch, Kurt; Frerichs, Heinke; Schmitz, Oliver; Ahn, Joon-Wook; Canal, Gustavo; Evans, Todd; Soukhanovskii, Vsevolod

    2016-10-01

    Explorations are under way to optimize the magnetic topology in the plasma edge of NSTX-U with the goal of improving neutral and impurity fueling and exhaust. Advanced divertor configurations combined with resonant magnetic perturbation (RMP) fields are being considered to improve peak heat and particle loads, stabilize edge instabilities, adjust plasma refueling, and control impurity transport. In this study, the EMC3-EIRENE fluid plasma and kinetic neutral transport code is used to investigate snowflake divertor configurations with and without RMP fields. Analysis of the edge recycling sources show that RMP fields induce a transition from a linear recycling regime into a high recycling regime at densities that are lower than in non-perturbed cases. This transition is also accompanied by a shift in the spatial distribution of these recycling sources and neutral atoms, and is impacted by the strength of the perturbations. An overview of results from different standard and snowflake divertor configurations will be presented. This work was funded by the Department of Energy under Grant DE-SC0012315.

  5. Multi-resolution analysis for ENO schemes

    NASA Technical Reports Server (NTRS)

    Harten, Ami

    1991-01-01

    Given an function, u(x), which is represented by its cell-averages in cells which are formed by some unstructured grid, we show how to decompose the function into various scales of variation. This is done by considering a set of nested grids in which the given grid is the finest, and identifying in each locality the coarsest grid in the set from which u(x) can be recovered to a prescribed accuracy. This multi-resolution analysis was applied to essentially non-oscillatory (ENO) schemes in order to advance the solution by one time-step. This is accomplished by decomposing the numerical solution at the beginning of each time-step into levels of resolution, and performing the computation in each locality at the appropriate coarser grid. An efficient algorithm for implementing this program in the 1-D case is presented; this algorithm can be extended to the multi-dimensional case with Cartesian grids.

  6. Numerical Modeling for Springback Predictions by Considering the Variations of Elastic Modulus in Stamping Advanced High-Strength Steels (AHSS)

    NASA Astrophysics Data System (ADS)

    Kim, Hyunok; Kimchi, Menachem

    2011-08-01

    This paper presents a numerical modeling approach for predicting springback by considering the variations of elastic modulus on springback in stamping AHSS. Various stamping tests and finite-element method (FEM) simulation codes were used in this study. The cyclic loading-unloading tensile tests were conducted to determine the variations of elastic modulus for dual-phase (DP) 780 sheet steel. The biaxial bulge test was used to obtain plastic flow stress data. The non-linear reduction of elastic modulus for increasing the plastic strain was formulated by using the Yoshida model that was implemented in FEM simulations for springback. To understand the effects of material properties on springback, experiments were conducted with a simple geometry such as U-shape bending and the more complex geometry such as the curved flanging and S-rail stamping. Different measurement methods were used to confirm the final part geometry. Two different commercial FEM codes, LS-DYNA and DEFORM, were used to compare the experiments. The variable elastic modulus improved springback predictions in U-shape bending and curved flanging tests compared to FEM with the constant elastic modulus. However, in S-rail stamping tests, both FEM models with the isotropic hardening model showed limitations in predicting the sidewall curl of the S-rail part after springback. To consider the kinematic hardening and Bauschinger effects that result from material bending-unbending in S-rail stamping, the Yoshida model was used for FEM simulation of S-rail stamping and springback. The FEM predictions showed good improvement in correlating with experiments.

  7. 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.

  8. Towards Direct Numerical Simulation of mass and energy fluxes at the soil-atmospheric interface with advanced Lattice Boltzmann methods

    NASA Astrophysics Data System (ADS)

    Wang, Ying; Krafczyk, Manfred; Geier, Martin; Schönherr, Martin

    2014-05-01

    The quantification of soil evaporation and of soil water content dynamics near the soil surface are critical in the physics of land-surface processes on many scales and are dominated by multi-component and multi-phase mass and energy fluxes between the ground and the atmosphere. Although it is widely recognized that both liquid and gaseous water movement are fundamental factors in the quantification of soil heat flux and surface evaporation, their computation has only started to be taken into account using simplified macroscopic models. As the flow field over the soil can be safely considered as turbulent, it would be natural to study the detailed transient flow dynamics by means of Large Eddy Simulation (LES [1]) where the three-dimensional flow field is resolved down to the laminar sub-layer. Yet this requires very fine resolved meshes allowing a grid resolution of at least one order of magnitude below the typical grain diameter of the soil under consideration. In order to gain reliable turbulence statistics, up to several hundred eddy turnover times have to be simulated which adds up to several seconds of real time. Yet, the time scale of the receding saturated water front dynamics in the soil is on the order of hours. Thus we are faced with the task of solving a transient turbulent flow problem including the advection-diffusion of water vapour over the soil-atmospheric interface represented by a realistic tomographic reconstruction of a real porous medium taken from laboratory probes. Our flow solver is based on the Lattice Boltzmann method (LBM) [2] which has been extended by a Cumulant approach similar to the one described in [3,4] to minimize the spurious coupling between the degrees of freedom in previous LBM approaches and can be used as an implicit LES turbulence model due to its low numerical dissipation and increased stability at high Reynolds numbers. The kernel has been integrated into the research code Virtualfluids [5] and delivers up to 30% of the

  9. Numerical modeling of turbulent supersonic reacting coaxial jets

    NASA Technical Reports Server (NTRS)

    Eklund, Dean R.; Hassan, H. A.; Drummond, J. Philip

    1989-01-01

    The paper considers the mixing and subsequent combustion within turbulent reacting shear layers. A computer program was developed to solve the axisymmetric Reynolds averaged Navier-Stokes equations. The numerical method integrates the Reynolds averaged Navier-Stokes equations using a finite volume approach while advancing the solution forward in time using a Runge-Kutta scheme. Three separate flowfields are investigated and it is found that no single turbulence model considered could accurately predict the degree of mixing for all three cases.

  10. 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.

  11. Technically Extended MultiParameter Optimization (TEMPO): An Advanced Robust Scoring Scheme To Calculate Central Nervous System Druggability and Monitor Lead Optimization.

    PubMed

    Ghose, Arup K; Ott, Gregory R; Hudkins, Robert L

    2017-01-18

    At the discovery stage, it is important to understand the drug design concepts for a CNS drug compared to those for a non-CNS drug. Previously, we published on ideal CNS drug property space and defined in detail the physicochemical property distribution of CNS versus non-CNS oral drugs, the application of radar charting (a graphical representation of multiple physicochemical properties used during CNS lead optimization), and a recursive partition classification tree to differentiate between CNS- and non-CNS drugs. The objective of the present study was to further understand the differentiation of physicochemical properties between CNS and non-CNS oral drugs by the development and application of a new CNS scoring scheme: Technically Extended MultiParameter Optimization (TEMPO). In this multiparameter method, we identified eight key physicochemical properties critical for accurately assessing CNS druggability: (1) number of basic amines, (2) carbon-heteroatom (non-carbon, non-hydrogen) ratio, (3) number of aromatic rings, (4) number of chains, (5) number of rotatable bonds, (6) number of H-acceptors, (7) computed octanol/water partition coefficient (AlogP), and (8) number of nonconjugated C atoms in nonaromatic rings. Significant features of the CNS-TEMPO penalty score are the extension of the multiparameter approach to generate an accurate weight factor for each physicochemical property, the use of limits on both sides of the computed property space range during the penalty calculation, and the classification of CNS and non-CNS drug scores. CNS-TEMPO significantly outperformed CNS-MPO and the Schrödinger QikProp CNS parameter (QP_CNS) in evaluating CNS drugs and has been extensively applied in support of CNS lead optimization programs.

  12. 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.

  13. ULTRA-SHARP nonoscillatory convection schemes for high-speed steady multidimensional flow

    NASA Technical Reports Server (NTRS)

    Leonard, B. P.; Mokhtari, Simin

    1990-01-01

    For convection-dominated flows, classical second-order methods are notoriously oscillatory and often unstable. For this reason, many computational fluid dynamicists have adopted various forms of (inherently stable) first-order upwinding over the past few decades. Although it is now well known that first-order convection schemes suffer from serious inaccuracies attributable to artificial viscosity or numerical diffusion under high convection conditions, these methods continue to enjoy widespread popularity for numerical heat transfer calculations, apparently due to a perceived lack of viable high accuracy alternatives. But alternatives are available. For example, nonoscillatory methods used in gasdynamics, including currently popular TVD schemes, can be easily adapted to multidimensional incompressible flow and convective transport. This, in itself, would be a major advance for numerical convective heat transfer, for example. But, as is shown, second-order TVD schemes form only a small, overly restrictive, subclass of a much more universal, and extremely simple, nonoscillatory flux-limiting strategy which can be applied to convection schemes of arbitrarily high order accuracy, while requiring only a simple tridiagonal ADI line-solver, as used in the majority of general purpose iterative codes for incompressible flow and numerical heat transfer. The new universal limiter and associated solution procedures form the so-called ULTRA-SHARP alternative for high resolution nonoscillatory multidimensional steady state high speed convective modelling.

  14. The Impact of Microphysical Schemes on Hurricane Intensity and Track

    NASA Technical Reports Server (NTRS)

    Tao, Wei-Kuo; Shi, Jainn Jong; Chen, Shuyi S.; Lang, Stephen; Lin, Pay-Liam; Hong, Song-You; Peters-Lidard, Christa; Hou, Arthur

    2011-01-01

    During the past decade, both research and operational numerical weather prediction models [e.g. the Weather Research and Forecasting Model (WRF)] have started using more complex microphysical schemes originally developed for high-resolution cloud resolving models (CRMs) with 1-2 km or less horizontal resolutions. WRF is a next-generation meso-scale forecast model and assimilation system. It incorporates a modern software framework, advanced dynamics, numerics and data assimilation techniques, a multiple moveable nesting capability, and improved physical packages. WRF can be used for a wide range of applications, from idealized research to operational forecasting, with an emphasis on horizontal grid sizes in the range of 1-10 km. The current WRF includes several different microphysics options. At NASA Goddard, four different cloud microphysics options have been implemented into WRF. The performance of these schemes is compared to those of the other microphysics schemes available in WRF for an Atlantic hurricane case (Katrina). In addition, a brief review of previous modeling studies on the impact of microphysics schemes and processes on the intensity and track of hurricanes is presented and compared against the current Katrina study. In general, all of the studies show that microphysics schemes do not have a major impact on track forecasts but do have more of an effect on the simulated intensity. Also, nearly all of the previous studies found that simulated hurricanes had the strongest deepening or intensification when using only warm rain physics. This is because all of the simulated precipitating hydrometeors are large raindrops that quickly fall out near the eye-wall region, which would hydrostatically produce the lowest pressure. In addition, these studies suggested that intensities become unrealistically strong when evaporative cooling from cloud droplets and melting from ice particles are removed as this results in much weaker downdrafts in the simulated

  15. Final Progress Report: Collaborative Research: Decadal-to-Centennial Climate & Climate Change Studies with Enhanced Variable and Uniform Resolution GCMs Using Advanced Numerical Techniques

    SciTech Connect

    Fox-Rabinovitz, M; Cote, J

    2009-06-05

    The joint U.S-Canadian project has been devoted to: (a) decadal climate studies using developed state-of-the-art GCMs (General Circulation Models) with enhanced variable and uniform resolution; (b) development and implementation of advanced numerical techniques; (c) research in parallel computing and associated numerical methods; (d) atmospheric chemistry experiments related to climate issues; (e) validation of regional climate modeling strategies for nested- and stretched-grid models. The variable-resolution stretched-grid (SG) GCMs produce accurate and cost-efficient regional climate simulations with mesoscale resolution. The advantage of the stretched grid approach is that it allows us to preserve the high quality of both global and regional circulations while providing consistent interactions between global and regional scales and phenomena. The major accomplishment for the project has been the successful international SGMIP-1 and SGMIP-2 (Stretched-Grid Model Intercomparison Project, phase-1 and phase-2) based on this research developments and activities. The SGMIP provides unique high-resolution regional and global multi-model ensembles beneficial for regional climate modeling and broader modeling community. The U.S SGMIP simulations have been produced using SciDAC ORNL supercomputers. Collaborations with other international participants M. Deque (Meteo-France) and J. McGregor (CSIRO, Australia) and their centers and groups have been beneficial for the strong joint effort, especially for the SGMIP activities. The WMO/WCRP/WGNE endorsed the SGMIP activities in 2004-2008. This project reflects a trend in the modeling and broader communities to move towards regional and sub-regional assessments and applications important for the U.S. and Canadian public, business and policy decision makers, as well as for international collaborations on regional, and especially climate related issues.

  16. Efficient implementation of weighted ENO schemes

    NASA Technical Reports Server (NTRS)

    Jiang, Guang-Shan; Shu, Chi-Wang

    1995-01-01

    In this paper, we further analyze, test, modify and improve the high order WENO (weighted essentially non-oscillatory) finite difference schemes of Liu, Osher and Chan. It was shown by Liu et al. that WENO schemes constructed from the r-th order (in L1 norm) ENO schemes are (r+1)-th order accurate. We propose a new way of measuring the smoothness of a numerical solution, emulating the idea of minimizing the total variation of the approximation, which results in a 5-th order WENO scheme for the case r = 3, instead of the 4-th order with the original smoothness measurement by Liu et al. This 5-th order WENO scheme is as fast as the 4-th order WENO scheme of Liu et al., and both schemes are about twice as fast as the 4-th order ENO schemes on vector supercomputers and as fast on serial and parallel computers. For Euler systems of gas dynamics, we suggest computing the weights from pressure and entropy instead of the characteristic values to simplify the costly characteristic procedure. The resulting WENO schemes are about twice as fast as the WENO schemes using the characteristic decompositions to compute weights, and work well for problems which do not contain strong shocks or strong reflected waves. We also prove that, for conservation laws with smooth solutions, all WENO schemes are convergent. Many numerical tests, including the 1D steady state nozzle flow problem and 2D shock entropy wave interaction problem, are presented to demonstrate the remarkable capability of the WENO schemes, especially the WENO scheme using the new smoothness measurement, in resolving complicated shock and flow structures. We have also applied Yang's artificial compression method to the WENO schemes to sharpen contact discontinuities.

  17. Development of an inviscid flux scheme for thermochemical nonequilibrium flow

    NASA Astrophysics Data System (ADS)

    Campbell, Charles Hugh

    Solutions to the governing equations that model hypersonic aerothermodynamics rely heavily on the mathematical and numerical technology that characterizes Computational Fluid Dynamics. Many areas of significant investigation are relevant to advancing state of the art hypersonic aerothermodynamic engineering and applied research analyses. Due to the relatively high energy achieved by spacecraft during launch, physical models for thermal nonequilibrium and chemical nonequilibrium are necessary to develop adequate numerical reentry simulations. In addition, complex features of the Navier Stokes equations require sophisticated mathematical and numerical techniques in order to develop reasonably accurate simulations in an acceptable amount of time. The objective of this work is to present the development of a new inviscid flux evaluation method. This new method, referred to as the Flux Consistent scheme, is closely related to the Modified Steger-Warming method. The unique characteristics of this new flux scheme involve an original eigenvalue implementation. This original eigenvalue formulation, however, leads to incorrect flux magnitudes which must be corrected in the total flux to provide an accurate representation of the inviscid fluxes. The mathematical technique used to identify flux magnitude errors in the Flux Consistent scheme is also applied to the Modified Steger-Warming flux evaluation method. This assessment leads to the characterization of flux errors in the Modified Steger-Warming scheme which are generated by eigenvalue differences between the left and right cell interface flow states. These Modified Steger-Warming flux errors are shown to vanish for supersonic conditions. Two hypotheses in reference to the Modified Steger-Warming scheme are proposed. The first is that sonic glitch problems occurring in some Steger-Warming simulations are the result of the flux error vanishing at supersonic conditions. The second hypothesis concerning the Steger

  18. Advanced Nodal P3/SP3 Axial Transport Solvers for the MPACT 2D/1D Scheme

    SciTech Connect

    Stimpson, Shane G; Collins, Benjamin S

    2015-01-01

    As part of its initiative to provide multiphysics simulations of nuclear reactor cores, the Consortium for Advanced Simulation of Light Water Reactors (CASL) is developing the Virtual Environment for Reactor Applications Core Simulator (VERA-CS). The MPACT code, which is the primary neutron transport solver of VERA-CS, employs the two-dimensional/one-dimensional (2D/1D) method to solve 3-dimensional neutron transport problems and provide sub-pin-level resolution of the power distribution. While 2D method of characteristics is used to solve for the transport effects within each plane, 1D-nodal methods are used axially. There have been extensive studies of the 2D/1D method with a variety nodal methods, and the P3/SP3 solver has proved to be an effective method of providing higher-fidelity solutions while maintaining a low computational burden.The current implementation in MPACT wraps a one-node nodal expansion method (NEM) kernel for each moment, iterating between them and performing multiple sweeps to resolve flux distributions. However, it has been observed that this approach is more sensitive to convergence problems. This paper documents the theory and application two new nodal P3/SP3 approaches to be used within the 2D/1D method in MPACT. These two approaches aim to provide enhanced stability compared with the pre-existing one-node approach. Results from the HY-NEM-SP3 solver show that the accuracy is consistent with the one-node formulations and provides improved convergence for some problems; but the solver has issues with cases in thin planes. Although the 2N-SENM-SP3 solver is still under development, it is intended to resolve the issues with HY-NEM-SP3 but it will incur some additional computational burden by necessitating an additional 1D-CMFD-P3 solver to generate the second moment cell-averaged scalar flux.

  19. Uncertainty of Microphysics Schemes in CRMs

    NASA Astrophysics Data System (ADS)

    Tao, W. K.; van den Heever, S. C.; Wu, D.; Saleeby, S. M.; Lang, S. E.

    2015-12-01

    Microphysics is the framework through which to understand the links between interactive aerosol, cloud and precipitation processes. These processes play a critical role in the water and energy cycle. CRMs with advanced microphysics schemes have been used to study the interaction between aerosol, cloud and precipitation processes at high resolution. But, there are still many uncertainties associated with these microphysics schemes. This has arisen, in part, from the fact microphysical processes cannot be measured directly; instead, cloud properties, which can be measured, are and have been used to validate model results. The utilization of current and future global high-resolution models is rapidly increasing and are at what has been traditional CRM resolutions and are using microphysics schemes that were developed in traditional CRMs. A potential NASA satellite mission called the Cloud and Precipitation Processes Mission (CaPPM) is currently being planned for submission to the NASA Earth Science Decadal Survey. This mission could provide the necessary global estimates of cloud and precipitation properties with which to evaluate and improve dynamical and microphysical parameterizations and the feedbacks. In order to facilitate the development of this mission, CRM simulations have been conducted to identify microphysical processes responsible for the greatest uncertainties in CRMs. In this talk, we will present results from numerical simulations conducted using two CRMs (NU-WRF and RAMS) with different dynamics, radiation, land surface and microphysics schemes. Specifically, we will conduct sensitivity tests to examine the uncertainty of the some of the key ice processes (i.e. riming, melting, freezing and shedding) in these two-microphysics schemes. The idea is to quantify how these two different models' respond (surface rainfall and its intensity, strength of cloud drafts, LWP/IWP, convective-stratiform-anvil area distribution) to changes of these key ice

  20. 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.

  1. Invariant Discretization Schemes Using Evolution-Projection Techniques

    NASA Astrophysics Data System (ADS)

    Bihlo, Alexander; Nave, Jean-Christophe

    2013-08-01

    Finite difference discretization schemes preserving a subgroup of the maximal Lie invariance group of the one-dimensional linear heat equation are determined. These invariant schemes are constructed using the invariantization procedure for non-invariant schemes of the heat equation in computational coordinates. We propose a new methodology for handling moving discretization grids which are generally indispensable for invariant numerical schemes. The idea is to use the invariant grid equation, which determines the locations of the grid point at the next time level only for a single integration step and then to project the obtained solution to the regular grid using invariant interpolation schemes. This guarantees that the scheme is invariant and allows one to work on the simpler stationary grids. The discretization errors of the invariant schemes are established and their convergence rates are estimated. Numerical tests are carried out to shed some light on the numerical p! roperties of invariant discretization schemes using the proposed evolution-projection strategy.

  2. 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.

  3. 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.

  4. One-qubit fingerprinting schemes

    SciTech Connect

    Beaudrap, J. Niel de

    2004-02-01

    Fingerprinting is a technique in communication complexity in which two parties (Alice and Bob) with large data sets send short messages to a third party (a referee), who attempts to compute some function of the larger data sets. For the equality function, the referee attempts to determine whether Alice's data and Bob's data are the same. In this paper, we consider the extreme scenario of performing fingerprinting where Alice and Bob both send either one bit (classically) or one qubit (in the quantum regime) messages to the referee for the equality problem. Restrictive bounds are demonstrated for the error probability of one-bit fingerprinting schemes, and show that it is easy to construct one-qubit fingerprinting schemes which can outperform any one-bit fingerprinting scheme. The author hopes that this analysis will provide results useful for performing physical experiments, which may help to advance implementations for more general quantum communication protocols.

  5. Splined version of FLEXSTAB: A critical analysis of alternate schemes

    NASA Technical Reports Server (NTRS)

    Weber, J. A.

    1977-01-01

    Recommendations are made for improved aerodynamic models and numerical schemes to be considered for inclusion into the FLEXSTAB computer program system. These recommendations are based on a critical analysis of numerical technology.

  6. WENO-enhanced gas-kinetic scheme for direct simulations of compressible transition and turbulence

    NASA Astrophysics Data System (ADS)

    Kumar, G.; Girimaji, S. S.; Kerimo, J.

    2013-02-01

    The recently developed Gas Kinetic Method (GKM) for computing fluid flow is enhanced with advanced reconstruction (interpolation) schemes to enable direct simulations of highly compressible transition and turbulence fields. Variants of Weighted Essentially Non-Oscillatory (WENO) reconstruction schemes of different orders of accuracy are implemented and examined along with more elementary van Leer method. The competing schemes are evaluated for their accuracy, efficiency and numerical stability. The computed results are compared against the Rapid Distortion Theory for the case of compressible shear turbulence and 'pressure-released' Burgers solution. In the case of decaying isotropic turbulence, the efficacy of the reconstruction schemes is evaluated by comparison against a 'gold standard' high-resolution simulation. The capabilities of the reconstruction schemes to capture linear, non-linear, pressure-released and viscous flow physics as well as solenoidal and dilatational features of the flow fields are established in isolation and combination. The most suitable WENO variant for integration with GKM is identified. Another important outcome of the study is the finding that temperature-interpolation is superior to energy-interpolation in avoiding negative temperatures arising due to the Gibbs phenomenon. Overall, this work advances the applicability of kinetic theory based GKM to a wider range of high Mach number flow physics.

  7. 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.

  8. A Numerical Instability in an ADI Algorithm for Gyrokinetics

    SciTech Connect

    E.A. Belli; G.W. Hammett

    2004-12-17

    We explore the implementation of an Alternating Direction Implicit (ADI) algorithm for a gyrokinetic plasma problem and its resulting numerical stability properties. This algorithm, which uses a standard ADI scheme to divide the field solve from the particle distribution function advance, has previously been found to work well for certain plasma kinetic problems involving one spatial and two velocity dimensions, including collisions and an electric field. However, for the gyrokinetic problem we find a severe stability restriction on the time step. Furthermore, we find that this numerical instability limitation also affects some other algorithms, such as a partially implicit Adams-Bashforth algorithm, where the parallel motion operator v{sub {parallel}} {partial_derivative}/{partial_derivative}z is treated implicitly and the field terms are treated with an Adams-Bashforth explicit scheme. Fully explicit algorithms applied to all terms can be better at long wavelengths than these ADI or partially implicit algorithms.

  9. 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).

  10. Numerical discretization for nonlinear diffusion filter

    NASA Astrophysics Data System (ADS)

    Mustaffa, I.; Mizuar, I.; Aminuddin, M. M. M.; Dasril, Y.

    2015-05-01

    Nonlinear diffusion filters are famously used in machine vision for image denoising and restoration. This paper presents a study on the effects of different numerical discretization of nonlinear diffusion filter. Several numerical discretization schemes are presented; namely semi-implicit, AOS, and fully implicit schemes. The results of these schemes are compared by visual results, objective measurement e.g. PSNR and MSE. The results are also compared to a Daubechies wavelet denoising method. It is acknowledged that the two preceding scheme have already been discussed in literature, however comparison to the latter scheme has not been made. The semi-implicit scheme uses an additive operator splitting (AOS) developed to overcome the shortcoming of the explicit scheme i.e., stability for very small time steps. Although AOS has proven to be efficient, from the nonlinear diffusion filter results with different discretization schemes, examples shows that implicit schemes are worth pursuing.

  11. Advanced coding and modulation schemes for TDRSS

    NASA Technical Reports Server (NTRS)

    Harrell, Linda; Kaplan, Ted; Berman, Ted; Chang, Susan

    1993-01-01

    This paper describes the performance of the Ungerboeck and pragmatic 8-Phase Shift Key (PSK) Trellis Code Modulation (TCM) coding techniques with and without a (255,223) Reed-Solomon outer code as they are used for Tracking Data and Relay Satellite System (TDRSS) S-Band and Ku-Band return services. The performance of these codes at high data rates is compared to uncoded Quadrature PSK (QPSK) and rate 1/2 convolutionally coded QPSK in the presence of Radio Frequency Interference (RFI), self-interference, and hardware distortions. This paper shows that the outer Reed-Solomon code is necessary to achieve a 10(exp -5) Bit Error Rate (BER) with an acceptable level of degradation in the presence of RFI. This paper also shows that the TCM codes with or without the Reed-Solomon outer code do not perform well in the presence of self-interference. In fact, the uncoded QPSK signal performs better than the TCM coded signal in the self-interference situation considered in this analysis. Finally, this paper shows that the E(sub b)/N(sub 0) degradation due to TDRSS hardware distortions is approximately 1.3 dB with a TCM coded signal or a rate 1/2 convolutionally coded QPSK signal and is 3.2 dB with an uncoded QPSK signal.

  12. Advanced coding and modulation schemes for TDRSS

    NASA Astrophysics Data System (ADS)

    Harrell, Linda; Kaplan, Ted; Berman, Ted; Chang, Susan

    1993-11-01

    This paper describes the performance of the Ungerboeck and pragmatic 8-Phase Shift Key (PSK) Trellis Code Modulation (TCM) coding techniques with and without a (255,223) Reed-Solomon outer code as they are used for Tracking Data and Relay Satellite System (TDRSS) S-Band and Ku-Band return services. The performance of these codes at high data rates is compared to uncoded Quadrature PSK (QPSK) and rate 1/2 convolutionally coded QPSK in the presence of Radio Frequency Interference (RFI), self-interference, and hardware distortions. This paper shows that the outer Reed-Solomon code is necessary to achieve a 10(exp -5) Bit Error Rate (BER) with an acceptable level of degradation in the presence of RFI. This paper also shows that the TCM codes with or without the Reed-Solomon outer code do not perform well in the presence of self-interference. In fact, the uncoded QPSK signal performs better than the TCM coded signal in the self-interference situation considered in this analysis. Finally, this paper shows that the E(sub b)/N(sub 0) degradation due to TDRSS hardware distortions is approximately 1.3 dB with a TCM coded signal or a rate 1/2 convolutionally coded QPSK signal and is 3.2 dB with an uncoded QPSK signal.

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

    NASA Technical Reports Server (NTRS)

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

    1989-01-01

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

  14. On the application of ENO scheme with subcell resolution to conservation laws with stiff source terms

    NASA Technical Reports Server (NTRS)

    Chang, Shih-Hung

    1991-01-01

    Two approaches are used to extend the essentially non-oscillatory (ENO) schemes to treat conservation laws with stiff source terms. One approach is the application of the Strang time-splitting method. Here the basic ENO scheme and the Harten modification using subcell resolution (SR), ENO/SR scheme, are extended this way. The other approach is a direct method and a modification of the ENO/SR. Here the technique of ENO reconstruction with subcell resolution is used to locate the discontinuity within a cell and the time evolution is then accomplished by solving the differential equation along characteristics locally and advancing in the characteristic direction. This scheme is denoted ENO/SRCD (subcell resolution - characteristic direction). All the schemes are tested on the equation of LeVeque and Yee (NASA-TM-100075, 1988) modeling reacting flow problems. Numerical results show that these schemes handle this intriguing model problem very well, especially with ENO/SRCD which produces perfect resolution at the discontinuity.

  15. Numerical Hydrodynamics and Magnetohydrodynamics in General Relativity.

    PubMed

    Font, José A

    2008-01-01

    This article presents a comprehensive overview of numerical hydrodynamics and magneto-hydrodynamics (MHD) in general relativity. Some significant additions have been incorporated with respect to the previous two versions of this review (2000, 2003), most notably the coverage of general-relativistic MHD, a field in which remarkable activity and progress has occurred in the last few years. Correspondingly, the discussion of astrophysical simulations in general-relativistic hydrodynamics is enlarged to account for recent relevant advances, while those dealing with general-relativistic MHD are amply covered in this review for the first time. The basic outline of this article is nevertheless similar to its earlier versions, save for the addition of MHD-related issues throughout. Hence, different formulations of both the hydrodynamics and MHD equations are presented, with special mention of conservative and hyperbolic formulations well adapted to advanced numerical methods. A large sample of numerical approaches for solving such hyperbolic systems of equations is discussed, paying particular attention to solution procedures based on schemes exploiting the characteristic structure of the equations through linearized Riemann solvers. As previously stated, a comprehensive summary of astrophysical simulations in strong gravitational fields is also presented. These are detailed in three basic sections, namely gravitational collapse, black-hole accretion, and neutron-star evolutions; despite the boundaries, these sections may (and in fact do) overlap throughout the discussion. The material contained in these sections highlights the numerical challenges of various representative simulations. It also follows, to some extent, the chronological development of the field, concerning advances in the formulation of the gravitational field, hydrodynamics and MHD equations and the numerical methodology designed to solve them. To keep the length of this article reasonable, an effort has

  16. 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.

  17. Finance schemes for funding private orthodontic treatment.

    PubMed

    Perks, S

    1997-02-01

    Over the last ten years there has been a steady increase in the volume of private dental treatment and numerous finance schemes have been developed to help both patients and dentists. Private orthodontic treatment is increasing and the purpose of this article is to summarise the main features of the schemes currently available to fund private orthodontic treatment and to provide a source of reference.

  18. 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.

  19. Comprehensive numerical methodology for direct numerical simulations of compressible Rayleigh-Taylor instability

    NASA Astrophysics Data System (ADS)

    Reckinger, Scott J.; Livescu, Daniel; Vasilyev, Oleg V.

    2016-05-01

    An investigation of compressible Rayleigh-Taylor instability (RTI) using Direct Numerical Simulations (DNS) requires efficient numerical methods, advanced boundary conditions, and consistent initialization in order to capture the wide range of scales and vortex dynamics present in the system, while reducing the computational impact associated with acoustic wave generation and the subsequent interaction with the flow. An advanced computational framework is presented that handles the challenges introduced by considering the compressive nature of RTI systems, which include sharp interfacial density gradients on strongly stratified background states, acoustic wave generation and removal at computational boundaries, and stratification dependent vorticity production. The foundation of the numerical methodology described here is the wavelet-based grid adaptivity of the Parallel Adaptive Wavelet Collocation Method (PAWCM) that maintains symmetry in single-mode RTI systems to extreme late-times. PAWCM is combined with a consistent initialization, which reduces the generation of acoustic disturbances, and effective boundary treatments, which prevent acoustic reflections. A dynamic time integration scheme that can handle highly nonlinear and potentially stiff systems, such as compressible RTI, completes the computational framework. The numerical methodology is used to simulate two-dimensional single-mode RTI to extreme late-times for a wide range of flow compressibility and variable density effects. The results show that flow compressibility acts to reduce the growth of RTI for low Atwood numbers, as predicted from linear stability analysis.

  20. Numerical solution of the full potential equation using a chimera grid approach

    NASA Technical Reports Server (NTRS)

    Holst, Terry L.

    1995-01-01

    A numerical scheme utilizing a chimera zonal grid approach for solving the full potential equation in two spatial dimensions is described. Within each grid zone a fully-implicit approximate factorization scheme is used to advance the solution one interaction. This is followed by the explicit advance of all common zonal grid boundaries using a bilinear interpolation of the velocity potential. The presentation is highlighted with numerical results simulating the flow about a two-dimensional, nonlifting, circular cylinder. For this problem, the flow domain is divided into two parts: an inner portion covered by a polar grid and an outer portion covered by a Cartesian grid. Both incompressible and compressible (transonic) flow solutions are included. Comparisons made with an analytic solution as well as single grid results indicate that the chimera zonal grid approach is a viable technique for solving the full potential equation.

  1. Numerical methods for incompressible viscous flows with engineering applications

    NASA Technical Reports Server (NTRS)

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

    1988-01-01

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

  2. Sparse Parallel MRI Based on Accelerated Operator Splitting Schemes

    PubMed Central

    Xie, Weisi; Su, Zhenghang

    2016-01-01

    Recently, the sparsity which is implicit in MR images has been successfully exploited for fast MR imaging with incomplete acquisitions. In this paper, two novel algorithms are proposed to solve the sparse parallel MR imaging problem, which consists of l1 regularization and fidelity terms. The two algorithms combine forward-backward operator splitting and Barzilai-Borwein schemes. Theoretically, the presented algorithms overcome the nondifferentiable property in l1 regularization term. Meanwhile, they are able to treat a general matrix operator that may not be diagonalized by fast Fourier transform and to ensure that a well-conditioned optimization system of equations is simply solved. In addition, we build connections between the proposed algorithms and the state-of-the-art existing methods and prove their convergence with a constant stepsize in Appendix. Numerical results and comparisons with the advanced methods demonstrate the efficiency of proposed algorithms. PMID:27746824

  3. Numerical computation of transonic flow governed by the full-potential equation

    NASA Technical Reports Server (NTRS)

    Holst, T. L.

    1983-01-01

    Numerical solution techniques for solving transonic flow fields governed by the full potential equation are discussed. In a general sense relaxation schemes suitable for the numerical solution of elliptic partial differential equations are presented and discussed with emphasis on transonic flow applications. The presentation can be divided into two general categories: An introductory treatment of the basic concepts associated with the numerical solution of elliptic partial differential equations and a more advanced treatment of current procedures used to solve the full potential equation for transonic flow fields. The introductory material is presented for completeness and includes a brief introduction (Chapter 1), governing equations (Chapter 2), classical relaxation schemes (Chapter 3), and early concepts regarding transonic full potential equation algorithms (Chapter 4).

  4. 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.

  5. An authentication scheme for secure access to healthcare services.

    PubMed

    Khan, Muhammad Khurram; Kumari, Saru

    2013-08-01

    Last few decades have witnessed boom in the development of information and communication technologies. Health-sector has also been benefitted with this advancement. To ensure secure access to healthcare services some user authentication mechanisms have been proposed. In 2012, Wei et al. proposed a user authentication scheme for telecare medical information system (TMIS). Recently, Zhu pointed out offline password guessing attack on Wei et al.'s scheme and proposed an improved scheme. In this article, we analyze both of these schemes for their effectiveness in TMIS. We show that Wei et al.'s scheme and its improvement proposed by Zhu fail to achieve some important characteristics necessary for secure user authentication. We find that security problems of Wei et al.'s scheme stick with Zhu's scheme; like undetectable online password guessing attack, inefficacy of password change phase, traceability of user's stolen/lost smart card and denial-of-service threat. We also identify that Wei et al.'s scheme lacks forward secrecy and Zhu's scheme lacks session key between user and healthcare server. We therefore propose an authentication scheme for TMIS with forward secrecy which preserves the confidentiality of air messages even if master secret key of healthcare server is compromised. Our scheme retains advantages of Wei et al.'s scheme and Zhu's scheme, and offers additional security. The security analysis and comparison results show the enhanced suitability of our scheme for TMIS.

  6. A compatible Lagrangian hydrodynamic scheme for multicomponent flows with mixing

    SciTech Connect

    Chang, Chong; Stagg, Alan K

    2012-01-01

    We present a Lagrangian time integration scheme and compatible discretization for total energy conservation in multicomponent mixing simulations. Mixing behavior results from relative motion between species. Species velocities are determined by solving species momentum equations in a Lagrangian manner. Included in the species momentum equations are species artificial viscosity (since each species can undergo compression) and inter-species momentum exchange. Thermal energy for each species is also solved, including compression work and thermal dissipation caused by momentum exchange. The present procedure is applicable to mixing of an arbitrary number of species that may not be in pressure or temperature equilibrium. A traditional staggered stencil has been adopted to describe motion of each species. The computational mesh for the mixture is constructed in a Lagrangian manner using the mass-averaged mixture velocity. Species momentum equations are solved at the vertices of the mesh, and temporary species meshes are constructed and advanced in time using the resulting species velocities. Following the Lagrangian step, species quantities are advected (mapped) from the species meshes to the mixture mesh. Momentum exchange between species introduces work that must be included in an energy-conserving discretization scheme. This work has to be transformed to dissipation in order to effect a net change in species thermal energy. The dissipation between interacting species pairs is obtained by combining the momentum exchange work. The dissipation is then distributed to the species involved using a distribution factor based on species specific heats. The resulting compatible discretization scheme provides total energy conservation of the whole mixture. In addition, the numerical scheme includes conservative local energy exchange between species in mixture. Due to the relatively large species interaction coefficients, both the species momenta and energies are calculated

  7. High order accurate finite difference schemes based on symmetry preservation

    NASA Astrophysics Data System (ADS)

    Ozbenli, Ersin; Vedula, Prakash

    2016-11-01

    A new algorithm for development of high order accurate finite difference schemes for numerical solution of partial differential equations using Lie symmetries is presented. Considering applicable symmetry groups (such as those relevant to space/time translations, Galilean transformation, scaling, rotation and projection) of a partial differential equation, invariant numerical schemes are constructed based on the notions of moving frames and modified equations. Several strategies for construction of invariant numerical schemes with a desired order of accuracy are analyzed. Performance of the proposed algorithm is demonstrated using analysis of one-dimensional partial differential equations, such as linear advection diffusion equations inviscid Burgers equation and viscous Burgers equation, as our test cases. Through numerical simulations based on these examples, the expected improvement in accuracy of invariant numerical schemes (up to fourth order) is demonstrated. Advantages due to implementation and enhanced computational efficiency inherent in our proposed algorithm are presented. Extension of the basic framework to multidimensional partial differential equations is also discussed.

  8. On the use of advanced numerical models for the evaluation of dosimetric parameters and the verification of exposure limits at workplaces.

    PubMed

    Catarinucci, L; Tarricone, L

    2009-12-01

    With the next transposition of the 2004/40/EC Directive, employers will become responsible for the electromagnetic field level at the workplace. To make this task easier, the scientific community is compiling practical guidelines to be followed. This work aims at enriching such guidelines, especially for the dosimetric issues. More specifically, some critical aspects related to the application of numerical dosimetric techniques for the verification of the safety limit compliance have been highlighted. In particular, three different aspects have been considered: the dosimetric parameter dependence on the shape and the inner characterisation of the exposed subject as well as on the numerical algorithm used, and the correlation between reference limits and basic restriction. Results and discussions demonstrate how, even by using sophisticated numerical techniques, in some cases a complex interpretation of the result is mandatory.

  9. Parallelization of implicit finite difference schemes in computational fluid dynamics

    NASA Technical Reports Server (NTRS)

    Decker, Naomi H.; Naik, Vijay K.; Nicoules, Michel

    1990-01-01

    Implicit finite difference schemes are often the preferred numerical schemes in computational fluid dynamics, requiring less stringent stability bounds than the explicit schemes. Each iteration in an implicit scheme involves global data dependencies in the form of second and higher order recurrences. Efficient parallel implementations of such iterative methods are considerably more difficult and non-intuitive. The parallelization of the implicit schemes that are used for solving the Euler and the thin layer Navier-Stokes equations and that require inversions of large linear systems in the form of block tri-diagonal and/or block penta-diagonal matrices is discussed. Three-dimensional cases are emphasized and schemes that minimize the total execution time are presented. Partitioning and scheduling schemes for alleviating the effects of the global data dependencies are described. An analysis of the communication and the computation aspects of these methods is presented. The effect of the boundary conditions on the parallel schemes is also discussed.

  10. 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.

  11. 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.

  12. Coupling between the JULES land-surface scheme and the CCATT-BRAMS atmospheric chemistry model (JULES-CCATT-BRAMS1.0): applications to numerical weather forecasting and the CO2 budget in South America

    NASA Astrophysics Data System (ADS)

    Moreira, D. S.; Freitas, S. R.; Bonatti, J. P.; Mercado, L. M.; Rosário, N. M. É.; Longo, K. M.; Miller, J. B.; Gloor, M.; Gatti, L. V.

    2013-01-01

    This article presents the development of a new numerical system denominated JULES-CCATT-BRAMS, which resulted from the coupling of the JULES surface model to the CCATT-BRAMS atmospheric chemistry model. The performance of this system in relation to several meteorological variables (wind speed at 10 m, air temperature at 2 m, dew point temperature at 2 m, pressure reduced to mean sea level and 6 h accumulated precipitation) and the CO2 concentration above an extensive area of South America is also presented, focusing on the Amazon basin. The evaluations were conducted for two periods, the wet (March) and dry (September) seasons of 2010. The statistics used to perform the evaluation included bias (BIAS) and root mean squared error (RMSE). The errors were calculated in relation to observations at conventional stations in airports and automatic stations. In addition, CO2 concentrations in the first model level were compared with meteorological tower measurements and vertical CO2 profiles were compared with aircraft data. The results of this study show that the JULES model coupled to CCATT-BRAMS provided a significant gain in performance in the evaluated atmospheric fields relative to those simulated by the LEAF (version 3) surface model originally utilized by CCATT-BRAMS. Simulations of CO2 concentrations in Amazonia and a comparison with observations are also discussed and show that the system presents a gain in performance relative to previous studies. Finally, we discuss a wide range of numerical studies integrating coupled atmospheric, land surface and chemistry processes that could be produced with the system described here. Therefore, this work presents to the scientific community a free tool, with good performance in relation to the observed data and re-analyses, able to produce atmospheric simulations/forecasts at different resolutions, for any period of time and in any region of the globe.

  13. PRICE: primitive centred schemes for hyperbolic systems

    NASA Astrophysics Data System (ADS)

    Toro, E. F.; Siviglia, A.

    2003-08-01

    We present first- and higher-order non-oscillatory primitive (PRI) centred (CE) numerical schemes for solving systems of hyperbolic partial differential equations written in primitive (or non-conservative) form. Non-conservative systems arise in a variety of fields of application and they are adopted in that form for numerical convenience, or more importantly, because they do not posses a known conservative form; in the latter case there is no option but to apply non-conservative methods. In addition we have chosen a centred, as distinct from upwind, philosophy. This is because the systems we are ultimately interested in (e.g. mud flows, multiphase flows) are exceedingly complicated and the eigenstructure is difficult, or very costly or simply impossible to obtain. We derive six new basic schemes and then we study two ways of extending the most successful of these to produce second-order non-oscillatory methods. We have used the MUSCL-Hancock and the ADER approaches. In the ADER approach we have used two ways of dealing with linear reconstructions so as to avoid spurious oscillations: the ADER TVD scheme and ADER with ENO reconstruction. Extensive numerical experiments suggest that all the schemes are very satisfactory, with the ADER/ENO scheme being perhaps the most promising, first for dealing with source terms and secondly, because higher-order extensions (greater than two) are possible. Work currently in progress includes the application of some of these ideas to solve the mud flow equations. The schemes presented are generic and can be applied to any hyperbolic system in non-conservative form and for which solutions include smooth parts, contact discontinuities and weak shocks. The advantage of the schemes presented over upwind-based methods is simplicity and efficiency, and will be fully realized for hyperbolic systems in which the provision of upwind information is very costly or is not available.

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

    SciTech Connect

    Thompson, Kelly Glen

    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

  15. A spatial discretization scheme for solving the transport equation on unstructured grids of polyhedra

    NASA Astrophysics Data System (ADS)

    Thompson, Kelly Glen

    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 Comer 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

  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 modeling of late Glacial Laurentide advance of ice across Hudson Strait: Insights into terrestrial and marine geology, mass balance, and calving flux

    USGS Publications Warehouse

    Pfeffer, W.T.; Dyurgerov, M.; Kaplan, M.; Dwyer, J.; Sassolas, C.; Jennings, A.; Raup, B.; Manley, W.

    1997-01-01

    A time-dependent finite element model was used to reconstruct the advance of ice from a late Glacial dome on northern Quebec/Labrador across Hudson Strait to Meta Incognita Peninsula (Baffin Island) and subsequently to the 9.9-9.6 ka 14C Gold Cove position on Hall Peninsula. Terrestrial geological and geophysical information from Quebec and Labrador was used to constrain initial and boundary conditions, and the model results are compared with terrestrial geological information from Baffin Island and considered in the context of the marine event DC-0 and the Younger Dryas cooling. We conclude that advance across Hudson Strait from Ungava Bay to Baffin Island is possible using realistic glacier physics under a variety of reasonable boundary conditions. Production of ice flux from a dome centered on northeastern Quebec and Labrador sufficient to deliver geologically inferred ice thickness at Gold Cove (Hall Peninsula) appears to require extensive penetration of sliding south from Ungava Bay. The discharge of ice into the ocean associated with advance and retreat across Hudson Strait does not peak at a time coincident with the start of the Younger Dryas and is less than minimum values proposed to influence North Atlantic thermohaline circulation; nevertheless, a significant fraction of freshwater input to the North Atlantic may have been provided abruptly and at a critical time by this event.

  18. Twin Signature Schemes, Revisited

    NASA Astrophysics Data System (ADS)

    Schäge, Sven

    In this paper, we revisit the twin signature scheme by Naccache, Pointcheval and Stern from CCS 2001 that is secure under the Strong RSA (SRSA) assumption and improve its efficiency in several ways. First, we present a new twin signature scheme that is based on the Strong Diffie-Hellman (SDH) assumption in bilinear groups and allows for very short signatures and key material. A big advantage of this scheme is that, in contrast to the original scheme, it does not require a computationally expensive function for mapping messages to primes. We prove this new scheme secure under adaptive chosen message attacks. Second, we present a modification that allows to significantly increase efficiency when signing long messages. This construction uses collision-resistant hash functions as its basis. As a result, our improvements make the signature length independent of the message size. Our construction deviates from the standard hash-and-sign approach in which the hash value of the message is signed in place of the message itself. We show that in the case of twin signatures, one can exploit the properties of the hash function as an integral part of the signature scheme. This improvement can be applied to both the SRSA based and SDH based twin signature scheme.

  19. Convenient total variation diminishing conditions for nonlinear difference schemes

    NASA Technical Reports Server (NTRS)

    Tadmor, Eitan

    1986-01-01

    Convenient conditions for nonlinear difference schemes to be total-variation diminishing (TVD) are reviewed. It is shown that such schemes share the TVD property, provided their numerical fluxes meet a certain positivity condition at extrema values but can be arbitrary otherwise. The conditions are invariant under different incremental representations of the nonlinear schemes, and thus provide a simplified generalization of the TVD conditions due to Harten and others.

  20. Stable Difference Schemes for the Neutron Transport Equation

    NASA Astrophysics Data System (ADS)

    Ashyralyev, Allaberen; Taskin, Abdulgafur

    2011-09-01

    The initial boundary value problem for the neutron transport equation is considered. The first and second orders of accuracy difference schemes for the approximate solution of this problem are presented. In applications, the stability estimates for solutions of difference schemes for the approximate solution of the neutron transport equation are obtained. Numerical techniques are developed and algorithms are tested on an example in MATLAB.

  1. 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.

  2. Advanced Tsunami Numerical Simulations and Energy Considerations by use of 3D-2D Coupled Models: The October 11, 1918, Mona Passage Tsunami

    NASA Astrophysics Data System (ADS)

    López-Venegas, Alberto M.; Horrillo, Juan; Pampell-Manis, Alyssa; Huérfano, Victor; Mercado, Aurelio

    2015-06-01

    The most recent tsunami observed along the coast of the island of Puerto Rico occurred on October 11, 1918, after a magnitude 7.2 earthquake in the Mona Passage. The earthquake was responsible for initiating a tsunami that mostly affected the northwestern coast of the island. Runup values from a post-tsunami survey indicated the waves reached up to 6 m. A controversy regarding the source of the tsunami has resulted in several numerical simulations involving either fault rupture or a submarine landslide as the most probable cause of the tsunami. Here we follow up on previous simulations of the tsunami from a submarine landslide source off the western coast of Puerto Rico as initiated by the earthquake. Improvements on our previous study include: (1) higher-resolution bathymetry; (2) a 3D-2D coupled numerical model specifically developed for the tsunami; (3) use of the non-hydrostatic numerical model NEOWAVE (non-hydrostatic evolution of ocean WAVE) featuring two-way nesting capabilities; and (4) comprehensive energy analysis to determine the time of full tsunami wave development. The three-dimensional Navier-Stokes model tsunami solution using the Navier-Stokes algorithm with multiple interfaces for two fluids (water and landslide) was used to determine the initial wave characteristic generated by the submarine landslide. Use of NEOWAVE enabled us to solve for coastal inundation, wave propagation, and detailed runup. Our results were in agreement with previous work in which a submarine landslide is favored as the most probable source of the tsunami, and improvement in the resolution of the bathymetry yielded inundation of the coastal areas that compare well with values from a post-tsunami survey. Our unique energy analysis indicates that most of the wave energy is isolated in the wave generation region, particularly at depths near the landslide, and once the initial wave propagates from the generation region its energy begins to stabilize.

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

    NASA Technical Reports Server (NTRS)

    Runchal, Akshai K.

    1987-01-01

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

  4. On the dynamics of some grid adaption schemes

    NASA Technical Reports Server (NTRS)

    Sweby, Peter K.; Yee, Helen C.

    1994-01-01

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

  5. 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.

  6. High resolution schemes and the entropy condition

    NASA Technical Reports Server (NTRS)

    Osher, S.; Chakravarthy, S.

    1983-01-01

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

  7. A low-order coupled chemistry meteorology model for testing online and offline data assimilation schemes

    NASA Astrophysics Data System (ADS)

    Haussaire, J.-M.; Bocquet, M.

    2015-08-01

    Bocquet and Sakov (2013) have introduced a low-order model based on the coupling of the chaotic Lorenz-95 model which simulates winds along a mid-latitude circle, with the transport of a tracer species advected by this zonal wind field. This model, named L95-T, can serve as a playground for testing data assimilation schemes with an online model. Here, the tracer part of the model is extended to a reduced photochemistry module. This coupled chemistry meteorology model (CCMM), the L95-GRS model, mimics continental and transcontinental transport and the photochemistry of ozone, volatile organic compounds and nitrogen oxides. Its numerical implementation is described. The model is shown to reproduce the major physical and chemical processes being considered. L95-T and L95-GRS are specifically designed and useful for testing advanced data assimilation schemes, such as the iterative ensemble Kalman smoother (IEnKS) which combines the best of ensemble and variational methods. These models provide useful insights prior to the implementation of data assimilation methods on larger models. We illustrate their use with data assimilation schemes on preliminary, yet instructive numerical experiments. In particular, online and offline data assimilation strategies can be conveniently tested and discussed with this low-order CCMM. The impact of observed chemical species concentrations on the wind field can be quantitatively estimated. The impacts of the wind chaotic dynamics and of the chemical species non-chaotic but highly nonlinear dynamics on the data assimilation strategies are illustrated.

  8. Second-Order-accurate Schemes for Magnetohydrodynamics with Divergence-free Reconstruction

    NASA Astrophysics Data System (ADS)

    Balsara, Dinshaw S.

    2004-03-01

    MHD on structured meshes and MHD on unstructured meshes because such analogies can guide the design of MHD schemes and AMR-MHD techniques on unstructured meshes. The present paper also lays out the roadmap for designing MHD schemes for structured and unstructured meshes that have better than second-order accuracy in space and time. All the schemes designed here are shown to be second-order-accurate. We also show that the accuracy does not depend on the quality of the Riemann solver. We have compared the numerical dissipation of the unsplit MHD schemes presented here with the dimensionally split MHD schemes that have been used in the past and found the former to be superior. The dissipation does depend on the Riemann solver, but the dependence becomes weaker as the quality of the interpolation is improved. Several stringent test problems are presented to show that the methods work, including problems involving high-velocity flows in low-plasma-β magnetospheric environments. Similar advances can be made in other fields, such as electromagnetics, radiation MHD, and incompressible flow, that rely on a Stokes-law type of update strategy.

  9. 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.

  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. Scheme of thinking quantum systems

    NASA Astrophysics Data System (ADS)

    Yukalov, V. I.; Sornette, D.

    2009-11-01

    A general approach describing quantum decision procedures is developed. The approach can be applied to quantum information processing, quantum computing, creation of artificial quantum intelligence, as well as to analyzing decision processes of human decision makers. Our basic point is to consider an active quantum system possessing its own strategic state. Processing information by such a system is analogous to the cognitive processes associated to decision making by humans. The algebra of probability operators, associated with the possible options available to the decision maker, plays the role of the algebra of observables in quantum theory of measurements. A scheme is advanced for a practical realization of decision procedures by thinking quantum systems. Such thinking quantum systems can be realized by using spin lattices, systems of magnetic molecules, cold atoms trapped in optical lattices, ensembles of quantum dots, or multilevel atomic systems interacting with electromagnetic field.

  12. Numerical solution of plasma fluid equations using locally refined grids

    SciTech Connect

    Colella, P., LLNL

    1997-01-26

    This paper describes a numerical method for the solution of plasma fluid equations on block-structured, locally refined grids. The plasma under consideration is typical of those used for the processing of semiconductors. The governing equations consist of a drift-diffusion model of the electrons and an isothermal model of the ions coupled by Poisson's equation. A discretization of the equations is given for a uniform spatial grid, and a time-split integration scheme is developed. The algorithm is then extended to accommodate locally refined grids. This extension involves the advancement of the discrete system on a hierarchy of levels, each of which represents a degree of refinement, together with synchronization steps to ensure consistency across levels. A brief discussion of a software implementation is followed by a presentation of numerical results.

  13. A chaos secure communication scheme based on multiplication modulation

    NASA Astrophysics Data System (ADS)

    Fallahi, Kia; Leung, Henry

    2010-02-01

    A secure spread spectrum communication scheme using multiplication modulation is proposed. The proposed system multiplies the message by chaotic signal. The scheme does not need to know the initial condition of the chaotic signals and the receiver is based on an extended Kalman filter (EKF). This signal encryption scheme lends itself to cheap implementation and can therefore be used effectively for ensuring security and privacy in commercial consumer electronics products. To illustrate the effectiveness of the proposed scheme, a numerical example based on Genesio-Tesi system and also Chen dynamical system is presented and the results are compared.

  14. 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.

  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. Force-controlled absorption in a fully-nonlinear numerical wave tank

    SciTech Connect

    Spinneken, Johannes Christou, Marios; Swan, Chris

    2014-09-01

    An active control methodology for the absorption of water waves in a numerical wave tank is introduced. This methodology is based upon a force-feedback technique which has previously been shown to be very effective in physical wave tanks. Unlike other methods, an a-priori knowledge of the wave conditions in the tank is not required; the absorption controller being designed to automatically respond to a wide range of wave conditions. In comparison to numerical sponge layers, effective wave absorption is achieved on the boundary, thereby minimising the spatial extent of the numerical wave tank. In contrast to the imposition of radiation conditions, the scheme is inherently capable of absorbing irregular waves. Most importantly, simultaneous generation and absorption can be achieved. This is an important advance when considering inclusion of reflective bodies within the numerical wave tank. In designing the absorption controller, an infinite impulse response filter is adopted, thereby eliminating the problem of non-causality in the controller optimisation. Two alternative controllers are considered, both implemented in a fully-nonlinear wave tank based on a multiple-flux boundary element scheme. To simplify the problem under consideration, the present analysis is limited to water waves propagating in a two-dimensional domain. The paper presents an extensive numerical validation which demonstrates the success of the method for a wide range of wave conditions including regular, focused and random waves. The numerical investigation also highlights some of the limitations of the method, particularly in simultaneously generating and absorbing large amplitude or highly-nonlinear waves. The findings of the present numerical study are directly applicable to related fields where optimum absorption is sought; these include physical wavemaking, wave power absorption and a wide range of numerical wave tank schemes.

  17. 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.

  18. 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.

  19. High order well-balanced schemes

    SciTech Connect

    Noelle, Sebastian; Xing, Yulong; Shu, Chi-wang

    2010-01-01

    In this paper the authors review some recent work on high-order well-balanced schemes. A characteristic feature of hyperbolic systems of balance laws is the existence of non-trivial equilibrium solutions, where the effects of convective fluxes and source terms cancel each other. Well-balanced schemes satisfy a discrete analogue of this balance and are therefore able to maintain an equilibrium state. They discuss two classes of schemes, one based on high-order accurate, non-oscillatory finite difference operators which are well-balanced for a general class of equilibria, and the other one based on well-balanced quadratures, which can - in principle - be applied to all equilibria. Applications include equilibria at rest, where the flow velocity vanishes, and also the more challenging moving flow equilibria. Numerical experiments show excellent resolution of unperturbed as well as slightly perturbed equilibria.

  20. 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

  1. Simulation of a supercellular storm using a three-dimensional mesoscale model with an explicit lightning flash scheme

    NASA Astrophysics Data System (ADS)

    Barthe, Christelle; Pinty, Jean-Pierre

    2007-03-01

    A complete lightning flash scheme is implemented in the three-dimensional (3-D) nonhydrostatic mesoscale model Méso-NH of the French community. The scheme, which is part of the electrical scheme, follows a new approach with two steps. First, lightning flashes are modeled as bidirectional leaders to mimic the vertical propagation of the initial discharge channels along the electric field. Then, a probabilistic branching algorithm is adapted from the dielectric breakdown concept to reinforce the flash propagation toward distant regions of high charge density but immersed in a weak electric field. This results in a high increase of the total length of the lightning flash channel and also in a better capture of the morphology of intracloud lightning flashes. The electrification and lightning schemes are tested for an ideal case of a supercellular storm. The model succeeds in reproducing the general features of a storm and the electric charge cycle. Sensitivity analyses show that the implementation of a branching stage is necessary and efficient enough to relax the growth of the electric field. The intracloud discharges generated by the model look realistic with a two-layer horizontal structure extending over tens of kilometers from the triggering area. The lightning flash length and the quantity of charge neutralized are ten times more important when the branching algorithm is taken into account. The main conclusion drawn from this study is the feasibility and the benefit of an advanced treatment of lightning flashes in 3-D numerical simulations with an electrification scheme.

  2. A 4OEC scheme for the biharmonic steady Navier-Stokes equations in non-rectangular domains

    NASA Astrophysics Data System (ADS)

    Sen, Shuvam; Kalita, Jiten C.

    2015-11-01

    Recently the biharmonic form of the Navier-Stokes (N-S) equations have been solved in various domains by using second order compact discretization. In this paper, we present a fourth order essentially compact (4OEC) finite difference scheme for the steady N-S equations in geometries beyond rectangular. As a further advancement to the earlier formulations on the classical biharmonic equation that were developed for Cartesian coordinate system, this scheme is capable of numerically solving the two-dimensional N-S equations using body fitted coordinate system. Despite the presence of extra derivative terms in the quasi-linear form of the biharmonic equation, our extended formulation continues to maintain its fourth order accuracy on a nine-point compact stencil. A spectral analysis on the scheme reveals its superior resolution properties. The formulation has been tested on fluid flow problems of varied complexities on different geometries which includes flow past an impulsively started circular cylinder and elliptic aerofoil with angles of attack. We present our numerical results and validate them with established numerical and experimental observations available in the literature; excellent comparison is obtained in all the cases.

  3. 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.

  4. 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…

  5. Hindi Numerals.

    ERIC Educational Resources Information Center

    Bright, William

    In most languages encountered by linguists, the numerals, considered as a paradigmatic set, constitute a morpho-syntactic problem of only moderate complexity. The Indo-Aryan language family of North India, however, presents a curious contrast. The relatively regular numeral system of Sanskrit, as it has developed historically into the modern…

  6. 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.

  7. 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).

  8. Call Admission Control Scheme Based on Statistical Information

    NASA Astrophysics Data System (ADS)

    Fujiwara, Takayuki; Oki, Eiji; Shiomoto, Kohei

    A call admission control (CAC) scheme based on statistical information is proposed, called the statistical CAC scheme. A conventional scheme needs to manage session information for each link to update the residual bandwidth of a network in real time. This scheme has a scalability problem in terms of network size. The statistical CAC rejects session setup requests in accordance to a pre-computed ratio, called the rejection ratio. The rejection ratio is computed by using statistical information about the bandwidth requested for each link so that the congestion probability is less than an upper bound specified by a network operator. The statistical CAC is more scalable in terms of network size than the conventional scheme because it does not need to keep accommodated session state information. Numerical results show that the statistical CAC, even without exact session state information, only slightly degrades network utilization compared with the conventional scheme.

  9. Novel Discretization Schemes for the Numerical Simulation of Membrane Dynamics

    DTIC Science & Technology

    2012-09-13

    air, indicating that inertial forces dominate. In con- trast, dragonfly wings are much lighter at m∗ = 1 and aerodynamic forces dominate. Another...Flapping Wing Micro Air Vehicle Using Finite Element Methods”. Proceedings of the World Congress on Engineering, WCE 2010, volume 2. 2010. [91

  10. Accurate spectral numerical schemes for kinetic equations with energy diffusion

    NASA Astrophysics Data System (ADS)

    Wilkening, Jon; Cerfon, Antoine J.; Landreman, Matt

    2015-08-01

    We examine the merits of using a family of polynomials that are orthogonal with respect to a non-classical weight function to discretize the speed variable in continuum kinetic calculations. We consider a model one-dimensional partial differential equation describing energy diffusion in velocity space due to Fokker-Planck collisions. This relatively simple case allows us to compare the results of the projected dynamics with an expensive but highly accurate spectral transform approach. It also allows us to integrate in time exactly, and to focus entirely on the effectiveness of the discretization of the speed variable. We show that for a fixed number of modes or grid points, the non-classical polynomials can be many orders of magnitude more accurate than classical Hermite polynomials or finite-difference solvers for kinetic equations in plasma physics. We provide a detailed analysis of the difference in behavior and accuracy of the two families of polynomials. For the non-classical polynomials, if the initial condition is not smooth at the origin when interpreted as a three-dimensional radial function, the exact solution leaves the polynomial subspace for a time, but returns (up to roundoff accuracy) to the same point evolved to by the projected dynamics in that time. By contrast, using classical polynomials, the exact solution differs significantly from the projected dynamics solution when it returns to the subspace. We also explore the connection between eigenfunctions of the projected evolution operator and (non-normalizable) eigenfunctions of the full evolution operator, as well as the effect of truncating the computational domain.

  11. Semi-passive, Chemical Oxidation Schemes for the Long-term Treatment of Contaminants

    SciTech Connect

    Frank W. Schwartz

    2005-12-13

    This research involves a combined experimental and modeling study that builds on our previous DOE-sponsored work in investigating how KMnO{sub 4} can be better used with in situ remediation of groundwater contaminated by chlorinated ethylenes (e.g., PCE, TCE, DCE). This study aims to provide scientific basis for developing a new long-term, semi-passive ISCO scheme that uses controlled release KMnO{sub 4} as a reactive barrier component. Specific objectives of the study are (1) to construct controlled release KMnO{sub 4} as a new reactive barrier component that could deliver permanganate at a controlled rate over long time periods of years, (2) to quantitatively describe release mechanisms associated with the controlled release KMnO{sub 4}, (3) to demonstrate efficacy of the new remediation scheme using proof-of-concept experiments, and (4) to design advanced forms of controlled release systems through numerical optimization. The new scheme operates in a long-term, semi-passive manner to control spreading of a dissolved contaminant plume with periodic replacement of the controlled release KMnO{sub 4} installed in the subsurface. As a first step in developing this remedial concept, we manufactured various prototype controlled release KMnO{sub 4} forms. Then we demonstrated using column experiments that the controlled release KMnO{sub 4} could deliver small amount of permanganate into flowing water at controlled rates over long time periods of years. An analytical model was also used to estimate the diffusivities and durations of the controlled release KMnO{sub 4}. Finally, proof-of-concept flow-tank experiments were performed to demonstrate the efficacy of the controlled release KMnO{sub 4} scheme in controlling dissolved TCE plume in a long-term, semi-passive manner. Another important thrust of our research effort involved numerical optimization of controlled release systems. This study used a numerical model that is capable of describing release patterns of active

  12. 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)

  13. A convexity preserving scheme for conservative advection transport

    NASA Astrophysics Data System (ADS)

    Xiao, Feng; Peng, Xindong

    2004-08-01

    A simple and practical scheme for advection transport equation is presented. The scheme, namely piecewise rational method (PRM), is a variant of the existing piecewise parabolic method (PPM) of Colella and Woodward (1984). Instead of the parabolic function, a rational function is used for the reconstruction. Making use of the convexity preserving nature of the rational function enables us to obtain oscillation-less numerical solutions, but avoids the adjustments of the cell-interface values to enforce the monotonicity in PPM. The PRM is very simple and computationally efficient. Our numerical results show that PRM is competitive to the PPM in many aspects, such as numerical accuracy and shape-preserving property.

  14. 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.

  15. Error estimates of numerical solutions for a cyclic plasticity problem

    NASA Astrophysics Data System (ADS)

    Han, W.

    A cyclic plasticity problem is numerically analyzed in [13], where a sub-optimal order error estimate is shown for a spatially discrete scheme. In this note, we prove an optimal order error estimate for the spatially discrete scheme under the same solution regularity condition. We also derive an error estimate for a fully discrete scheme for solving the plasticity problem.

  16. High-order compact MacCormack scheme for two-dimensional compressible and non-hydrostatic equations of the atmosphere

    NASA Astrophysics Data System (ADS)

    JavanNezhad, R.; Meshkatee, A. H.; Ghader, S.; Ahmadi-Givi, F.

    2016-09-01

    This study is devoted to application of the fourth-order compact MacCormack scheme to spatial differencing of the conservative form of two-dimensional and non-hydrostatic equation of a dry atmosphere. To advance the solution in time a four-stage Runge-Kutta method is used. To perform the simulations, two test cases including evolution of a warm bubble and a cold bubble in a neutral atmosphere with open and rigid boundaries are employed. In addition, the second-order MacCormack and the standard fourth-order compact MacCormack schemes are used to perform the simulations. Qualitative and quantitative assessment of the numerical results for different test cases exhibit the superiority of the fourth-order compact MacCormack scheme on the second-order method.

  17. 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.

  18. Algorithm composition scheme for problems in composite domains based on the difference potential method

    NASA Astrophysics Data System (ADS)

    Ryaben'kii, V. S.; Turchaninov, V. I.; Epshteyn, Ye. Yu.

    2006-10-01

    An algorithm composition scheme for the numerical solution of boundary value problems in composite domains is proposed and illustrated using an example. The scheme requires neither difference approximations of the boundary conditions nor matching conditions on the boundary between the subdomains. The scheme is suited for multiprocessor computers.

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

    NASA Technical Reports Server (NTRS)

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

    2002-01-01

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

  20. On Convergence of High Order Shock Capturing Difference Schemes

    NASA Astrophysics Data System (ADS)

    Ostapenko, V.

    2010-11-01

    A convergence of high order shock capturing difference schemes is analyzed. Notions of weak finite difference approximations which conserve a sense on discontinuous solutions are introduced. Necessary and sufficient conditions of these approximations are obtained. It is shown that among the explicit two-layer in time conservative difference schemes there are no schemes which can have high order of weak approximation. A compact scheme of the same third order of classical and weak approximations is constructed. There is demonstrated an advantage of this scheme in comparison to TVD scheme at shock-capturing computations. A difference approximation of ɛ Rankine-Hugoniot (RH) conditions is investigated. It is shown that TVD type schemes (in contrast to non-TVD schemes, whose numerical fluxes are smooth enough) can approximate ɛ RH-conditions at most with the first order. Given examples show that non-TVD schemes (in contrast to TVD schemes) can have the second order of integral convergence through the smearing shocks and as a result can conserve a higher accuracy in the post shock regions.

  1. Augmented weighted diamond form of the linear nodal scheme for Cartesian coordinate systems

    SciTech Connect

    Walters, W.F.

    1985-01-01

    The equations of the high order linear nodal numerical scheme are cast in an augmented weighted difference form for three-dimensional Cartesian nodes. The coupling exhibited by these equations indicate that this new algorithm is simpler and hence faster than previous nodal schemes of this degree of accuracy. A well-logging problem and a fast reactor problem are examined. The new scheme developed here is compared with the classical linear-linear nodal scheme and the diamond difference scheme. For the well-logging problem, it is found that the new scheme is both faster and simpler than the classical linear-linear nodal scheme while sacrificing little in accuracy. Even though the new scheme is more accurate than the diamond difference scheme for the reactor problem, the results indicate that state of the art acceleration methods are needed for nodal schemes.

  2. Accurate analysis of planar optical waveguide devices using higher-order FDTD scheme.

    PubMed

    Kong, Fanmin; Li, Kang; Liu, Xin

    2006-11-27

    A higher-order finite-difference time-domain (HO-FDTD) numerical method is proposed for the time-domain analysis of planar optical waveguide devices. The anisotropic perfectly matched layer (APML) absorbing boundary condition for the HO-FDTD scheme is implemented and the numerical dispersion of this scheme is studied. The numerical simulations for the parallel-slab directional coupler are presented and the computing results using this scheme are in highly accordance with analytical solutions. Compared with conventional FDTD method, this scheme can save considerable computational resource without sacrificing solution accuracy and especially could be applied in the accurate analysis of optical devices.

  3. Convergence Acceleration for Multistage Time-Stepping Schemes

    NASA Technical Reports Server (NTRS)

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

    2006-01-01

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

  4. A modified symplectic PRK scheme for seismic wave modeling

    NASA Astrophysics Data System (ADS)

    Liu, Shaolin; Yang, Dinghui; Ma, Jian

    2017-02-01

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

  5. Hybridization schemes for clusters

    NASA Astrophysics Data System (ADS)

    Wales, David J.

    The concept of an optimum hybridization scheme for cluster compounds is developed with particular reference to electron counting. The prediction of electron counts for clusters and the interpretation of the bonding is shown to depend critically upon the presumed hybridization pattern of the cluster vertex atoms. This fact has not been properly appreciated in previous work, particularly in applications of Stone's tensor surface harmonic (TSH) theory, but is found to be a useful tool when dealt with directly. A quantitative definition is suggested for the optimum cluster hybridization pattern based directly upon the ease of interpretation of the molecular orbitals, and results are given for a range of species. The relationship of this scheme to the detailed cluster geometry is described using Löwdin's partitioned perturbation theory, and the success and range of application of TSH theory are discussed.

  6. 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.

  7. Numerical Grid Generation and Potential Airfoil Analysis and Design

    DTIC Science & Technology

    1988-01-01

    contents include a discussion of grid generation concepts and schemes in the literature , iter- ative methods for numerical grid generation and two...to multicomponent rN airfoils, arbitrary multiple bodies and cascade grid generation for the first time. We present representative results as a... literature , iter- ative methods for numerical grid generation and two differential grid gen- eration schemes: (1) an elliptic, and (2) a parabolic scheme. A

  8. NUMERICAL NOISE PM SIMULATION IN CMAQ

    EPA Science Inventory

    We have found that numerical noise in the latest release of CMAQ using the yamo advection scheme when compiled on Linux cluster with pgf90 (5.0 or 6.0). We recommend to use -C option to eliminate the numerical noise.

  9. Scalable Nonlinear Compact Schemes

    SciTech Connect

    Ghosh, Debojyoti; Constantinescu, Emil M.; Brown, Jed

    2014-04-01

    In this work, we focus on compact schemes resulting in tridiagonal systems of equations, specifically the fifth-order CRWENO scheme. We propose a scalable implementation of the nonlinear compact schemes by implementing a parallel tridiagonal solver based on the partitioning/substructuring approach. We use an iterative solver for the reduced system of equations; however, we solve this system to machine zero accuracy to ensure that no parallelization errors are introduced. It is possible to achieve machine-zero convergence with few iterations because of the diagonal dominance of the system. The number of iterations is specified a priori instead of a norm-based exit criterion, and collective communications are avoided. The overall algorithm thus involves only point-to-point communication between neighboring processors. Our implementation of the tridiagonal solver differs from and avoids the drawbacks of past efforts in the following ways: it introduces no parallelization-related approximations (multiprocessor solutions are exactly identical to uniprocessor ones), it involves minimal communication, the mathematical complexity is similar to that of the Thomas algorithm on a single processor, and it does not require any communication and computation scheduling.

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

    NASA Technical Reports Server (NTRS)

    Chang, Sin-Chung

    2005-01-01

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

  11. 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

  12. Second order scheme for Maxwell's equations with discontinuous dielectric permittivity on structured meshes

    NASA Astrophysics Data System (ADS)

    Ismagilov, Timur Z.

    2013-10-01

    A second order finite volume scheme for numerical solution of Maxwell's equations with discontinuous dielectric permittivity on structured meshes is suggested. The scheme is based on approaches of Godunov, Lax-Wendroff and Van Leer. The distinctive feature of the suggested scheme is calculation and limitation of derivatives that ensures second order of approximation even in the cells adjacent to dielectric permittivity discontinuity. Numerical tests for problems with linear and curvilinear dielectric permittivity discontinuities confirm second order of approximation.

  13. Direct Numerical Simulations of Plunging Airfoils

    DTIC Science & Technology

    2010-01-07

    Schmidt and E Turkel, Numerical Solutions of the Euler Equations by Finite Volume Methods Using Runge-Kutta Time-Stepping Schemes, AIAA paper 81-1259...Ω ( p ∂vj ∂xj − σij ∂v i ∂xj ) dV (4) Definition 1 A numerical scheme to solve the viscous Navier-Stokes equations is said to be Kinetic Energy...Direct Numerical Simulations of Plunging Airfoils Yves Allaneau∗ and Antony Jameson† Stanford University, Stanford, California, 94305, USA This paper

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

    NASA Technical Reports Server (NTRS)

    Wada, Yasuhiro; Liou, Meng-Sing

    1994-01-01

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

  15. 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.

  16. Advanced boundary element methods in aeroacoustics and elastodynamics

    NASA Astrophysics Data System (ADS)

    Lee, Li

    In the first part of this dissertation, advanced boundary element methods (BEM) are developed for acoustic radiation in the presence of subsonic flows. A direct boundary integral formulation is first introduced for acoustic radiation in a uniform flow. This new formulation uses the Green's function derived from the adjoint operator of the governing differential equation. Therefore, it requires no coordinate transformation. This direct BEM formulation is then extended to acoustic radiation in a nonuniform-flow field. All the terms due to the nonuniform-flow effect are taken to the right-hand side and treated as source terms. The source terms result in a domain integral in the standard boundary integral formulation. The dual reciprocity method is then used to convert the domain integral into a number of boundary integrals. The second part of this dissertation is devoted to the development of advanced BEM algorithms to overcome the multi-frequency and nonuniqueness difficulties in steady-state elastodynamics. For the multi-frequency difficulty, two different interpolation schemes, borrowed from recent developments in acoustics, are first extended to elastodynamics to accelerate the process of matrix re-formation. Then, a hybrid scheme that retains only the merits of the two different interpolation schemes is suggested. To overcome the nonuniqueness difficulty, an enhanced CHIEF (Combined Helmholtz Integral Equation Formulation) method using a linear combination of the displacement and the traction boundary integral equations on the surface of a small interior volume is proposed. Numerical examples are given to demonstrate all the advanced BEM formulations.

  17. Massive momentum-subtraction scheme

    NASA Astrophysics Data System (ADS)

    Boyle, Peter; Del Debbio, Luigi; Khamseh, Ava

    2017-03-01

    A new renormalization scheme is defined for fermion bilinears in QCD at nonvanishing quark masses. This new scheme, denoted RI/mSMOM, preserves the benefits of the nonexceptional momenta introduced in the RI/SMOM scheme and allows a definition of renormalized composite fields away from the chiral limit. Some properties of the scheme are investigated by performing explicit one-loop computation in dimensional regularization.

  18. Quantum messages with signatures forgeable in arbitrated quantum signature schemes

    NASA Astrophysics Data System (ADS)

    Kim, Taewan; Choi, Jeong Woon; Jho, Nam-Su; Lee, Soojoon

    2015-02-01

    Even though a method to perfectly sign quantum messages has not been known, the arbitrated quantum signature scheme has been considered as one of the good candidates. However, its forgery problem has been an obstacle to the scheme becoming a successful method. In this paper, we consider one situation, which is slightly different from the forgery problem, that we use to check whether at least one quantum message with signature can be forged in a given scheme, although all the messages cannot be forged. If there are only a finite number of forgeable quantum messages in the scheme, then the scheme can be secured against the forgery attack by not sending forgeable quantum messages, and so our situation does not directly imply that we check whether the scheme is secure against the attack. However, if users run a given scheme without any consideration of forgeable quantum messages, then a sender might transmit such forgeable messages to a receiver and in such a case an attacker can forge the messages if the attacker knows them. Thus it is important and necessary to look into forgeable quantum messages. We show here that there always exists such a forgeable quantum message-signature pair for every known scheme with quantum encryption and rotation, and numerically show that there are no forgeable quantum message-signature pairs that exist in an arbitrated quantum signature scheme.

  19. Modified kinetic flux vector splitting schemes for compressible flows

    NASA Astrophysics Data System (ADS)

    Chen, Yibing; Jiang, Song

    2009-06-01

    We investigate the traditional kinetic flux vector splitting (KFVS) and BGK schemes for the compressible Euler equations. First, based on a careful study of the behavior of the discrete physical variables across the contact discontinuity, we analyze quantitatively the mechanism of inducing spurious oscillations of the velocity and pressure in the vicinity of the contact discontinuity for the first-order KFVS and BGK schemes. Then, with the help of this analysis, we propose a first-order modified KFVS (MKFVS) scheme which is oscillation-free in the vicinity of the contact discontinuity, provided certain consistent conditions are satisfied. Moreover, by using piecewise linear reconstruction and van Leer's limiter, the first-order MKFVS scheme is extended to a second-order one, consequently, a nonoscillatory second-order MKFVS scheme is constructed. Finally, by combing the MKFVS schemes with the γ-model, we successfully extend the MKFVS schemes to multi-flows, and propose therefore a first- and second-order MKFVS schemes for multi-fluid computations, which are nonoscillatory across fluid interfaces. A number of numerical examples presented in this paper validate the theoretic analysis and demonstrate the good performance of the MKFVS schemes in simulation of contact discontinuities for both single- and multi-fluids.

  20. Scheme for contact angle and its hysteresis in a multiphase lattice Boltzmann method.

    PubMed

    Wang, Lei; Huang, Hai-bo; Lu, Xi-Yun

    2013-01-01

    In this paper, a scheme for specifying contact angle and its hysteresis is incorporated into a multiphase lattice Boltzmann method. The scheme is validated through investigations of the dynamic behaviors of a droplet sliding along two kinds of walls: a smooth (ideal) wall and a rough or chemically inhomogeneous (nonideal) wall. For an ideal wall, the wettability of solid substrates is able to be prescribed. For a nonideal wall, arbitrary contact angle hysteresis can be obtained through adjusting advancing and receding angles. Significantly different phenomena can be recovered for the two kinds of walls. For instance, a droplet on an inclined ideal wall under gravity is impossible to stay stationary. However, the droplet on a nonideal wall may be pinned due to contact angle hysteresis. The steady interface shapes of the droplet on an inclined nonideal wall under gravity or in a shear flow quantitatively agree well with the previous numerical studies. Besides, the complex motion of a droplet creeping like an inchworm could be simulated. The scheme is found suitable for the study of contact line problems with and without contact angle hysteresis.

  1. Application of modified Patankar schemes to stiff biogeochemical models for the water column

    NASA Astrophysics Data System (ADS)

    Burchard, Hans; Deleersnijder, Eric; Meister, Andreas

    2005-12-01

    In this paper, we apply recently developed positivity preserving and conservative Modified Patankar-type solvers for ordinary differential equations to a simple stiff biogeochemical model for the water column. The performance of this scheme is compared to schemes which are not unconditionally positivity preserving (the first-order Euler and the second- and fourth-order Runge-Kutta schemes) and to schemes which are not conservative (the first- and second-order Patankar schemes). The biogeochemical model chosen as a test ground is a standard nutrient-phytoplankton-zooplankton-detritus (NPZD) model, which has been made stiff by substantially decreasing the half saturation concentration for nutrients. For evaluating the stiffness of the biogeochemical model, so-called numerical time scales are defined which are obtained empirically by applying high-resolution numerical schemes. For all ODE solvers under investigation, the temporal error is analysed for a simple exponential decay law. The performance of all schemes is compared to a high-resolution high-order reference solution. As a result, the second-order modified Patankar-Runge-Kutta scheme gives a good agreement with the reference solution even for time steps 10 times longer than the shortest numerical time scale of the problem. Other schemes do either compute negative values for non-negative state variables (fully explicit schemes), violate conservation (the Patankar schemes) or show low accuracy (all first-order schemes).

  2. Accelerating development of advanced inverters :

    SciTech Connect

    Neely, Jason C.; Gonzalez, Sigifredo; Ropp, Michael; Schutz, Dustin

    2013-11-01

    The high penetration of utility interconnected photovoltaic (PV) systems is causing heightened concern over the effect that variable renewable generation will have on the electrical power system (EPS). These concerns have initiated the need to amend the utility interconnection standard to allow advanced inverter control functionalities that provide: (1) reactive power control for voltage support, (2) real power control for frequency support and (3) better tolerance of grid disturbances. These capabilities are aimed at minimizing the negative impact distributed PV systems may have on EPS voltage and frequency. Unfortunately, these advanced control functions may interfere with island detection schemes, and further development of advanced inverter functions requires a study of the effect of advanced functions on the efficacy of antiislanding schemes employed in industry. This report summarizes the analytical, simulation and experimental work to study interactions between advanced inverter functions and anti-islanding schemes being employed in distributed PV systems.

  3. ESCAP mobile training scheme.

    PubMed

    Yasas, F M

    1977-01-01

    In response to a United Nations resolution, the Mobile Training Scheme (MTS) was set up to provide training to the trainers of national cadres engaged in frontline and supervisory tasks in social welfare and rural development. The training is innovative in its being based on an analysis of field realities. The MTS team consisted of a leader, an expert on teaching methods and materials, and an expert on action research and evaluation. The country's trainers from different departments were sent to villages to work for a short period and to report their problems in fulfilling their roles. From these grass roots experiences, they made an analysis of the job, determining what knowledge, attitude and skills it required. Analysis of daily incidents and problems were used to produce indigenous teaching materials drawn from actual field practice. How to consider the problems encountered through government structures for policy making and decisions was also learned. Tasks of the students were to identify the skills needed for role performance by job analysis, daily diaries and project histories; to analyze the particular community by village profiles; to produce indigenous teaching materials; and to practice the role skills by actual role performance. The MTS scheme was tried in Nepal in 1974-75; 3 training programs trained 25 trainers and 51 frontline workers; indigenous teaching materials were created; technical papers written; and consultations were provided. In Afghanistan the scheme was used in 1975-76; 45 participants completed the training; seminars were held; and an ongoing Council was created. It is hoped that the training program will be expanded to other countries.

  4. New LNG process scheme

    SciTech Connect

    Foglietta, J.H.

    1999-07-01

    A new LNG cycle has been developed for base load liquefaction facilities. This new design offers a different technical and economical solution comparing in efficiency with the classical technologies. The new LNG scheme could offer attractive business opportunities to oil and gas companies that are trying to find paths to monetize gas sources more effectively; particularly for remote or offshore locations where smaller scale LNG facilities might be applicable. This design offers also an alternative route to classic LNG projects, as well as alternative fuel sources. Conceived to offer simplicity and access to industry standard equipment, This design is a hybrid result of combining a standard refrigeration system and turboexpander technology.

  5. Robust Neighboring Optimal Guidance for the Advanced Launch System

    NASA Technical Reports Server (NTRS)

    Hull, David G.

    1993-01-01

    In recent years, optimization has become an engineering tool through the availability of numerous successful nonlinear programming codes. Optimal control problems are converted into parameter optimization (nonlinear programming) problems by assuming the control to be piecewise linear, making the unknowns the nodes or junction points of the linear control segments. Once the optimal piecewise linear control (suboptimal) control is known, a guidance law for operating near the suboptimal path is the neighboring optimal piecewise linear control (neighboring suboptimal control). Research conducted under this grant has been directed toward the investigation of neighboring suboptimal control as a guidance scheme for an advanced launch system.

  6. Numerical Integration

    ERIC Educational Resources Information Center

    Sozio, Gerry

    2009-01-01

    Senior secondary students cover numerical integration techniques in their mathematics courses. In particular, students would be familiar with the "midpoint rule," the elementary "trapezoidal rule" and "Simpson's rule." This article derives these techniques by methods which secondary students may not be familiar with and an approach that…

  7. A Simplified Scheme for Kinematic Source Inversion

    NASA Astrophysics Data System (ADS)

    Iglesias, A.; Castro-Artola, O.; Singh, S.; Hjorleifsdottir, V.; Legrand, D.

    2013-05-01

    It is well known that different kinematic source inversion schemes lead to non-unique solutions. For this reason, a simplified scheme, which yields the main characteristics of the rupture process, rather than the details, may be desirable. In this work we propose a modification of the frequency-domain inversion scheme of Cotton & Campillo (1995) to extract kinematic parameters using simplified geometries (ellipses). The forward problem is re-parameterized by including one or two ellipses in which the displacement is smoothly distributed. For the ellipses we invert for the position of the centers within the fault plane, the major and minor semi-axes, the maximum displacements, the angles of rotation and a parameter that controls the distribution of slip. A simulated annealing scheme is used to invert near-source displacements. We first test the method on synthetic displacement records corresponding to the Guerrero-Oaxaca earthquake (20/03/2012, Mw=7.5) by comparing the results obtained from the modified technique with the original method. In the next step, we use displacements obtained by double numerical integration of recorded accelerograms. We find that, in spite of the simple geometry, the modified method leads to a good fit between observed and synthetic displacements and recovers the main rupture characteristics.

  8. A new scheme of force reflecting control

    NASA Technical Reports Server (NTRS)

    Kim, Won S.

    1992-01-01

    A new scheme of force reflecting control has been developed that incorporates position-error-based force reflection and robot compliance control. The operator is provided with a kinesthetic force feedback which is proportional to the position error between the operator-commanded and the actual position of the robot arm. Robot compliance control, which increases the effective compliance of the robot, is implemented by low pass filtering the outputs of the force/torque sensor mounted on the base of robot hand and using these signals to alter the operator's position command. This position-error-based force reflection scheme combined with shared compliance control has been implemented successfully to the Advanced Teleoperation system consisting of dissimilar master-slave arms. Stability measurements have demonstrated unprecedentedly high force reflection gains of up to 2 or 3, even though the slave arm is much stiffer than operator's hand holding the force reflecting hand controller. Peg-in-hole experiments were performed with eight different operating modes to evaluate the new force-reflecting control scheme. Best task performance resulted with this new control scheme.

  9. 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.

  10. The Impact of Microphysical Schemes on Intensity and Track of Hurricane

    NASA Technical Reports Server (NTRS)

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

    2010-01-01

    During the past decade, both research and operational numerical weather prediction models [e.g. Weather Research and Forecasting Model (WRF)] have started using more complex microphysical schemes originally developed for high-resolution cloud resolving models (CRMs) with a 1-2 km or less horizontal resolutions. The WRF is a next-generation meso-scale forecast model and assimilation system that has incorporated a modern software framework, advanced dynamics, numeric and data assimilation techniques, a multiple moveable nesting capability, and improved physical packages. The WRF model can be used for a wide range of applications, from idealized research to operational forecasting, with an emphasis on horizontal grid sizes in the range of 1-10 km. The current WRF includes several different microphysics options. At Goddard, four different cloud microphysics schemes (warm rain only, two-class of ice, two three-class of ice with either graupel or hail) are implemented into the WRF. The performances of these schemes have been compared to those from other WRF microphysics scheme options for an Atlantic hurricane case. In addition, a brief review and comparison on the previous modeling studies on the impact of microphysics schemes and microphysical processes on intensity and track of hurricane will be presented. Generally, almost all modeling studies found that the microphysics schemes did not have major impacts on track forecast, but did have more effect on the intensity. All modeling studies found that the simulated hurricane has rapid deepening and/or intensification for the warm rain-only case. It is because all hydrometeors were very large raindrops, and they fell out quickly at and near the eye-wall region. This would hydrostatically produce the lowest pressure. In addition, these modeling studies suggested that the simulated hurricane becomes unrealistically strong by removing the evaporative cooling of cloud droplets and melting of ice particles. This is due to the

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

    NASA Astrophysics Data System (ADS)

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

    2017-02-01

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

  12. The standard upwind compact difference schemes for incompressible flow simulations

    NASA Astrophysics Data System (ADS)

    Fan, Ping

    2016-10-01

    Compact difference schemes have been used extensively for solving the incompressible Navier-Stokes equations. However, the earlier formulations of the schemes are of central type (called central compact schemes, CCS), which are dispersive and susceptible to numerical instability. To enhance stability of CCS, the optimal upwind compact schemes (OUCS) are developed recently by adding high order dissipative terms to CCS. In this paper, it is found that OUCS are essentially not of the upwind type because they do not use upwind-biased but central type of stencils. Furthermore, OUCS are not the most optimal since orders of accuracy of OUCS are at least one order lower than the maximum achievable orders. New upwind compact schemes (called standard upwind compact schemes, SUCS) are developed in this paper. In contrast to OUCS, SUCS are constructed based completely on upwind-biased stencils and hence can gain adequate numerical dissipation with no need for introducing optimization calculations. Furthermore, SUCS can achieve the maximum achievable orders of accuracy and hence be more compact than OUCS. More importantly, SUCS have prominent advantages on combining the stable and high resolution properties which are demonstrated from the global spectral analyses and typical numerical experiments.

  13. Handling geophysical flows: Numerical modelling using Graphical Processing Units

    NASA Astrophysics Data System (ADS)

    Garcia-Navarro, Pilar; Lacasta, Asier; Juez, Carmelo; Morales-Hernandez, Mario

    2016-04-01

    Computational tools may help engineers in the assessment of sediment transport during the decision-making processes. The main requirements are that the numerical results have to be accurate and simulation models must be fast. The present work is based on the 2D shallow water equations in combination with the 2D Exner equation [1]. The resulting numerical model accuracy was already discussed in previous work. Regarding the speed of the computation, the Exner equation slows down the already costly 2D shallow water model as the number of variables to solve is increased and the numerical stability is more restrictive. On the other hand, the movement of poorly sorted material over steep areas constitutes a hazardous environmental problem. Computational tools help in the predictions of such landslides [2]. In order to overcome this problem, this work proposes the use of Graphical Processing Units (GPUs) for decreasing significantly the simulation time [3, 4]. The numerical scheme implemented in GPU is based on a finite volume scheme. The mathematical model and the numerical implementation are compared against experimental and field data. In addition, the computational times obtained with the Graphical Hardware technology are compared against Single-Core (sequential) and Multi-Core (parallel) CPU implementations. References [Juez et al.(2014)] Juez, C., Murillo, J., & Garca-Navarro, P. (2014) A 2D weakly-coupled and efficient numerical model for transient shallow flow and movable bed. Advances in Water Resources. 71 93-109. [Juez et al.(2013)] Juez, C., Murillo, J., & Garca-Navarro, P. (2013) . 2D simulation of granular flow over irregular steep slopes using global and local coordinates. Journal of Computational Physics. 225 166-204. [Lacasta et al.(2014)] Lacasta, A., Morales-Hernndez, M., Murillo, J., & Garca-Navarro, P. (2014) An optimized GPU implementation of a 2D free surface simulation model on unstructured meshes Advances in Engineering Software. 78 1-15. [Lacasta

  14. Accuracy of schemes with nonuniform meshes for compressible fluid flows

    NASA Technical Reports Server (NTRS)

    Turkel, E.

    1985-01-01

    The accuracy of the space discretization for time-dependent problems when a nonuniform mesh is used is considered. Many schemes reduce to first-order accuracy while a popular finite volume scheme is even inconsistent for general grids. This accuracy is based on physical variables. However, when accuracy is measured in computational variables then second-order accuracy can be obtained. This is meaningful only if the mesh accurately reflects the properties of the solution. In addition, the stability properties of some improved accurate schemes are analyzed and it can be shown that they also allow for larger time steps when Runge-Kutta type methods are used to advance in time.

  15. Large eddy simulations and direct numerical simulations of high speed turbulent reacting flows

    NASA Technical Reports Server (NTRS)

    Givi, Peyman; Madnia, Cyrus K.; Steinberger, Craig J.

    1990-01-01

    This research is involved with the implementation of advanced computational schemes based on large eddy simulations (LES) and direct numerical simulations (DNS) to study the phenomenon of mixing and its coupling with chemical reactions in compressible turbulent flows. In the efforts related to LES, a research program to extend the present capabilities of this method was initiated for the treatment of chemically reacting flows. In the DNS efforts, the focus is on detailed investigations of the effects of compressibility, heat release, and non-equilibrium kinetics modelings in high speed reacting flows. Emphasis was on the simulations of simple flows, namely homogeneous compressible flows, and temporally developing high speed mixing layers.

  16. Advanced geometries and regimes

    SciTech Connect

    Bulanov, S. S.; Bulanov, S. V.; Turchetti, G.; Limpouch, J.; Klimo, O.; Psikal, J.; Margarone, D.; Korn, G.

    2013-07-26

    We review and discuss different schemes of laser ion acceleration as well as advanced target geometries in connection with the development of the laser-driven proton source for hadron therapy of oncological diseases, which is a part of the ELIMED project.

  17. Development of a fully implicit particle-in-cell scheme for gyrokinetic electromagnetic turbulence simulation in XGC1

    NASA Astrophysics Data System (ADS)

    Ku, Seung-Hoe; Hager, R.; Chang, C. S.; Chacon, L.; Chen, G.; EPSI Team

    2016-10-01

    The cancelation problem has been a long-standing issue for long wavelengths modes in electromagnetic gyrokinetic PIC simulations in toroidal geometry. As an attempt of resolving this issue, we implemented a fully implicit time integration scheme in the full-f, gyrokinetic PIC code XGC1. The new scheme - based on the implicit Vlasov-Darwin PIC algorithm by G. Chen and L. Chacon - can potentially resolve cancelation problem. The time advance for the field and the particle equations is space-time-centered, with particle sub-cycling. The resulting system of equations is solved by a Picard iteration solver with fixed-point accelerator. The algorithm is implemented in the parallel velocity formalism instead of the canonical parallel momentum formalism. XGC1 specializes in simulating the tokamak edge plasma with magnetic separatrix geometry. A fully implicit scheme could be a way to accurate and efficient gyrokinetic simulations. We will test if this numerical scheme overcomes the cancelation problem, and reproduces the dispersion relation of Alfven waves and tearing modes in cylindrical geometry. Funded by US DOE FES and ASCR, and computing resources provided by OLCF through ALCC.

  18. Multigrid solutions to quasi-elliptic schemes

    NASA Technical Reports Server (NTRS)

    Brandt, A.; Taasan, S.

    1985-01-01

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

  19. An efficient class of WENO schemes with adaptive order

    NASA Astrophysics Data System (ADS)

    Balsara, Dinshaw S.; Garain, Sudip; Shu, Chi-Wang

    2016-12-01

    Finite difference WENO schemes have established themselves as very worthy performers for entire classes of applications that involve hyperbolic conservation laws. In this paper we report on two major advances that make finite difference WENO schemes more efficient. The first advance consists of realizing that WENO schemes require us to carry out stencil operations very efficiently. In this paper we show that the reconstructed polynomials for any one-dimensional stencil can be expressed most efficiently and economically in Legendre polynomials. By using Legendre basis, we show that the reconstruction polynomials and their corresponding smoothness indicators can be written very compactly. The smoothness indicators are written as a sum of perfect squares. Since this is a computationally expensive step, the efficiency of finite difference WENO schemes is enhanced by the innovation which is reported here. The second advance consists of realizing that one can make a non-linear hybridization between a large, centered, very high accuracy stencil and a lower order WENO scheme that is nevertheless very stable and capable of capturing physically meaningful extrema. This yields a class of adaptive order WENO schemes, which we call WENO-AO (for adaptive order). Thus we arrive at a WENO-AO(5,3) scheme that is at best fifth order accurate by virtue of its centered stencil with five zones and at worst third order accurate by virtue of being non-linearly hybridized with an r = 3 CWENO scheme. The process can be extended to arrive at a WENO-AO(7,3) scheme that is at best seventh order accurate by virtue of its centered stencil with seven zones and at worst third order accurate. We then recursively combine the above two schemes to arrive at a WENO-AO(7,5,3) scheme which can achieve seventh order accuracy when that is possible; graciously drop down to fifth order accuracy when that is the best one can do; and also operate stably with an r = 3 CWENO scheme when that is the only thing

  20. Revisit to the THINC scheme: A simple algebraic VOF algorithm

    NASA Astrophysics Data System (ADS)

    Xiao, Feng; , Satoshi, Ii; Chen, Chungang

    2011-08-01

    This short note presents an improved multi-dimensional algebraic VOF method to capture moving interfaces. The interface jump in the THINC (tangent of hyperbola for INterface capturing) scheme is adaptively scaled to a proper thickness according to the interface orientation. The numerical accuracy in computing multi-dimensional moving interfaces is significantly improved. Without any geometrical reconstruction, the proposed method is extremely simple and easy to use, and its numerical accuracy is superior to other existing methods of its kind and comparable to the conventional PLIC (piecewise linear interface calculation) type VOF schemes.

  1. A rotationally biased upwind difference scheme for the Euler equations

    NASA Technical Reports Server (NTRS)

    Davis, S. F.

    1983-01-01

    The upwind difference schemes of Godunov, Osher, Roe and van Leer are able to resolve one dimensional steady shocks for the Euler equations within one or two mesh intervals. Unfortunately, this resolution is lost in two dimensions when the shock crosses the computing grid at an oblique angle. To correct this problem, a numerical scheme was developed which automatically locates the angle at which a shock might be expected to cross the computing grid and then constructs separate finite difference formulas for the flux components normal and tangential to this direction. Numerical results which illustrate the ability of this method to resolve steady oblique shocks are presented.

  2. A Comparison of three high-precision quadrature schemes

    SciTech Connect

    Bailey, David H.; Li, Xiaoye S.

    2003-07-01

    The authors have implemented three numerical quadrature schemes, using the new Arbitrary Precision (ARPREC) software package, with the objective of seeking a completely ''automatic'' arbitrary precision quadrature facility, namely one that does not rely on a priori information of the function to be integrated. Such a facility is required, for example, to permit the experimental identification of definite integrals based on their numerical values. The performance and accuracy of these three quadrature schemes are compared using a suite of 15 integrals, ranging from continuous, well-behaved functions on finite intervals to functions with vertical derivatives and integrable singularities at endpoints, as well as several integrals on an infinite interval.

  3. The upwind control volume scheme for unstructured triangular grids

    NASA Technical Reports Server (NTRS)

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

    1989-01-01

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

  4. Numerical Optimization

    DTIC Science & Technology

    1992-12-01

    fisica matematica . ABSTRACT - We consider a new method for the numerical solution both of non- linear systems of equations and of cornplementauity... Matematica , Serie V11 Volume 9 , Roma (1989), 521-543 An Inexact Continuous Method for the Solution of Large Systems of Equations and Complementarity...34 - 00185 Roma - Italy APPENDIX 2 A Quadratically Convergent Method for Unear Programming’ Stefano Herzel Dipartimento di Matematica -G. Castelnuovo

  5. Sensitivity of Age-of-Air Calculations to the Choice of Advection Scheme

    NASA Technical Reports Server (NTRS)

    Eluszkiewicz, Janusz; Hemler, Richard S.; Mahlman, Jerry D.; Bruhwiler, Lori; Takacs, Lawrence L.

    2000-01-01

    The age of air has recently emerged as a diagnostic of atmospheric transport unaffected by chemical parameterizations, and the features in the age distributions computed in models have been interpreted in terms of the models' large-scale circulation field. This study shows, however, that in addition to the simulated large-scale circulation, three-dimensional age calculations can also be affected by the choice of advection scheme employed in solving the tracer continuity equation, Specifically, using the 3.0deg latitude X 3.6deg longitude and 40 vertical level version of the Geophysical Fluid Dynamics Laboratory SKYHI GCM and six online transport schemes ranging from Eulerian through semi-Lagrangian to fully Lagrangian, it will be demonstrated that the oldest ages are obtained using the nondiffusive centered-difference schemes while the youngest ages are computed with a semi-Lagrangian transport (SLT) scheme. The centered- difference schemes are capable of producing ages older than 10 years in the mesosphere, thus eliminating the "young bias" found in previous age-of-air calculations. At this stage, only limited intuitive explanations can be advanced for this sensitivity of age-of-air calculations to the choice of advection scheme, In particular, age distributions computed online with the National Center for Atmospheric Research Community Climate Model (MACCM3) using different varieties of the SLT scheme are substantially older than the SKYHI SLT distribution. The different varieties, including a noninterpolating-in-the-vertical version (which is essentially centered-difference in the vertical), also produce a narrower range of age distributions than the suite of advection schemes employed in the SKYHI model. While additional MACCM3 experiments with a wider range of schemes would be necessary to provide more definitive insights, the older and less variable MACCM3 age distributions can plausibly be interpreted as being due to the semi-implicit semi

  6. A three-dimensional boundary layer scheme: stability and accuracy analyses

    NASA Astrophysics Data System (ADS)

    Horri-Naceur, Jalil; Buisine, Daniel

    2002-03-01

    We present a numerical scheme for the calculation of incompressible three-dimensional boundary layers (3DBL), designed to take advantage of the 3DBL model's overall hyperbolic nature, which is linked to the existence of wedge-shaped dependence and influence zones. The proposed scheme, explicit along the wall and implicit in the normal direction, allows large time steps, thus enabling fast convergence. In order to keep this partly implicit character, the control volumes for the mass and momentum balances are not staggered along the wall. This results in a lack of numerical viscosity, making the scheme unstable. The implementation of a numerical diffusion, suited to the local zone of influence, restores the stability of the boundary layer scheme while preserving second-order space accuracy. The purpose of this article is to present the analytical and numerical studies carried out to establish the scheme's accuracy and stability properties. Copyright

  7. Probabilistic Analysis of the Upwind Scheme for Transport Equations

    NASA Astrophysics Data System (ADS)

    Delarue, François; Lagoutière, Frédéric

    2011-01-01

    We provide a probabilistic analysis of the upwind scheme for d-dimensional transport equations. We associate a Markov chain with the numerical scheme and then obtain a backward representation formula of Kolmogorov type for the numerical solution. We then understand that the error induced by the scheme is governed by the fluctuations of the Markov chain around the characteristics of the flow. We show, in various situations, that the fluctuations are of diffusive type. As a by-product, we recover recent results due to Merlet and Vovelle (Numer Math 106: 129-155, 2007) and Merlet (SIAM J Numer Anal 46(1):124-150, 2007): we prove that the scheme is of order 1/2 in {L^{infty}([0,T],L^1(mathbb R^d))} for an integrable initial datum of bounded variation and of order 1/2- ɛ, for all ɛ > 0, in {L^{infty}([0,T] × mathbb R^d)} for an initial datum of Lipschitz regularity. Our analysis provides a new interpretation of the numerical diffusion phenomenon.

  8. Resolution-optimised nonlinear scheme for secondary derivatives

    NASA Astrophysics Data System (ADS)

    Li, Li; Yu, Changping; Chen, Zhe; Li, Xinliang

    2016-02-01

    A 5-point-stencil optimised nonlinear scheme with spectral-like resolution within the whole wave number range for secondary derivatives is devised. The proposed scheme can compensate for the dissipation deficiency of traditional linear schemes and suppress the spurious energy accumulation that occurs at high wave numbers, both of which are frequently encountered in large eddy simulation. The new scheme is composed of a linear fourth-order central scheme term and an artificial viscosity term. These two terms are connected by a nonlinear weight. The proposed nonlinear weight is designed based on Fourier analysis, rather than Taylor analysis, to guarantee a spectral-like resolution. Moreover, the accuracy is not affected by the optimisation, and the new scheme reaches fourth-order accuracy. The new scheme is tested numerically using the one-dimensional diffusion problem, one-dimensional steady viscous Burger's shock, two-dimensional vortex decaying, three-dimensional isotropic decaying turbulence and fully developed turbulent channel flow. All the tests confirm that the new scheme has spectral-like resolution and can improve the accuracy of the energy spectrum, dissipation rate and high-order statistics of turbulent flows.

  9. Numerical analysis of turbulent coaxial flow with internal heat generation

    NASA Technical Reports Server (NTRS)

    Lin, A.; Weinstein, H.

    1981-01-01

    A computational method with which to obtain a physical understanding of the turbulent field of two coaxial jets entering an axisymmetric chamber is developed. Even the laminar field of this flow is quite complicated. This is due to the many different domains which exist in the field especially in the entrance region. Physically, three regions may be identified: the wall region, the initial region near the axis of symmetry and the mixing region. Advancing downstream, these regions change relative size with the ratio of the two jets' mass fluxes as the main parameter. The turbulent field of these flows is much more complicated due to the difference in the effective transport coefficients and turbulence level from region to region. However, being aware beforehand of the complications and the different regions of this field, the appropriate turbulence model and numerical scheme can be adjusted to treat the problem.

  10. An optimized spectral difference scheme for CAA problems

    NASA Astrophysics Data System (ADS)

    Gao, Junhui; Yang, Zhigang; Li, Xiaodong

    2012-05-01

    In the implementation of spectral difference (SD) method, the conserved variables at the flux points are calculated from the solution points using extrapolation or interpolation schemes. The errors incurred in using extrapolation and interpolation would result in instability. On the other hand, the difference between the left and right conserved variables at the edge interface will introduce dissipation to the SD method when applying a Riemann solver to compute the flux at the element interface. In this paper, an optimization of the extrapolation and interpolation schemes for the fourth order SD method on quadrilateral element is carried out in the wavenumber space through minimizing their dispersion error over a selected band of wavenumbers. The optimized coefficients of the extrapolation and interpolation are presented. And the dispersion error of the original and optimized schemes is plotted and compared. An improvement of the dispersion error over the resolvable wavenumber range of SD method is obtained. The stability of the optimized fourth order SD scheme is analyzed. It is found that the stability of the 4th order scheme with Chebyshev-Gauss-Lobatto flux points, which is originally weakly unstable, has been improved through the optimization. The weak instability is eliminated completely if an additional second order filter is applied on selected flux points. One and two dimensional linear wave propagation analyses are carried out for the optimized scheme. It is found that in the resolvable wavenumber range the new SD scheme is less dispersive and less dissipative than the original scheme, and the new scheme is less anisotropic for 2D wave propagation. The optimized SD solver is validated with four computational aeroacoustics (CAA) workshop benchmark problems. The numerical results with optimized schemes agree much better with the analytical data than those with the original schemes.

  11. A Comparison of Some Difference Schemes for a Parabolic Problem of Zero-Coupon Bond Pricing

    NASA Astrophysics Data System (ADS)

    Chernogorova, Tatiana; Vulkov, Lubin

    2009-11-01

    This paper describes a comparison of some numerical methods for solving a convection-diffusion equation subjected by dynamical boundary conditions which arises in the zero-coupon bond pricing. The one-dimensional convection-diffusion equation is solved by using difference schemes with weights including standard difference schemes as the monotone Samarskii's scheme, FTCS and Crank-Nicolson methods. The schemes are free of spurious oscillations and satisfy the positivity and maximum principle as demanded for the financial and diffusive solution. Numerical results are compared with analytical solutions.

  12. Generalized formulation of a class of explicit and implicit TVD schemes

    NASA Technical Reports Server (NTRS)

    Yee, H. C.

    1985-01-01

    A one parameter family of second order explicit and implicit total variation diminishing (TVD) schemes is reformulated so that a simpler and wider group of limiters is included. The resulting scheme can be viewed as a symmetrical algorithm with a variety of numerical dissipation terms that are designed for weak solutions of hyperbolic problems. This is a generalization of Roe and Davis's recent works to a wider class of symmetric schemes other than Lax-Wendroff. The main properties of the present class of schemes are that they can be implicit, and when steady state calculations are sought, the numerical solution is independent of the time step.

  13. Linearly first- and second-order, unconditionally energy stable schemes for the phase field crystal model

    NASA Astrophysics Data System (ADS)

    Yang, Xiaofeng; Han, Daozhi

    2017-02-01

    In this paper, we develop a series of linear, unconditionally energy stable numerical schemes for solving the classical phase field crystal model. The temporal discretizations are based on the first order Euler method, the second order backward differentiation formulas (BDF2) and the second order Crank-Nicolson method, respectively. The schemes lead to linear elliptic equations to be solved at each time step, and the induced linear systems are symmetric positive definite. We prove that all three schemes are unconditionally energy stable rigorously. Various classical numerical experiments in 2D and 3D are performed to validate the accuracy and efficiency of the proposed schemes.

  14. Final Progress Report submitted via the DOE Energy Link (E-Link) in June 2009 [Collaborative Research: Decadal-to-Centennial Climate & Climate Change Studies with Enhanced Variable and Uniform Resolution GCMs Using Advanced Numerical Techniques

    SciTech Connect

    Fox-Rabinovitz, M; Cote, J

    2009-10-09

    The joint U.S-Canadian project has been devoted to: (a) decadal climate studies using developed state-of-the-art GCMs (General Circulation Models) with enhanced variable and uniform resolution; (b) development and implementation of advanced numerical techniques; (c) research in parallel computing and associated numerical methods; (d) atmospheric chemistry experiments related to climate issues; (e) validation of regional climate modeling strategies for nested- and stretched-grid models. The variable-resolution stretched-grid (SG) GCMs produce accurate and cost-efficient regional climate simulations with mesoscale resolution. The advantage of the stretched grid approach is that it allows us to preserve the high quality of both global and regional circulations while providing consistent interactions between global and regional scales and phenomena. The major accomplishment for the project has been the successful international SGMIP-1 and SGMIP-2 (Stretched-Grid Model Intercomparison Project, phase-1 and phase-2) based on this research developments and activities. The SGMIP provides unique high-resolution regional and global multi-model ensembles beneficial for regional climate modeling and broader modeling community. The U.S SGMIP simulations have been produced using SciDAC ORNL supercomputers. The results of the successful SGMIP multi-model ensemble simulations of the U.S. climate are available at the SGMIP web site (http://essic.umd.edu/~foxrab/sgmip.html) and through the link to the WMO/WCRP/WGNE web site: http://collaboration.cmc.ec.gc.ca/science/wgne. Collaborations with other international participants M. Deque (Meteo-France) and J. McGregor (CSIRO, Australia) and their centers and groups have been beneficial for the strong joint effort, especially for the SGMIP activities. The WMO/WCRP/WGNE endorsed the SGMIP activities in 2004-2008. This project reflects a trend in the modeling and broader communities to move towards regional and sub-regional assessments and

  15. Impact of different parameterization schemes on simulation of mesoscale convective system over south-east India

    NASA Astrophysics Data System (ADS)

    Madhulatha, A.; Rajeevan, M.

    2017-01-01

    Main objective of the present paper is to examine the role of various parameterization schemes in simulating the evolution of mesoscale convective system (MCS) occurred over south-east India. Using the Weather Research and Forecasting (WRF) model, numerical experiments are conducted by considering various planetary boundary layer, microphysics, and cumulus parameterization schemes. Performances of different schemes are evaluated by examining boundary layer, reflectivity, and precipitation features of MCS using ground-based and satellite observations. Among various physical parameterization schemes, Mellor-Yamada-Janjic (MYJ) boundary layer scheme is able to produce deep boundary layer height by simulating warm temperatures necessary for storm initiation; Thompson (THM) microphysics scheme is capable to simulate the reflectivity by reasonable distribution of different hydrometeors during various stages of system; Betts-Miller-Janjic (BMJ) cumulus scheme is able to capture the precipitation by proper representation of convective instability associated with MCS. Present analysis suggests that MYJ, a local turbulent kinetic energy boundary layer scheme, which accounts strong vertical mixing; THM, a six-class hybrid moment microphysics scheme, which considers number concentration along with mixing ratio of rain hydrometeors; and BMJ, a closure cumulus scheme, which adjusts thermodynamic profiles based on climatological profiles might have contributed for better performance of respective model simulations. Numerical simulation carried out using the above combination of schemes is able to capture storm initiation, propagation, surface variations, thermodynamic structure, and precipitation features reasonably well. This study clearly demonstrates that the simulation of MCS characteristics is highly sensitive to the choice of parameterization schemes.

  16. Enhanced efficiency of plasma acceleration in the laser-induced cavity pressure acceleration scheme

    NASA Astrophysics Data System (ADS)

    Badziak, J.; Rosiński, M.; Jabłoński, S.; Pisarczyk, T.; Chodukowski, T.; Parys, P.; Rączka, P.; Krousky, E.; Ullschmied, J.; Liska, R.; Kucharik, M.

    2015-01-01

    Among various methods for the acceleration of dense plasmas the mechanism called laser-induced cavity pressure acceleration (LICPA) is capable of achieving the highest energetic efficiency. In the LICPA scheme, a projectile placed in a cavity is accelerated along a guiding channel by the laser-induced thermal plasma pressure or by the radiation pressure of an intense laser radiation trapped in the cavity. This arrangement leads to a significant enhancement of the hydrodynamic or electromagnetic forces driving the projectile, relative to standard laser acceleration schemes. The aim of this paper is to review recent experimental and numerical works on LICPA with the emphasis on the acceleration of heavy plasma macroparticles and dense ion beams. The main experimental part concerns the research carried out at the kilojoule sub-nanosecond PALS laser facility in Prague. Our measurements performed at this facility, supported by advanced two-dimensional hydrodynamic simulations, have demonstrated that the LICPA accelerator working in the long-pulse hydrodynamic regime can be a highly efficient tool for the acceleration of heavy plasma macroparticles to hyper-velocities and the generation of ultra-high-pressure (>100 Mbar) shocks through the collision of the macroparticle with a solid target. The energetic efficiency of the macroparticle acceleration and the shock generation has been found to be significantly higher than that for other laser-based methods used so far. Using particle-in-cell simulations it is shown that the LICPA scheme is highly efficient also in the short-pulse high-intensity regime and, in particular, may be used for production of intense ion beams of multi-MeV to GeV ion energies with the energetic efficiency of tens of per cent, much higher than for conventional laser acceleration schemes.

  17. Entropy Splitting and Numerical Dissipation

    NASA Technical Reports Server (NTRS)

    Yee, H. C.; Vinokur, M.; Djomehri, M. J.

    1999-01-01

    A rigorous stability estimate for arbitrary order of accuracy of spatial central difference schemes for initial-boundary value problems of nonlinear symmetrizable systems of hyperbolic conservation laws was established recently by Olsson and Oliger (1994) and Olsson (1995) and was applied to the two-dimensional compressible Euler equations for a perfect gas by Gerritsen and Olsson (1996) and Gerritsen (1996). The basic building block in developing the stability estimate is a generalized energy approach based on a special splitting of the flux derivative via a convex entropy function and certain homogeneous properties. Due to some of the unique properties of the compressible Euler equations for a perfect gas, the splitting resulted in the sum of a conservative portion and a non-conservative portion of the flux derivative. hereafter referred to as the "Entropy Splitting." There are several potential desirable attributes and side benefits of the entropy splitting for the compressible Euler equations that were not fully explored in Gerritsen and Olsson. The paper has several objectives. The first is to investigate the choice of the arbitrary parameter that determines the amount of splitting and its dependence on the type of physics of current interest to computational fluid dynamics. The second is to investigate in what manner the splitting affects the nonlinear stability of the central schemes for long time integrations of unsteady flows such as in nonlinear aeroacoustics and turbulence dynamics. If numerical dissipation indeed is needed to stabilize the central scheme, can the splitting help minimize the numerical dissipation compared to its un-split cousin? Extensive numerical study on the vortex preservation capability of the splitting in conjunction with central schemes for long time integrations will be presented. The third is to study the effect of the non-conservative proportion of splitting in obtaining the correct shock location for high speed complex shock

  18. A piecewise linear approximation scheme for hereditary optimal control problems

    NASA Technical Reports Server (NTRS)

    Cliff, E. M.; Burns, J. A.

    1977-01-01

    An approximation scheme based on 'piecewise linear' approximations of L2 spaces is employed to formulate a numerical method for solving quadratic optimal control problems governed by linear retarded functional differential equations. This piecewise linear method is an extension of the so called averaging technique. It is shown that the Riccati equation for the linear approximation is solved by simple transformation of the averaging solution. Thus, the computational requirements are essentially the same. Numerical results are given.

  19. Transformed Flux-Form Semi-Lagrangian Scheme

    DTIC Science & Technology

    2008-01-01

    5) which is the Korteweg-de Vries ( KDV ) equation with the exact solution , ( ) ( )2 2, sechs t A...term. Evidently equation (7) has the analytical solution (6), and therefore it can be used to verify the stability of the numerical schemes since...in ocean models since any diffusion and dispersion in the numerical solution of the Rossby soliton are computational errors. Interested readers are

  20. Advanced adaptive computational methods for Navier-Stokes simulations in rotorcraft aerodynamics

    NASA Technical Reports Server (NTRS)

    Stowers, S. T.; Bass, J. M.; Oden, J. T.

    1993-01-01

    A phase 2 research and development effort was conducted in area transonic, compressible, inviscid flows with an ultimate goal of numerically modeling complex flows inherent in advanced helicopter blade designs. The algorithms and methodologies therefore are classified as adaptive methods, which are error estimation techniques for approximating the local numerical error, and automatically refine or unrefine the mesh so as to deliver a given level of accuracy. The result is a scheme which attempts to produce the best possible results with the least number of grid points, degrees of freedom, and operations. These types of schemes automatically locate and resolve shocks, shear layers, and other flow details to an accuracy level specified by the user of the code. The phase 1 work involved a feasibility study of h-adaptive methods for steady viscous flows, with emphasis on accurate simulation of vortex initiation, migration, and interaction. Phase 2 effort focused on extending these algorithms and methodologies to a three-dimensional topology.

  1. 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.

  2. The Dynamics of Some Iterative Implicit Schemes

    NASA Technical Reports Server (NTRS)

    Yee, H. C.; Sweby, P. K.

    1994-01-01

    The global asymptotic nonlinear behavior of some standard iterative procedures in solving nonlinear systems of algebraic equations arising from four implicit linear multistep methods (LMMs) in discretizing 2 x 2 systems of first-order autonomous nonlinear ordinary differential equations is analyzed using the theory of dynamical systems. With the aid of parallel Connection Machines (CM-2 and CM-5), the associated bifurcation diagrams as a function of the time step, and the complex behavior of the associated 'numerical basins of attraction' of these iterative implicit schemes are revealed and compared. Studies showed that all of the four implicit LMMs exhibit a drastic distortion and segmentation but less shrinkage of the basin of attraction of the true solution than standard explicit methods. The numerical basins of attraction of a noniterative implicit procedure mimic more closely the basins of attraction of the differential equations than the iterative implicit procedures for the four implicit LMMs.

  3. A new flux splitting scheme for Euler equations of gas dynamics

    SciTech Connect

    Li, Xindong; Hu, Zongmin; Jiang, Zonglin

    2015-03-10

    A new flux splitting method named K-CUSP scheme is proposed in the paper. The major difference between K-CUSP and two traditional CUSP schemes (H-CUSP and E-CUSP) is that all kinematic quantities and all thermodynamic quantities in total enthalpy will be separately split into convective term and pressure term. The present scheme adopts the cell-face Mach number splitting method of AUSM+ scheme and the interface flux of pressure term is given a new way in the subsonic regime. Numerical solutions demonstrate that the new scheme inherits the simplicity and robustness of FVS schemes, which overcomes the shortcomings of pressure overshoot of shock wave in H-CUSP and E-CUSP schemes, but also retains the high-resolution of FDS schemes, which achieves the high accuracy of contact discontinuity and shock discontinuity.

  4. A Novel Communication Range Recognition (CRR) Scheme for Spatial Localization of Passive RFID Tags

    NASA Astrophysics Data System (ADS)

    Wada, Tomotaka; Uchitomi, Norie; Ota, Yuuki; Hori, Toshihiro; Mutsuura, Kouichi; Okada, Hiromi

    RFID (Radio Frequency Identification) technology is expected to be used as a localization tool. By the localization of RFID tags, a mobile robot equipped with an RFID reader can recognize the surrounding environment. In this paper, we propose a novel effective scheme called the communication range recognition (CRR) scheme for localizing RFID tags. In this scheme, an RFID reader determines the boundaries of the communication range when it is appropriately positioned by the robot. We evaluate the estimated position accuracy through numerous experiments. We show that the moving distance of the RFID reader in the proposed scheme is lower than that in conventional schemes.

  5. Compact-reconstruction weighted essentially non-oscillatory schemes for hyperbolic conservation laws

    NASA Astrophysics Data System (ADS)

    Ghosh, Debojyoti

    A new class of non-linear compact interpolation schemes is introduced in this dissertation that have a high spectral resolution and are non-oscillatory across discontinuities. The Compact-Reconstruction Weighted Essentially Non-Oscillatory (CRWENO) schemes use a solution-dependent combination of lower-order compact schemes to yield a high-order accurate, non-oscillatory scheme. Fifth-order accurate CRWENO schemes are constructed and their numerical properties are analyzed. These schemes have lower absolute errors and higher spectral resolution than the WENO scheme of the same order. The schemes are applied to scalar conservation laws and the Euler equations of fluid dynamics. The order of convergence and the higher accuracy of the CRWENO schemes are verified for smooth solutions. Significant improvements are observed in the resolution of discontinuities and extrema as well as the preservation of flow features over large convection distances. The computational cost of the CRWENO schemes is assessed and the reduced error in the solution outweighs the additional expense of the implicit scheme, thus resulting in higher numerical efficiency. This conclusion extends to the reconstruction of conserved and primitive variables for the Euler equations, but not to the characteristic-based reconstruction. Further improvements are observed in the accuracy and resolution of the schemes with alternative formulations for the non-linear weights. The CRWENO schemes are integrated into a structured, finite-volume Navier-Stokes solver and applied to problems of practical relevance. Steady and unsteady flows around airfoils are solved to validate the scheme for curvi-linear grids, as well as overset grids with relative motion. The steady flow around a three-dimensional wing and the unsteady flow around a full-scale rotor are solved. It is observed that though lower-order schemes suffice for the accurate prediction of aerodynamic forces, the CRWENO scheme yields improved resolution of

  6. An efficient time advancing strategy for energy-preserving simulations

    NASA Astrophysics Data System (ADS)

    Capuano, F.; Coppola, G.; de Luca, L.

    2015-08-01

    Energy-conserving numerical methods are widely employed within the broad area of convection-dominated systems. Semi-discrete conservation of energy is usually obtained by adopting the so-called skew-symmetric splitting of the non-linear convective term, defined as a suitable average of the divergence and advective forms. Although generally allowing global conservation of kinetic energy, it has the drawback of being roughly twice as expensive as standard divergence or advective forms alone. In this paper, a general theoretical framework has been developed to derive an efficient time-advancement strategy in the context of explicit Runge-Kutta schemes. The novel technique retains the conservation properties of skew-symmetric-based discretizations at a reduced computational cost. It is found that optimal energy conservation can be achieved by properly constructed Runge-Kutta methods in which only divergence and advective forms for the convective term are used. As a consequence, a considerable improvement in computational efficiency over existing practices is achieved. The overall procedure has proved to be able to produce new schemes with a specified order of accuracy on both solution and energy. The effectiveness of the method as well as the asymptotic behavior of the schemes is demonstrated by numerical simulation of Burgers' equation.

  7. Three discontinuous Galerkin schemes for the anisotropic heat conduction equation on non-aligned grids

    NASA Astrophysics Data System (ADS)

    Held, M.; Wiesenberger, M.; Stegmeir, A.

    2016-02-01

    We present and discuss three discontinuous Galerkin (dG) discretizations for the anisotropic heat conduction equation on non-aligned cylindrical grids. Our non-aligned scheme relies on a self-adjoint local dG (LDG) discretization of the elliptic operator. It conserves the energy exactly and converges with arbitrary order. The pollution by numerical perpendicular heat fluxes decreases with superconvergence rates. We compare this scheme with aligned schemes that are based on the flux-coordinate independent approach for the discretization of parallel derivatives. Here, the dG method provides the necessary interpolation. The first aligned discretization can be used in an explicit time-integrator. However, the scheme violates conservation of energy and shows up stagnating convergence rates for very high resolutions. We overcome this partly by using the adjoint of the parallel derivative operator to construct a second self-adjoint aligned scheme. This scheme preserves energy, but reveals unphysical oscillations in the numerical tests, which result in a decreased order of convergence. Both aligned schemes exhibit low numerical heat fluxes into the perpendicular direction and are superior for flute-modes with finite parallel gradients. We build our argumentation on various numerical experiments on all three schemes for a general axisymmetric magnetic field, which is closed by a comparison to the aligned finite difference (FD) schemes of Stegmeir et al. (2014) and Stegmeir et al. (submitted for publication).

  8. Numerical solution of multiscale electromagnetic systems

    NASA Astrophysics Data System (ADS)

    Tobon Llano, Luis Eduardo

    The Discontinuous Galerkin time domain (DGTD) method is promising in modeling of realistic multiscale electromagnetic systems. This method defines the basic concept for implementing the communication between multiple domains with different scales. Constructing a DGTD system consists of several careful choices: (a) governing equations; (b) element shape and corresponding basis functions for the spatial discretization of each subdomain; (c) numerical fluxes onto interfaces to bond all subdomains together; and (d) time stepping scheme based on properties of a discretized system. This work present the advances in each one of these steps. First, a unified framework based on the theory of differential forms and the finite element method is used to analyze the discretization of the Maxwell's equations. Based on this study, field intensities (E and H) are associated to 1-forms and curl-conforming basis functions; flux densities (D and B) are associated to 2-forms and divergence-conforming basis functions; and the constitutive relations are defined by Hodge operators. A different approach is the study of numerical dispersion. Semidiscrete analysis is the traditional method, but for high order elements modal analysis is prefered. From these analyses, we conclude that a correct discretization of fields belonging to different p-form (e.g., E and B ) uses basis functions with same order of interpolation; however, different order of interpolation must be used if two fields belong to the same p-form (e.g., E and H). An alternative method to evaluate numerical dispersion based on evaluation of dispersive Hodge operators is also presented. Both dispersion analyses are equivalent and reveal same fundamental results. Eigenvalues, eigenvector and transient results are studied to verify accuracy and computational costs of different schemes. Two different approaches are used for implementing the DG Method. The first is based on E and H fields, which use curl-conforming basis functions

  9. A no-key-exchange secure image sharing scheme based on Shamir's three-pass cryptography protocol and the multiple-parameter fractional Fourier transform.

    PubMed

    Lang, Jun

    2012-01-30

    In this paper, we propose a novel secure image sharing scheme based on Shamir's three-pass protocol and the multiple-parameter fractional Fourier transform (MPFRFT), which can safely exchange information with no advance distribution of either secret keys or public keys between users. The image is encrypted directly by the MPFRFT spectrum without the use of phase keys, and information can be shared by transmitting the encrypted image (or message) three times between users. Numerical simulation results are given to verify the performance of the proposed algorithm.

  10. 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.

  11. Entropy-bounded discontinuous Galerkin scheme for Euler equations

    NASA Astrophysics Data System (ADS)

    Lv, Yu; Ihme, Matthias

    2015-08-01

    An entropy-bounded Discontinuous Galerkin (EBDG) scheme is proposed in which the solution is regularized by constraining the entropy. The resulting scheme is able to stabilize the solution in the vicinity of discontinuities and retains the optimal accuracy for smooth solutions. The properties of the limiting operator according to the entropy-minimum principle are proofed, and an optimal CFL-criterion is derived. We provide a rigorous description for locally imposing entropy constraints to capture multiple discontinuities. Significant advantages of the EBDG-scheme are the general applicability to arbitrary high-order elements and its simple implementation for multi-dimensional configurations. Numerical tests confirm the properties of the scheme, and particular focus is attributed to the robustness in treating discontinuities on arbitrary meshes.

  12. 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.

  13. Embedded WENO: A design strategy to improve existing WENO schemes

    NASA Astrophysics Data System (ADS)

    van Lith, Bart S.; ten Thije Boonkkamp, Jan H. M.; IJzerman, Wilbert L.

    2017-02-01

    Embedded WENO methods utilise all adjacent smooth substencils to construct a desirable interpolation. Conventional WENO schemes under-use this possibility close to large gradients or discontinuities. We develop a general approach for constructing embedded versions of existing WENO schemes. Embedded methods based on the WENO schemes of Jiang and Shu [1] and on the WENO-Z scheme of Borges et al. [2] are explicitly constructed. Several possible choices are presented that result in either better spectral properties or a higher order of convergence for sufficiently smooth solutions. However, these improvements carry over to discontinuous solutions. The embedded methods are demonstrated to be indeed improvements over their standard counterparts by several numerical examples. All the embedded methods presented have no added computational effort compared to their standard counterparts.

  14. Chaotic communication scheme with multiplication

    NASA Astrophysics Data System (ADS)

    Bobreshov, A. M.; Karavaev, A. A.

    2007-05-01

    A new scheme of data transmission with nonlinear admixing is described, in which the two mutually inverse operations (multiplication and division) ensure multiplicative mixing of the informative and chaotic signals that provides a potentially higher degree of security. A special feature of the proposed scheme is the absence of limitations (related to the division by zero) imposed on the types of informative signals.

  15. Numerical Propulsion System Simulation

    NASA Technical Reports Server (NTRS)

    Naiman, Cynthia

    2006-01-01

    The NASA Glenn Research Center, in partnership with the aerospace industry, other government agencies, and academia, is leading the effort to develop an advanced multidisciplinary analysis environment for aerospace propulsion systems called the Numerical Propulsion System Simulation (NPSS). NPSS is a framework for performing analysis of complex systems. The initial development of NPSS focused on the analysis and design of airbreathing aircraft engines, but the resulting NPSS framework may be applied to any system, for example: aerospace, rockets, hypersonics, power and propulsion, fuel cells, ground based power, and even human system modeling. NPSS provides increased flexibility for the user, which reduces the total development time and cost. It is currently being extended to support the NASA Aeronautics Research Mission Directorate Fundamental Aeronautics Program and the Advanced Virtual Engine Test Cell (AVETeC). NPSS focuses on the integration of multiple disciplines such as aerodynamics, structure, and heat transfer with numerical zooming on component codes. Zooming is the coupling of analyses at various levels of detail. NPSS development includes capabilities to facilitate collaborative engineering. The NPSS will provide improved tools to develop custom components and to use capability for zooming to higher fidelity codes, coupling to multidiscipline codes, transmitting secure data, and distributing simulations across different platforms. These powerful capabilities extend NPSS from a zero-dimensional simulation tool to a multi-fidelity, multidiscipline system-level simulation tool for the full development life cycle.

  16. A new flux splitting scheme

    NASA Technical Reports Server (NTRS)

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

    1991-01-01

    A new flux splitting scheme is proposed. The scheme is remarkably simple and yet its accuracy rivals and in some cases surpasses that of Roe's solver in the Euler and Navier-Stokes solutions performed in this study. The scheme is robust and converges as fast as the Roe splitting. An approximately defined cell-face advection Mach number is proposed using values from the two straddling cells via associated characteristic speeds. This interface Mach number is then used to determine the upwind extrapolation for the convective quantities. Accordingly, the name of the scheme is coined as Advection Upstream Splitting Method (AUSM). A new pressure splitting is introduced which is shown to behave successfully, yielding much smoother results than other existing pressure splittings. Of particular interest is the supersonic blunt body problem in which the Roe scheme gives anomalous solutions. The AUSM produces correct solutions without difficulty for a wide range of flow conditions as well as grids.

  17. Numerical noise in ocean and estuarine models

    USGS Publications Warehouse

    Walters, R.; Carey, G.F.

    1984-01-01

    Approximate methods for solving the shallow water equations may lead to solutions exhibiting large fictitious, numerically-induced oscillations. The analysis of the discrete dispersion relation and modal solutions of small wavelengths provides a powerful technique for assessing the sensitivity of alternative numerical schemes to irregular data which may lead to such oscillatory numerical noise. For those schemes where phase speed vanishes at a finite wavenumber or there are multiple roots for wavenumber, oscillation modes can exist which are uncoupled from the dynamics of the problem. The discrete modal analysis approach is used here to identify two classes of spurious oscillation modes associated respectively with the two different asymptotic limits corresponding to estuarine and large scale ocean models. The analysis provides further insight into recent numerical results for models which include large spatial scales and Coriolis acceleration. ?? 1984.

  18. r-modified Crank-Nicholson difference schemes for one dimensional nonlinear viscous Burgers' equation for an incompressible flow

    NASA Astrophysics Data System (ADS)

    Ashyralyev, Allaberen; Gambo, Yusuf Ya'u.

    2016-08-01

    The nonlocal boundary value problem for viscous Burgers' equation is considered. Solutions to the 1-D equation are presented numerically by Rothe, Crank-Nicholson and r-modified Crank-Nicholson difference schemes. Matlab codes for all the three schemes are designed based on the idea of fixed-point iteration procedure and modified Gauss elimination method. The numerical results are compared.

  19. 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.

  20. A second-order characteristic line scheme for solving a juvenile-adult model of amphibians.

    PubMed

    Deng, Keng; Wang, Yi

    2015-01-01

    In this paper, we develop a second-order characteristic line scheme for a nonlinear hierarchical juvenile-adult population model of amphibians. The idea of the scheme is not to follow the characteristics from the initial data, but for each time step to find the origins of the grid nodes at the previous time level. Numerical examples are presented to demonstrate the accuracy of the scheme and its capability to handle solutions with singularity.

  1. A NON-OSCILLATORY SCHEME FOR OPEN CHANNEL FLOWS. (R825200)

    EPA Science Inventory

    In modeling shocks in open channel flows, the traditional finite difference schemes become inefficient and warrant special numerical treatment for smooth computations. This paper provides a general introduction to the non-oscillatory high-resolution methodology, coupled with the ...

  2. Basic numerical methods. [of unsteady and transonic flow

    NASA Technical Reports Server (NTRS)

    Steger, Joseph L.; Van Dalsem, William R.

    1989-01-01

    Some of the basic finite-difference schemes that can be used to solve the nonlinear equations that describe unsteady inviscid and viscous transonic flow are reviewed. Numerical schemes for solving the unsteady Euler and Navier-Stokes, boundary-layer, and nonlinear potential equations are described. Emphasis is given to the elementary ideas used in constructing various numerical procedures, not specific details of any one procedure.

  3. High-Resolution Shock-Capturing Schemes For A Real Gas

    NASA Technical Reports Server (NTRS)

    Montagne, L. L.; Yee, H. C.; Vinokur, M.

    1992-01-01

    Report presents comparative study of several high-resolution explicit numerical-simulation schemes capturing shocks in one-dimensional flows of real gas. One-dimensional schemes compared with respect to: ability to capture shocks, resolution of shocks, overall accuracy, and computational efficiency.

  4. Round-off error propagation in four generally applicable, recursive, least-squares-estimation schemes

    NASA Technical Reports Server (NTRS)

    Verhaegen, M. H.

    1987-01-01

    The numerical robustness of four generally applicable, recursive, least-squares-estimation schemes is analyzed by means of a theoretical round-off propagation study. This study highlights a number of practical, interesting insights of widely used recursive least-squares schemes. These insights have been confirmed in an experimental study as well.

  5. Numerical integration routines for near-earth operations

    NASA Technical Reports Server (NTRS)

    Powers, W. F.

    1973-01-01

    Two general purpose numerical integration schemes were built into the NASA-JSC computer system. The state-of-the-art of numerical integration, the particular integrators built into the JSC computer system, and the use of the new integration packages are described. Background information about numerical integration and the variable-order, variable-stepsize Adams numerical integration technique is discussed. Results concerning the PEACE parameter optimization program are given along with recommendations and conclusions.

  6. 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

  7. Linearized Implicit Numerical Method for Burgers' Equation

    NASA Astrophysics Data System (ADS)

    Mukundan, Vijitha; Awasthi, Ashish

    2016-12-01

    In this work, a novel numerical scheme based on method of lines (MOL) is proposed to solve the nonlinear time dependent Burgers' equation. The Burgers' equation is semi discretized in spatial direction by using MOL to yield system of nonlinear ordinary differential equations in time. The resulting system of nonlinear differential equations is integrated by an implicit finite difference method. We have not used Cole-Hopf transformation which gives less accurate solution for very small values of kinematic viscosity. Also, we have not considered nonlinear solvers that are computationally costlier and take more running time.In the proposed scheme nonlinearity is tackled by Taylor series and the use of fully discretized scheme is easy and practical. The proposed method is unconditionally stable in the linear sense. Furthermore, efficiency of the proposed scheme is demonstrated using three test problems.

  8. Design and Analysis of a Dynamic Mobility Management Scheme for Wireless Mesh Network

    PubMed Central

    Roy, Sudipta

    2013-01-01

    Seamless mobility management of the mesh clients (MCs) in wireless mesh network (WMN) has drawn a lot of attention from the research community. A number of mobility management schemes such as mesh network with mobility management (MEMO), mesh mobility management (M3), and wireless mesh mobility management (WMM) have been proposed. The common problem with these schemes is that they impose uniform criteria on all the MCs for sending route update message irrespective of their distinct characteristics. This paper proposes a session-to-mobility ratio (SMR) based dynamic mobility management scheme for handling both internet and intranet traffic. To reduce the total communication cost, this scheme considers each MC's session and mobility characteristics by dynamically determining optimal threshold SMR value for each MC. A numerical analysis of the proposed scheme has been carried out. Comparison with other schemes shows that the proposed scheme outperforms MEMO, M3, and WMM with respect to total cost. PMID:24311982

  9. High-Order Central WENO Schemes for Multi-Dimensional Hamilton-Jacobi Equations

    NASA Technical Reports Server (NTRS)

    Bryson, Steve; Levy, Doron; Biegel, Bryan (Technical Monitor)

    2002-01-01

    We present new third- and fifth-order Godunov-type central schemes for approximating solutions of the Hamilton-Jacobi (HJ) equation in an arbitrary number of space dimensions. These are the first central schemes for approximating solutions of the HJ equations with an order of accuracy that is greater than two. In two space dimensions we present two versions for the third-order scheme: one scheme that is based on a genuinely two-dimensional Central WENO reconstruction, and another scheme that is based on a simpler dimension-by-dimension reconstruction. The simpler dimension-by-dimension variant is then extended to a multi-dimensional fifth-order scheme. Our numerical examples in one, two and three space dimensions verify the expected order of accuracy of the schemes.

  10. Design and analysis of a dynamic mobility management scheme for wireless mesh network.

    PubMed

    Majumder, Abhishek; Roy, Sudipta

    2013-01-01

    Seamless mobility management of the mesh clients (MCs) in wireless mesh network (WMN) has drawn a lot of attention from the research community. A number of mobility management schemes such as mesh network with mobility management (MEMO), mesh mobility management (M(3)), and wireless mesh mobility management (WMM) have been proposed. The common problem with these schemes is that they impose uniform criteria on all the MCs for sending route update message irrespective of their distinct characteristics. This paper proposes a session-to-mobility ratio (SMR) based dynamic mobility management scheme for handling both internet and intranet traffic. To reduce the total communication cost, this scheme considers each MC's session and mobility characteristics by dynamically determining optimal threshold SMR value for each MC. A numerical analysis of the proposed scheme has been carried out. Comparison with other schemes shows that the proposed scheme outperforms MEMO, M(3), and WMM with respect to total cost.

  11. Advances in Doppler OCT

    PubMed Central

    Liu, Gangjun; Chen, Zhongping

    2014-01-01

    We review the principle and some recent applications of Doppler optical coherence tomography (OCT). The advances of the phase-resolved Doppler OCT method are described. Functional OCT algorithms which are based on an extension of the phase-resolved scheme are also introduced. Recent applications of Doppler OCT for quantification of flow, imaging of microvasculature and vocal fold vibration, and optical coherence elastography are briefly discussed. PMID:24443649

  12. [Hypofractionation in locally advanced breast cancer: "flash" scheme].

    PubMed

    Padilha, Marisa; Gonçalves, Sara; Fardilha, Carlos; Melo, Gilberto; Miranda, Cristina; Alves, Paula

    2013-01-01

    Introdução: O carcinoma da mama é uma das principais causas de morte no nosso país. No Serviço de Radioterapia do Instituto Português de Oncologia de Coimbra de Coimbra utilizamos, desde há mais de 30 anos, um esquema de hipofraccionamento de radioterapia, denominado “Flash”, como opção terapêutica em doentes idosos ou com baixo Performance Status, portadores de carcinoma da mama localmente avançado ou com estádios IIb ou IV, com intenção neoadjuvante ou paliativa. Objectivos: Avaliar a resposta ao tratamento, nomeadamente sobrevivência global aos três anos, resposta local e toxicidades aguda e crónica, no grupo de doentes seleccionados submetidos a esquema de hipofraccionamento, em estudo retrospectivo. Metodologia: Entre Janeiro de 2006 e Dezembro de 2008, um total de 83 doentes com diagnóstico de Carcinoma da Mama Localmente Avançado ou com estádios IIb ou IV, foi submetido a “Flash” mamário. A dose de radioterapia prescrita foi de 13Gy / 2Fr / 3 dias (em 23 doentes - 27,7%) e 26Gy / 4Fr / 2,5 semanas (em 60 doentes - 72,3%), com fotões de 4 MV, sobre a mama afectada. Foi avaliada sobrevivência global segundo o método de Kaplan-Meier. A análise estatística foi efectuada através da aplicação SPSS, versão 17.0 e os testes estatísticos foram avaliados ao nível de significância de 5%. Resultados: 80 doentes (96,4%) que efectuaram “Flash” mamário eram do género feminino, com idades compreendidas entre os 59 e os 93 anos (idade média 80,72 + 5,87 anos) e Performance Status (Karnosfsky: 0 - 100) entre 90 e 50%. Em 72 doentes (86,7%) o diagnóstico histológico foi Carcinoma Ductal Invasivo. A cirurgia após a realização do “Flash” Mamário foi realizada em 44 doentes (53%) após evidência de resposta local à radioterapia, sendo a Mastectomia Radical Modificada a técnica cirúrgica mais frequente. Efectuou-se o diagnóstico de metastização óssea em 10 doentes (12%), sendo que a taxa de sobrevivência global foi de 68,7% (57 doentes), em quatro anos. Dez doentes (12%) morreram por progressão da doença ou persistência tumoral Em 42 doentes (50,6%) não se verificaram evidência ou progressão de doença e três doentes (3,6%) apresentaram melhoria clínica. Conclusões:O “Flash Mamário” é uma modalidade de tratamento segura, relativamente aos efeitos secundários, e opção terapêutica válida para doentes idosos ou com baixo Performance Status, com o diagnóstico de carcinoma localmente avançado ou estádio IIb ou IV, a título neoadjuvante ou paliativo. Há menor risco de recidiva/progressão, nos doentes com melhor estado geral, sendo a taxa de sobrevivência global maior.

  13. A Multiserver Biometric Authentication Scheme for TMIS using Elliptic Curve Cryptography.

    PubMed

    Chaudhry, Shehzad Ashraf; Khan, Muhammad Tawab; Khan, Muhammad Khurram; Shon, Taeshik

    2016-11-01

    Recently several authentication schemes are proposed for telecare medicine information system (TMIS). Many of such schemes are proved to have weaknesses against known attacks. Furthermore, numerous such schemes cannot be used in real time scenarios. Because they assume a single server for authentication across the globe. Very recently, Amin et al. (J. Med. Syst. 39(11):180, 2015) designed an authentication scheme for secure communication between a patient and a medical practitioner using a trusted central medical server. They claimed their scheme to extend all security requirements and emphasized the efficiency of their scheme. However, the analysis in this article proves that the scheme designed by Amin et al. is vulnerable to stolen smart card and stolen verifier attacks. Furthermore, their scheme is having scalability issues along with inefficient password change and password recovery phases. Then we propose an improved scheme. The proposed scheme is more practical, secure and lightweight than Amin et al.'s scheme. The security of proposed scheme is proved using the popular automated tool ProVerif.

  14. On large time step TVD scheme for hyperbolic conservation laws and its efficiency evaluation

    NASA Astrophysics Data System (ADS)

    Qian, ZhanSen; Lee, Chun-Hian

    2012-08-01

    A large time step (LTS) TVD scheme originally proposed by Harten is modified and further developed in the present paper and applied to Euler equations in multidimensional problems. By firstly revealing the drawbacks of Harten's original LTS TVD scheme, and reasoning the occurrence of the spurious oscillations, a modified formulation of its characteristic transformation is proposed and a high resolution, strongly robust LTS TVD scheme is formulated. The modified scheme is proven to be capable of taking larger number of time steps than the original one. Following the modified strategy, the LTS TVD schemes for Yee's upwind TVD scheme and Yee-Roe-Davis's symmetric TVD scheme are constructed. The family of the LTS schemes is then extended to multidimensional by time splitting procedure, and the associated boundary condition treatment suitable for the LTS scheme is also imposed. The numerical experiments on Sod's shock tube problem, inviscid flows over NACA0012 airfoil and ONERA M6 wing are performed to validate the developed schemes. Computational efficiencies for the respective schemes under different CFL numbers are also evaluated and compared. The results reveal that the improvement is sizable as compared to the respective single time step schemes, especially for the CFL number ranging from 1.0 to 4.0.

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

    SciTech Connect

    Liu, Fang; Lin, Lin; Vigil-Fowler, Derek; Lischner, Johannes; Kemper, Alexander F.; Sharifzadeh, Sahar; Jornada, Felipe H. da; Deslippe, Jack; Yang, Chao; and others

    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.

  16. Extension of Low Dissipative High Order Hydrodynamics Schemes for MHD Equations

    NASA Technical Reports Server (NTRS)

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

    2002-01-01

    The objective of this paper is to extend our recently developed highly parallelizable nonlinear stable high order schemes for complex multiscale hydrodynamic applications to the viscous MHD (magnetohydrodynamic) equations. These schemes employed multiresolution wavelets as adaptive numerical dissipation controls to limit the amount and to aid the selection and/or blending of the appropriate types of dissipation to be used. The new scheme is formulated for both the conservative and non-conservative form of the MHD equations in curvi-linear grids. The three features of the present MHD scheme over existing schemes in the open literature are as follows. First, the scheme is constructed for long-time integrations of shock/turbulence/combustion magnetized flows. Available schemes are too diffusive for long-time integrations and/or turbulence/combustion problems. Second, unlike existing schemes for the conservative MHD equations which suffer from ill-conditioned eigen-decompositions, the present scheme makes use of a well-conditioned eigen-decomposition to solve the conservative form of the MHD equations. This is due to, partly. the fact that the divergence of the magnetic field condition is a different type of constraint from its incompressible Navier-Stokes cousin. Third, a new approach to minimize the numerical error of the divergence free magnetic condition for high order scheme is introduced.

  17. Residual Distribution Schemes for Conservation Laws Via Adaptive Quadrature

    NASA Technical Reports Server (NTRS)

    Barth, Timothy; Abgrall, Remi; Biegel, Bryan (Technical Monitor)

    2000-01-01

    This paper considers a family of nonconservative numerical discretizations for conservation laws which retains the correct weak solution behavior in the limit of mesh refinement whenever sufficient order numerical quadrature is used. Our analysis of 2-D discretizations in nonconservative form follows the 1-D analysis of Hou and Le Floch. For a specific family of nonconservative discretizations, it is shown under mild assumptions that the error arising from non-conservation is strictly smaller than the discretization error in the scheme. In the limit of mesh refinement under the same assumptions, solutions are shown to satisfy an entropy inequality. Using results from this analysis, a variant of the "N" (Narrow) residual distribution scheme of van der Weide and Deconinck is developed for first-order systems of conservation laws. The modified form of the N-scheme supplants the usual exact single-state mean-value linearization of flux divergence, typically used for the Euler equations of gasdynamics, by an equivalent integral form on simplex interiors. This integral form is then numerically approximated using an adaptive quadrature procedure. This renders the scheme nonconservative in the sense described earlier so that correct weak solutions are still obtained in the limit of mesh refinement. Consequently, we then show that the modified form of the N-scheme can be easily applied to general (non-simplicial) element shapes and general systems of first-order conservation laws equipped with an entropy inequality where exact mean-value linearization of the flux divergence is not readily obtained, e.g. magnetohydrodynamics, the Euler equations with certain forms of chemistry, etc. Numerical examples of subsonic, transonic and supersonic flows containing discontinuities together with multi-level mesh refinement are provided to verify the analysis.

  18. Advances in Solar Power Forecasting

    NASA Astrophysics Data System (ADS)

    Haupt, S. E.; Kosovic, B.; Drobot, S.

    2014-12-01

    The National Center for Atmospheric Research and partners are building a blended SunCast Solar Power Forecasting system. This system includes several short-range nowcasting models and improves upon longer range numerical weather prediction (NWP) models as part of the "Public-Private-Academic Partnership to Advance Solar Power Forecasting." The nowcasting models being built include statistical learning models that include cloud regime prediction, multiple sky imager-based advection models, satellite image-based advection models, and rapid update NWP models with cloud assimilation. The team has also integrated new modules into the Weather Research and Forecasting Model (WRF) to better predict clouds, aerosols, and irradiance. The modules include a new shallow convection scheme; upgraded physics parameterizations of clouds; new radiative transfer modules that specify GHI, DNI, and DIF prediction; better satellite assimilation methods; and new aerosol estimation methods. These new physical models are incorporated into WRF-Solar, which is then integrated with publically available NWP models via the Dynamic Integrated Forecast (DICast) system as well as the Nowcast Blender to provide seamless forecasts at partner utility and balancing authority commercial solar farms. The improvements will be described and results to date discussed.

  19. Fourier analysis of finite element preconditioned collocation schemes

    NASA Technical Reports Server (NTRS)

    Deville, Michel O.; Mund, Ernest H.

    1990-01-01

    The spectrum of the iteration operator of some finite element preconditioned Fourier collocation schemes is investigated. The first part of the paper analyses one-dimensional elliptic and hyperbolic model problems and the advection-diffusion equation. Analytical expressions of the eigenvalues are obtained with use of symbolic computation. The second part of the paper considers the set of one-dimensional differential equations resulting from Fourier analysis (in the tranverse direction) of the 2-D Stokes problem. All results agree with previous conclusions on the numerical efficiency of finite element preconditioning schemes.

  20. On the application and extension of Harten's high resolution scheme

    NASA Technical Reports Server (NTRS)

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

    1982-01-01

    Extensions of a second order high resolution explicit method for the numerical computation of weak solutions of one dimensonal hyperbolic conservation laws are discussed. The main objectives were (1) to examine the shock resoluton of Harten's method for a two dimensional shock reflection problem, (2) to study the use of a high resolution scheme as a post-processor to an approximate steady state solution, and (3) to construct an implicit in the delta-form using Harten's scheme for the explicit operator and a simplified iteration matrix for the implicit operator.

  1. Crab Crossing Schemes and Studies for Electron Ion Collider

    SciTech Connect

    S. Ahmed, Y. Derbenev, V. Morozov, A. Castilla, G.A. Krafft, B. Yunn, Y. Zhang, J.R. Delayen

    2011-09-01

    This report shows our progress in crab crossing consideration for future electron-ion collider envisioned at JLab. In this design phase, we are evaluating two crabbing schemes viz., the deflecting and dispersive. The mathematical formulations and lattice design for these schemes are discussed in this paper. Numerical simulations involving particle tracking through a realistic deflecting RF cavity and optics illustrate the desired crab tilt of 25 mrad for 1.35 MV. Evolution of beam propagation are shown which provides the physical insight of the crabbing phenomenon.

  2. Iterative schemes for nonsymmetric and indefinite elliptic boundary value problems

    SciTech Connect

    Bramble, J.H.; Leyk, Z.; Pasciak, J.E.

    1993-01-01

    The purpose of this paper is twofold. The first is to describe some simple and robust iterative schemes for nonsymmetric and indefinite elliptic boundary value problems. The schemes are based in the Sobolev space H ([Omega]) and require minimal hypotheses. The second is to develop algorithms utilizing a coarse-grid approximation. This leads to iteration matrices whose eigenvalues lie in the right half of the complex plane. In fact, for symmetric indefinite problems, the iteration is reduced to a well-conditioned symmetric positive definite system which can be solved by conjugate gradient interation. Applications of the general theory as well as numerical examples are given. 20 refs., 8 tabs.

  3. A second order derivative scheme based on Bregman algorithm class

    NASA Astrophysics Data System (ADS)

    Campagna, Rosanna; Crisci, Serena; Cuomo, Salvatore; Galletti, Ardelio; Marcellino, Livia

    2016-10-01

    The algorithms based on the Bregman iterative regularization are known for efficiently solving convex constraint optimization problems. In this paper, we introduce a second order derivative scheme for the class of Bregman algorithms. Its properties of convergence and stability are investigated by means of numerical evidences. Moreover, we apply the proposed scheme to an isotropic Total Variation (TV) problem arising out of the Magnetic Resonance Image (MRI) denoising. Experimental results confirm that our algorithm has good performance in terms of denoising quality, effectiveness and robustness.

  4. 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.

  5. A review of thrust-vectoring schemes for fighter applications

    NASA Technical Reports Server (NTRS)

    Berrier, B. L.; Re, R. J.

    1978-01-01

    This paper presents a review of thrust vectoring schemes for advanced fighter applications. Results are presented from wind tunnel and system integration studies on thrust vectoring nozzle concepts. Vectoring data are presented from wind tunnel tests of axisymmetric C-D (convergent-divergent) and nonaxisymmetric wedge, C-D, single ramp and USB (upper-surface blowing) nozzle concepts. Results from recent airframe/nozzle integration studies on the impact of thrust vectoring on weight, cooling and performance characteristics are discussed. This review indicates that the aircraft designer has, at his disposal, a wide range of thrust vectoring schemes which offer potential for added or improved aircraft capability.

  6. A low-order coupled chemistry meteorology model for testing online and offline data assimilation schemes: L95-GRS (v1.0)

    NASA Astrophysics Data System (ADS)

    Haussaire, J.-M.; Bocquet, M.

    2016-01-01

    Bocquet and Sakov (2013) introduced a low-order model based on the coupling of the chaotic Lorenz-95 (L95) model, which simulates winds along a mid-latitude circle, with the transport of a tracer species advected by this zonal wind field. This model, named L95-T, can serve as a playground for testing data assimilation schemes with an online model. Here, the tracer part of the model is extended to a reduced photochemistry module. This coupled chemistry meteorology model (CCMM), the L95-GRS (generic reaction set) model, mimics continental and transcontinental transport and the photochemistry of ozone, volatile organic compounds and nitrogen oxides. Its numerical implementation is described. The model is shown to reproduce the major physical and chemical processes being considered. L95-T and L95-GRS are specifically designed and useful for testing advanced data assimilation schemes, such as the iterative ensemble Kalman smoother (IEnKS), which combines the best of ensemble and variational methods. These models provide useful insights prior to the implementation of data assimilation methods into larger models. We illustrate their use with data assimilation schemes on preliminary yet instructive numerical experiments. In particular, online and offline data assimilation strategies can be conveniently tested and discussed with this low-order CCMM. The impact of observed chemical species concentrations on the wind field estimate can be quantitatively assessed. The impacts of the wind chaotic dynamics and of the chemical species non-chaotic but highly nonlinear dynamics on the data assimilation strategies are illustrated.

  7. Control Scheme of Tether Drag Deorbit System in Orbital Plane

    NASA Astrophysics Data System (ADS)

    Cui, Wei-Dong; Sun, Liang; Zhao, Guo-Wei

    In this paper, based on a dumbbell model of tethered satellite, a tension control scheme and a thrust control scheme of tether drag deorbit system in orbital plane are respectively proposed. In the tension control scheme, the tether tension can be measured by tension sensor and controlled by adjusting the tether length with a certain windlass mechanism, so that the librational angles could track the expected value; meanwhile, the tether could come back to the initial value. Because of the windlass mechanism, the slackness of tether can be avoided. In the thrust control scheme, the tether drag deorbit system is with a short tether in orbital maneuvering and the thrust acceleration imposed on the base satellite can be adjusted to avoid the slackness of tether and damp out the librational angles; besides, it is required that the regulation value of thrust acceleration meets with accuracy trajectory in practical engineering. Afterwards, a reasonable deorbit case of an abandoned GEO satellite is studied, in which the control of base satellite is considered; then, the advantages and disadvantages of two control schemes are analyzed and an improved control strategy is given. Numerical simulation results indicate that the slackness of tether can be eliminated and the librational angles are damped out according to the designed controllers, and the stability of the attitude of abandoned satellite is also guaranteed during flight. The proposed control schemes are feasible, which is useful for the flight safety.

  8. A Study of Failure Events in Drinking Water Systems As a Basis for Comparison and Evaluation of the Efficacy of Potable Reuse Schemes

    PubMed Central

    Onyango, Laura A.; Quinn, Chloe; Tng, Keng H.; Wood, James G.; Leslie, Greg

    2015-01-01

    Potable reuse is implemented in several countries around the world to augment strained water supplies. This article presents a public health perspective on potable reuse by comparing the critical infrastructure and institutional capacity characteristics of two well-established potable reuse schemes with conventional drinking water schemes in developed nations that have experienced waterborne outbreaks. Analysis of failure events in conventional water systems between 2003 and 2013 showed that despite advances in water treatment technologies, drinking water outbreaks caused by microbial contamination were still frequent in developed countries and can be attributed to failures in infrastructure or institutional practices. Numerous institutional failures linked to ineffective treatment protocols, poor operational practices, and negligence were detected. In contrast, potable reuse schemes that use multiple barriers, online instrumentation, and operational measures were found to address the events that have resulted in waterborne outbreaks in conventional systems in the past decade. Syndromic surveillance has emerged as a tool in outbreak detection and was useful in detecting some outbreaks; increases in emergency department visits and GP consultations being the most common data source, suggesting potential for an increasing role in public health surveillance of waterborne outbreaks. These results highlight desirable characteristics of potable reuse schemes from a public health perspective with potential for guiding policy on surveillance activities. PMID:27053920

  9. The representation of numerical magnitude

    PubMed Central

    Brannon, Elizabeth M

    2006-01-01

    The combined efforts of many fields are advancing our understanding of how number is represented. Researchers studying numerical reasoning in adult humans, developing humans and non-human animals are using a suite of behavioral and neurobiological methods to uncover similarities and differences in how each population enumerates and compares quantities to identify the neural substrates of numerical cognition. An important picture emerging from this research is that adult humans share with non-human animals a system for representing number as language-independent mental magnitudes and that this system emerges early in development. PMID:16546373

  10. Numerical Considerations for Lagrangian Stochastic Dispersion Models: Eliminating Rogue Trajectories, and the Importance of Numerical Accuracy

    NASA Astrophysics Data System (ADS)

    Bailey, Brian N.

    2017-01-01

    When Lagrangian stochastic models for turbulent dispersion are applied to complex atmospheric flows, some type of ad hoc intervention is almost always necessary to eliminate unphysical behaviour in the numerical solution. Here we discuss numerical strategies for solving the non-linear Langevin-based particle velocity evolution equation that eliminate such unphysical behaviour in both Reynolds-averaged and large-eddy simulation applications. Extremely large or `rogue' particle velocities are caused when the numerical integration scheme becomes unstable. Such instabilities can be eliminated by using a sufficiently small integration timestep, or in cases where the required timestep is unrealistically small, an unconditionally stable implicit integration scheme can be used. When the generalized anisotropic turbulence model is used, it is critical that the input velocity covariance tensor be realizable, otherwise unphysical behaviour can become problematic regardless of the integration scheme or size of the timestep. A method is presented to ensure realizability, and thus eliminate such behaviour. It was also found that the numerical accuracy of the integration scheme determined the degree to which the second law of thermodynamics or `well-mixed condition' was satisfied. Perhaps more importantly, it also determined the degree to which modelled Eulerian particle velocity statistics matched the specified Eulerian distributions (which is the ultimate goal of the numerical solution). It is recommended that future models be verified by not only checking the well-mixed condition, but perhaps more importantly by checking that computed Eulerian statistics match the Eulerian statistics specified as inputs.

  11. An operational phenological model for numerical pollen prediction

    NASA Astrophysics Data System (ADS)

    Scheifinger, Helfried

    2010-05-01

    The general prevalence of seasonal allergic rhinitis is estimated to be about 15% in Europe, and still increasing. Pre-emptive measures require both the reliable assessment of production and release of various pollen species and the forecasting of their atmospheric dispersion. For this purpose numerical pollen prediction schemes are being developed by a number of European weather services in order to supplement and improve the qualitative pollen prediction systems by state of the art instruments. Pollen emission is spatially and temporally highly variable throughout the vegetation period and not directly observed, which precludes a straightforward application of dispersion models to simulate pollen transport. Even the beginning and end of flowering, which indicates the time period of potential pollen emission, is not (yet) available in real time. One way to create a proxy for the beginning, the course and the end of the pollen emission is its simulation as function of real time temperature observations. In this work the European phenological data set of the COST725 initiative forms the basis of modelling the beginning of flowering of 15 species, some of which emit allergic pollen. In order to keep the problem as simple as possible for the sake of spatial interpolation, a 3 parameter temperature sum model was implemented in a real time operational procedure, which calculates the spatial distribution of the entry dates for the current day and 24, 48 and 72 hours in advance. As stand alone phenological model and combined with back trajectories it is thought to support the qualitative pollen prediction scheme at the Austrian national weather service. Apart from that it is planned to incorporate it in a numerical pollen dispersion model. More details, open questions and first results of the operation phenological model will be discussed and presented.

  12. Numerical Modelling of Electrical Discharges

    NASA Astrophysics Data System (ADS)

    Durán-Olivencia, F. J.; Pontiga, F.; Castellanos, A.

    2014-03-01

    The problem of the propagation of an electrical discharge between a spherical electrode and a plane has been solved by means of finite element methods (FEM) using a fluid approximation and assuming weak ionization and local equilibrium with the electric field. The numerical simulation of this type of problems presents the usual difficulties of convection-diffusion-reaction problems, in addition to those associated with the nonlinearities of the charged species velocities, the formation of steep gradients of the electric field and particle densities, and the coexistence of very different temporal scales. The effect of using different temporal discretizations for the numerical integration of the corresponding system of partial differential equations will be here investigated. In particular, the so-called θ-methods will be used, which allows to implement implicit, semi-explicit and fully explicit schemes in a simple way.

  13. A conservative difference scheme for solving the strongly coupled nonlinear fractional Schrödinger equations

    NASA Astrophysics Data System (ADS)

    Ran, Maohua; Zhang, Chengjian

    2016-12-01

    This paper focuses on numerically solving the strongly coupled nonlinear space fractional Schrödinger equations. First, the laws of conservation of mass and energy are given. Then, an implicit difference scheme is proposed, under the assumption that the analytical solution decays to zero when the space variable x tends to infinity. We show that the scheme conserves the mass and energy and is unconditionally stable with respect to the initial values. Moreover, the solvability, boundedness and convergence in the maximum norm are established. To avoid solving nonlinear systems, a linear difference scheme with two identities is proposed. Several numerical experiments are provided to confirm the theoretical results.

  14. A Computational Scheme for a Problem in the Zero-coupon Bond Pricing

    NASA Astrophysics Data System (ADS)

    Chernogorova, T.; Valkov, R.

    2010-11-01

    In this paper we derive a finite volume difference scheme for a degenerate parabolic equation with dynamical boundary conditions of zero-coupon bond pricing. We show that the system matrix of the discretization scheme is an M-matrix, so that the discretization is monotone. This provides the non-negativity of the price whit respect to time if the initial distribution is nonnegative. Then one can prove convergence of the numerical solution with rate of convergence O(h), where h denotes the mesh parameter [2]. Several numerical experiments show higher accuracy with comparison of known difference schemes near the boundary (degeneration).

  15. New parallelizable schemes for integrating the Dissipative Particle Dynamics with Energy conservation.

    PubMed

    Homman, Ahmed-Amine; Maillet, Jean-Bernard; Roussel, Julien; Stoltz, Gabriel

    2016-01-14

    This work presents new parallelizable numerical schemes for the integration of dissipative particle dynamics with energy conservation. So far, no numerical scheme introduced in the literature is able to correctly preserve the energy over long times and give rise to small errors on average properties for moderately small time steps, while being straightforwardly parallelizable. We present in this article two new methods, both straightforwardly parallelizable, allowing to correctly preserve the total energy of the system. We illustrate the accuracy and performance of these new schemes both on equilibrium and nonequilibrium parallel simulations.

  16. New scheme for braiding Majorana fermions

    PubMed Central

    Wu, Long-Hua; Liang, Qi-Feng; Hu, Xiao

    2014-01-01

    Non-Abelian statistics can be achieved by exchanging two vortices in topological superconductors with each grabbing a Majorana fermion (MF) as zero-energy quasi-particle at the cores. However, in experiments it is difficult to manipulate vortices. In the present work, we propose a way to braid MFs without moving vortices. The only operation required in the present scheme is to turn on and off local gate voltages, which liberates a MF from its original host vortex and transports it along the prepared track. We solve the time-dependent Bogoliubov–de Gennes equation numerically, and confirm that the MFs are protected provided the switching of gate voltages for exchanging MFs are adiabatic, which takes only several nano seconds given reasonable material parameters. By monitoring the time evolution of MF wave-functions, we show that non-Abelian statistics is achieved. PMID:27877725

  17. The upgraded scheme of Hefei Light Source

    SciTech Connect

    Li Weimin; Xu Hongliang; Wang Lin; Feng Guangyao; Zhang Shancai; Hao Hao

    2010-06-23

    To enhance the performance of Hefei Light Source, which was designed and constructed two decades ago, an upgrade project would be carried out in the near future. The detail upgrade scheme was described in this paper. Firstly, the magnet lattice of storage ring should be reconstructed with 4 DBA cells, whose advantages are lower beam emittance and more straight section available for insertion devices. Secondly, the beam diagnostics, main power supply, transverse and longitudinal multi-bunch feedback, beam control and manipulation system would be upgrade to improve the beam orbit stability. Finally, the injection system of storage ring and injector, which is composed of electron linac and beam transfer line, would be updated in order to assure smooth beam accumulation process under new low emittance lattice. With above improvement, it is hopeful to increase the brilliance of Hefei Light Source by two orders approximately. After three-year upgrade project, the performance of HLS would meet the demands of advanced SR users.

  18. Evaluation of a vibration source detection scheme

    SciTech Connect

    Jendrzejczyk, J.A.; Wambsganss, M.W.; Smith, R.K.

    1992-04-01

    When the Advanced Photon Source (APS) facility is commissioned, there will be many potential sources of local ground motion excitation (near-field sources). Some of these may be of sufficient amplitude and at a specific frequency so as to be detrimental to the stability of the storage ring beamline. A sampling of possible sources is as follows: 2500-hp chillers in the utility building; six cooling-tower fans that are powered by 75-hp electric motors; various water circulation pumps; power supplies, controllers, and transformers; and air-handling units and associated fans. To detect equipment that causes excessive ground excitation at a site as large as the APS, it will be necessary to have a validated source detection scheme. When performing low-amplitude vibration testing in and around Building 335 of Argonne National Laboratory (ANL), we observed a cyclic 8-Hz vibration. The cyclic nature of the signal is apparent in Fig. 1, which represents data measured on the floor at the main level of Building 335 on March 31, 1992. A simple vibration source location scheme, based on triangulation, was evaluated as a means to locate the source of the 8-Hz vibration and is the subject of this technical note. 1 ref.

  19. Optimal probabilistic dense coding schemes

    NASA Astrophysics Data System (ADS)

    Kögler, Roger A.; Neves, Leonardo

    2017-04-01

    Dense coding with non-maximally entangled states has been investigated in many different scenarios. We revisit this problem for protocols adopting the standard encoding scheme. In this case, the set of possible classical messages cannot be perfectly distinguished due to the non-orthogonality of the quantum states carrying them. So far, the decoding process has been approached in two ways: (i) The message is always inferred, but with an associated (minimum) error; (ii) the message is inferred without error, but only sometimes; in case of failure, nothing else is done. Here, we generalize on these approaches and propose novel optimal probabilistic decoding schemes. The first uses quantum-state separation to increase the distinguishability of the messages with an optimal success probability. This scheme is shown to include (i) and (ii) as special cases and continuously interpolate between them, which enables the decoder to trade-off between the level of confidence desired to identify the received messages and the success probability for doing so. The second scheme, called multistage decoding, applies only for qudits ( d-level quantum systems with d>2) and consists of further attempts in the state identification process in case of failure in the first one. We show that this scheme is advantageous over (ii) as it increases the mutual information between the sender and receiver.

  20. Nonlinear Secret Image Sharing Scheme

    PubMed Central

    Shin, Sang-Ho; Yoo, Kee-Young

    2014-01-01

    Over the past decade, most of secret image sharing schemes have been proposed by using Shamir's technique. It is based on a linear combination polynomial arithmetic. Although Shamir's technique based secret image sharing schemes are efficient and scalable for various environments, there exists a security threat such as Tompa-Woll attack. Renvall and Ding proposed a new secret sharing technique based on nonlinear combination polynomial arithmetic in order to solve this threat. It is hard to apply to the secret image sharing. In this paper, we propose a (t, n)-threshold nonlinear secret image sharing scheme with steganography concept. In order to achieve a suitable and secure secret image sharing scheme, we adapt a modified LSB embedding technique with XOR Boolean algebra operation, define a new variable m, and change a range of prime p in sharing procedure. In order to evaluate efficiency and security of proposed scheme, we use the embedding capacity and PSNR. As a result of it, average value of PSNR and embedding capacity are 44.78 (dB) and 1.74t⌈log2⁡m⌉ bit-per-pixel (bpp), respectively. PMID:25140334