Journal of Computational Physics, ISSN 0021-9991, 05/2016, Volume 313, pp. 726 - 753

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...

WENO schemes | Hyperbolic conservation laws | High resolution shock capturing schemes | Smoothness indicators | High-order methods | EFFICIENT IMPLEMENTATION | SMOOTHNESS INDICATOR | ESSENTIALLY NONOSCILLATORY SCHEMES | SIMULATION | PHYSICS, MATHEMATICAL | FLOW | ACCURACY | COMPUTER SCIENCE, INTERDISCIPLINARY APPLICATIONS | HYPERBOLIC CONSERVATION-LAWS | Discontinuity | Accuracy | Computation | Dissipation | Mathematical models | Critical point | Smoothness | Numerical stability

WENO schemes | Hyperbolic conservation laws | High resolution shock capturing schemes | Smoothness indicators | High-order methods | EFFICIENT IMPLEMENTATION | SMOOTHNESS INDICATOR | ESSENTIALLY NONOSCILLATORY SCHEMES | SIMULATION | PHYSICS, MATHEMATICAL | FLOW | ACCURACY | COMPUTER SCIENCE, INTERDISCIPLINARY APPLICATIONS | HYPERBOLIC CONSERVATION-LAWS | Discontinuity | Accuracy | Computation | Dissipation | Mathematical models | Critical point | Smoothness | Numerical stability

Journal Article

Journal of Computational Physics, ISSN 0021-9991, 12/2017, Volume 350, pp. 1 - 15

In this paper, a finite difference scheme is proposed to solve time–space fractional diffusion equation which has second-order accuracy in both time and space...

Trapezoidal rule | Riesz derivative | Fractional diffusion equation | Caputo derivative | NUMERICAL-METHODS | FINITE-DIFFERENCE SCHEMES | SUBDIFFUSION EQUATION | ALGORITHMS | HIGH-ORDER APPROXIMATION | PHYSICS, MATHEMATICAL | CAPUTO DERIVATIVES | SPECTRAL METHOD | DIMENSIONS | COMPUTER SCIENCE, INTERDISCIPLINARY APPLICATIONS | MODELS | COMPACT ADI SCHEME | Analysis | Numerical analysis | Differential equations

Trapezoidal rule | Riesz derivative | Fractional diffusion equation | Caputo derivative | NUMERICAL-METHODS | FINITE-DIFFERENCE SCHEMES | SUBDIFFUSION EQUATION | ALGORITHMS | HIGH-ORDER APPROXIMATION | PHYSICS, MATHEMATICAL | CAPUTO DERIVATIVES | SPECTRAL METHOD | DIMENSIONS | COMPUTER SCIENCE, INTERDISCIPLINARY APPLICATIONS | MODELS | COMPACT ADI SCHEME | Analysis | Numerical analysis | Differential equations

Journal Article

Journal of Computational Physics, ISSN 0021-9991, 10/2014, Volume 274, pp. 95 - 121

We develop a shock- and interface-capturing numerical method that is suitable for the simulation of multicomponent flows governed by the compressible...

Viscous | Shock-capturing | HLLC | Interface-capturing | Multicomponent flows | WENO | INTERFACE PROBLEMS | ESSENTIALLY NONOSCILLATORY SCHEMES | INDUCED COLLAPSE | HIGH-ORDER | PHYSICS, MATHEMATICAL | GHOST FLUID METHOD | RUNGE-KUTTA SCHEMES | COMPUTER SCIENCE, INTERDISCIPLINARY APPLICATIONS | MIXTURE TYPE ALGORITHM | SHOCK-WAVE LITHOTRIPSY | CAPTURING SCHEMES | MULTIMATERIAL FLOWS | Algorithms | Construction | Numerical analysis | Compressibility | Mathematical analysis | Mathematical models | Three dimensional | Navier-Stokes equations | shock-capturing | viscous | multicomponent flows | interface-capturing

Viscous | Shock-capturing | HLLC | Interface-capturing | Multicomponent flows | WENO | INTERFACE PROBLEMS | ESSENTIALLY NONOSCILLATORY SCHEMES | INDUCED COLLAPSE | HIGH-ORDER | PHYSICS, MATHEMATICAL | GHOST FLUID METHOD | RUNGE-KUTTA SCHEMES | COMPUTER SCIENCE, INTERDISCIPLINARY APPLICATIONS | MIXTURE TYPE ALGORITHM | SHOCK-WAVE LITHOTRIPSY | CAPTURING SCHEMES | MULTIMATERIAL FLOWS | Algorithms | Construction | Numerical analysis | Compressibility | Mathematical analysis | Mathematical models | Three dimensional | Navier-Stokes equations | shock-capturing | viscous | multicomponent flows | interface-capturing

Journal Article

Journal of Computational Physics, ISSN 0021-9991, 08/2018, Volume 366, pp. 120 - 143

For constructing high order accurate positivity-preserving schemes for convection–diffusion equations, we construct a simple positivity-preserving diffusion...

Positivity-preserving | Drift–diffusion | Discontinuous Galerkin finite element method | Convection–diffusion equations | High order accuracy | Glow discharge | TRIANGULAR MESHES | ACCURATE | Drift-diffusion | Convection-diffusion equations | PHYSICS, MATHEMATICAL | DISCHARGES | COMPUTER SCIENCE, INTERDISCIPLINARY APPLICATIONS | NAVIER-STOKES EQUATIONS | FINITE-ELEMENT-METHOD | EULER

Positivity-preserving | Drift–diffusion | Discontinuous Galerkin finite element method | Convection–diffusion equations | High order accuracy | Glow discharge | TRIANGULAR MESHES | ACCURATE | Drift-diffusion | Convection-diffusion equations | PHYSICS, MATHEMATICAL | DISCHARGES | COMPUTER SCIENCE, INTERDISCIPLINARY APPLICATIONS | NAVIER-STOKES EQUATIONS | FINITE-ELEMENT-METHOD | EULER

Journal Article

Journal of Computational Physics, ISSN 0021-9991, 11/2014, Volume 276, Issue C, pp. 613 - 634

For modeling scalar-wave propagation in geophysical problems using finite-difference schemes, optimizing the coefficients of the finite-difference operators...

Numerical modeling | Dispersion error | Optimized scheme | Wave propagation | Finite-difference stencil | Scalar wave | Finite-difference scheme | VELOCITY | COMPUTATIONAL ACOUSTICS | HETEROGENEOUS MEDIA | HIGH-ORDER | SIMULATION | PHYSICS, MATHEMATICAL | ACCURACY | COMPUTER SCIENCE, INTERDISCIPLINARY APPLICATIONS | PERFECTLY MATCHED LAYER | 4TH-ORDER | EQUATION | ABSORBING BOUNDARY-CONDITIONS | Models | Analysis | Geophysics | Errors | Accuracy | Mathematical analysis | Mathematical models | Dispersions | Standards | Finite difference method

Numerical modeling | Dispersion error | Optimized scheme | Wave propagation | Finite-difference stencil | Scalar wave | Finite-difference scheme | VELOCITY | COMPUTATIONAL ACOUSTICS | HETEROGENEOUS MEDIA | HIGH-ORDER | SIMULATION | PHYSICS, MATHEMATICAL | ACCURACY | COMPUTER SCIENCE, INTERDISCIPLINARY APPLICATIONS | PERFECTLY MATCHED LAYER | 4TH-ORDER | EQUATION | ABSORBING BOUNDARY-CONDITIONS | Models | Analysis | Geophysics | Errors | Accuracy | Mathematical analysis | Mathematical models | Dispersions | Standards | Finite difference method

Journal Article

International Journal for Numerical Methods in Fluids, ISSN 0271-2091, 07/2018, Volume 87, Issue 7, pp. 329 - 342

Summary A new third‐order WENO scheme is proposed to achieve the desired order of convergence at the critical points for scalar hyperbolic equations. A new...

finite‐difference WENO | nonlinear weights | hyperbolic conservation laws | smoothness indicators | Euler equations | consistency | discontinuity | finite-difference WENO | WENO SCHEME | EFFICIENT IMPLEMENTATION | FINITE-DIFFERENCE SCHEMES | PHYSICS, FLUIDS & PLASMAS | SMOOTHNESS INDICATOR | HIGH-ORDER | SIMULATION | FLOW | ACCURACY | SHOCK-CAPTURING SCHEMES | COMPUTER SCIENCE, INTERDISCIPLINARY APPLICATIONS | MATHEMATICS, INTERDISCIPLINARY APPLICATIONS | MECHANICS | HYPERBOLIC CONSERVATION-LAWS | Economic models | Error analysis | Solutions | Comparative studies | Mathematical models | Smoothness | Equations | Convergence

finite‐difference WENO | nonlinear weights | hyperbolic conservation laws | smoothness indicators | Euler equations | consistency | discontinuity | finite-difference WENO | WENO SCHEME | EFFICIENT IMPLEMENTATION | FINITE-DIFFERENCE SCHEMES | PHYSICS, FLUIDS & PLASMAS | SMOOTHNESS INDICATOR | HIGH-ORDER | SIMULATION | FLOW | ACCURACY | SHOCK-CAPTURING SCHEMES | COMPUTER SCIENCE, INTERDISCIPLINARY APPLICATIONS | MATHEMATICS, INTERDISCIPLINARY APPLICATIONS | MECHANICS | HYPERBOLIC CONSERVATION-LAWS | Economic models | Error analysis | Solutions | Comparative studies | Mathematical models | Smoothness | Equations | Convergence

Journal Article

International Journal for Numerical Methods in Fluids, ISSN 0271-2091, 09/2017, Volume 85, Issue 2, pp. 90 - 112

Summary In this article, we have devised a new reference smoothness indicator for third‐order weighted essentially non‐oscillatory (WENO) scheme to achieve...

nonlinear weights | hyperbolic conservation laws | Euler equations | smoothness indicator | discontinuity | WENO | FINITE-DIFFERENCE SCHEMES | PHYSICS, FLUIDS & PLASMAS | ESSENTIALLY NONOSCILLATORY SCHEMES | DISCONTINUOUS GALERKIN METHOD | HIGH-ORDER | ACCURACY | COMPUTER SCIENCE, INTERDISCIPLINARY APPLICATIONS | MATHEMATICS, INTERDISCIPLINARY APPLICATIONS | MECHANICS | UNSTRUCTURED GRIDS | SYSTEMS | HYPERBOLIC CONSERVATION-LAWS | Economic models | Construction | Accuracy | Essentially non-oscillatory schemes | Indicators | Smoothness | Convergence

nonlinear weights | hyperbolic conservation laws | Euler equations | smoothness indicator | discontinuity | WENO | FINITE-DIFFERENCE SCHEMES | PHYSICS, FLUIDS & PLASMAS | ESSENTIALLY NONOSCILLATORY SCHEMES | DISCONTINUOUS GALERKIN METHOD | HIGH-ORDER | ACCURACY | COMPUTER SCIENCE, INTERDISCIPLINARY APPLICATIONS | MATHEMATICS, INTERDISCIPLINARY APPLICATIONS | MECHANICS | UNSTRUCTURED GRIDS | SYSTEMS | HYPERBOLIC CONSERVATION-LAWS | Economic models | Construction | Accuracy | Essentially non-oscillatory schemes | Indicators | Smoothness | Convergence

Journal Article

Journal of Computational Physics, ISSN 0021-9991, 07/2014, Volume 268, pp. 17 - 38

High-order finite difference methods are efficient, easy to program, scale well in multiple dimensions and can be modified locally for various reasons (such as...

Summation-by-Parts schemes | Simultaneous Approximation Terms | NONLINEAR CONSERVATION-LAWS | FINITE-DIFFERENCE SCHEMES | ORDER NUMERICAL-SIMULATION | ENTROPY-STABLE SCHEMES | SHARP SHOCK RESOLUTION | EFFICIENT SOLUTION STRATEGY | PHYSICS, MATHEMATICAL | CONJUGATE HEAT-TRANSFER | RUNGE-KUTTA SCHEMES | TIME-DEPENDENT PROBLEMS | COMPUTER SCIENCE, INTERDISCIPLINARY APPLICATIONS | NAVIER-STOKES EQUATIONS | Operators | Construction | Stability | Computation | Mathematical analysis | Boundary conditions | Boundaries | Finite difference method | Mathematics - Numerical Analysis | Naturvetenskap | Computational Mathematics | Mathematics | Well posed problems; Energy estimates; Finite difference; Finite volume; Boundary conditions; Interface conditions; Stability; High order of accuracy | Natural Sciences | Beräkningsmatematik | Matematik

Summation-by-Parts schemes | Simultaneous Approximation Terms | NONLINEAR CONSERVATION-LAWS | FINITE-DIFFERENCE SCHEMES | ORDER NUMERICAL-SIMULATION | ENTROPY-STABLE SCHEMES | SHARP SHOCK RESOLUTION | EFFICIENT SOLUTION STRATEGY | PHYSICS, MATHEMATICAL | CONJUGATE HEAT-TRANSFER | RUNGE-KUTTA SCHEMES | TIME-DEPENDENT PROBLEMS | COMPUTER SCIENCE, INTERDISCIPLINARY APPLICATIONS | NAVIER-STOKES EQUATIONS | Operators | Construction | Stability | Computation | Mathematical analysis | Boundary conditions | Boundaries | Finite difference method | Mathematics - Numerical Analysis | Naturvetenskap | Computational Mathematics | Mathematics | Well posed problems; Energy estimates; Finite difference; Finite volume; Boundary conditions; Interface conditions; Stability; High order of accuracy | Natural Sciences | Beräkningsmatematik | Matematik

Journal Article

Journal of Computational Physics, ISSN 0021-9991, 11/2017, Volume 348, pp. 514 - 533

A new second-order numerical scheme based on an operator splitting is proposed for the Godunov–Peshkov–Romenski model of continuum mechanics. The homogeneous...

GPR | Operator splitting | Godunov–Peshkov–Romenski | Continuum mechanics | ADER | WENO | EQUATIONS | HIGH-ORDER | PHYSICS, MATHEMATICAL | HYPERBOLIC FORMULATION | Godunov-Peshkov-Romenski | LAWS | COMPUTER SCIENCE, INTERDISCIPLINARY APPLICATIONS | ADER SCHEMES | SYSTEMS | FINITE-VOLUME SCHEMES

GPR | Operator splitting | Godunov–Peshkov–Romenski | Continuum mechanics | ADER | WENO | EQUATIONS | HIGH-ORDER | PHYSICS, MATHEMATICAL | HYPERBOLIC FORMULATION | Godunov-Peshkov-Romenski | LAWS | COMPUTER SCIENCE, INTERDISCIPLINARY APPLICATIONS | ADER SCHEMES | SYSTEMS | FINITE-VOLUME SCHEMES

Journal Article

International Journal for Numerical Methods in Fluids, ISSN 0271-2091, 10/2019, Volume 91, Issue 4, pp. 159 - 182

Summary Many efforts have been made to improve the accuracy of the conventional weighted essentially nonoscillatory (WENO) scheme at transition points...

critical point | low‐dissipation | transition point | high performance | multistep WENO scheme | low-dissipation | EFFICIENT IMPLEMENTATION | HYPERBOLIC SYSTEMS | PHYSICS, FLUIDS & PLASMAS | STRATEGY | ESSENTIALLY NONOSCILLATORY SCHEMES | HIGH-ORDER | ACCURACY | COMPUTER SCIENCE, INTERDISCIPLINARY APPLICATIONS | MATHEMATICS, INTERDISCIPLINARY APPLICATIONS | MECHANICS | NUMERICAL-SIMULATION | EULER | Accuracy | Theoretical analysis | Critical point | Transition points | Connecting

critical point | low‐dissipation | transition point | high performance | multistep WENO scheme | low-dissipation | EFFICIENT IMPLEMENTATION | HYPERBOLIC SYSTEMS | PHYSICS, FLUIDS & PLASMAS | STRATEGY | ESSENTIALLY NONOSCILLATORY SCHEMES | HIGH-ORDER | ACCURACY | COMPUTER SCIENCE, INTERDISCIPLINARY APPLICATIONS | MATHEMATICS, INTERDISCIPLINARY APPLICATIONS | MECHANICS | NUMERICAL-SIMULATION | EULER | Accuracy | Theoretical analysis | Critical point | Transition points | Connecting

Journal Article

Journal of Computational Physics, ISSN 0021-9991, 10/2014, Volume 274, pp. 268 - 282

In this paper, a high order finite difference scheme for a two dimensional fractional Klein–Gordon equation subject to Neumann boundary conditions is proposed....

Two dimensional fractional Klein–Gordon equation | Compact difference scheme | Stability | Convergence | Two dimensional fractional Klein-Gordon equation | VARIATIONAL ITERATION METHOD | COMPUTER SCIENCE, INTERDISCIPLINARY APPLICATIONS | SUBDIFFUSION | SUB-DIFFUSION EQUATION | WISE ERROR ESTIMATE | HIGH-ORDER | SINE-GORDON | PHYSICS, MATHEMATICAL | Mathematical analysis | Klein-Gordon equation | Nonlinearity | Boundary conditions | Two dimensional | Finite difference method

Two dimensional fractional Klein–Gordon equation | Compact difference scheme | Stability | Convergence | Two dimensional fractional Klein-Gordon equation | VARIATIONAL ITERATION METHOD | COMPUTER SCIENCE, INTERDISCIPLINARY APPLICATIONS | SUBDIFFUSION | SUB-DIFFUSION EQUATION | WISE ERROR ESTIMATE | HIGH-ORDER | SINE-GORDON | PHYSICS, MATHEMATICAL | Mathematical analysis | Klein-Gordon equation | Nonlinearity | Boundary conditions | Two dimensional | Finite difference method

Journal Article

Journal of Computational Physics, ISSN 0021-9991, 2010, Volume 229, Issue 23, pp. 8952 - 8965

In this work, an adaptive central-upwind 6th-order weighted essentially non-oscillatory (WENO) scheme is developed. The scheme adapts between central and...

Numerical method | Compressible flow | High-order scheme | WENO SCHEME | EFFICIENT IMPLEMENTATION | COMPRESSIBLE TURBULENCE | COMPUTER SCIENCE, INTERDISCIPLINARY APPLICATIONS | HIGH-ORDER | SHOCK-TURBULENCE INTERACTION | PHYSICS, MATHEMATICAL | HYPERBOLIC CONSERVATION-LAWS | NUMERICAL-SIMULATION | Aerodynamics | Questions and answers | Blending | Numerical dissipation | Essentially non-oscillatory schemes | Mathematical models | Indicators | Smoothness | Optimization | Preserving

Numerical method | Compressible flow | High-order scheme | WENO SCHEME | EFFICIENT IMPLEMENTATION | COMPRESSIBLE TURBULENCE | COMPUTER SCIENCE, INTERDISCIPLINARY APPLICATIONS | HIGH-ORDER | SHOCK-TURBULENCE INTERACTION | PHYSICS, MATHEMATICAL | HYPERBOLIC CONSERVATION-LAWS | NUMERICAL-SIMULATION | Aerodynamics | Questions and answers | Blending | Numerical dissipation | Essentially non-oscillatory schemes | Mathematical models | Indicators | Smoothness | Optimization | Preserving

Journal Article

Journal of Computational Physics, ISSN 0021-9991, 11/2018, Volume 372, pp. 446 - 472

In this paper, a fourth-order compact gas-kinetic scheme (GKS) is developed for the compressible Euler and Navier–Stokes equations under the framework of...

Two-stage fourth-order discretization | High-order evolution model | Hermite WENO reconstruction | Compact gas-kinetic scheme | HERMITE WENO SCHEMES | EFFICIENT IMPLEMENTATION | ESSENTIALLY NONOSCILLATORY SCHEMES | DISCONTINUOUS GALERKIN METHOD | PHYSICS, MATHEMATICAL | FINITE-VOLUME | SHOCK-CAPTURING SCHEMES | COMPUTER SCIENCE, INTERDISCIPLINARY APPLICATIONS | UNSTRUCTURED MESHES | HYPERBOLIC CONSERVATION-LAWS | NUMERICAL-SIMULATION | FLOW SIMULATION | Gas utilities | Analysis | Aerospace engineering

Two-stage fourth-order discretization | High-order evolution model | Hermite WENO reconstruction | Compact gas-kinetic scheme | HERMITE WENO SCHEMES | EFFICIENT IMPLEMENTATION | ESSENTIALLY NONOSCILLATORY SCHEMES | DISCONTINUOUS GALERKIN METHOD | PHYSICS, MATHEMATICAL | FINITE-VOLUME | SHOCK-CAPTURING SCHEMES | COMPUTER SCIENCE, INTERDISCIPLINARY APPLICATIONS | UNSTRUCTURED MESHES | HYPERBOLIC CONSERVATION-LAWS | NUMERICAL-SIMULATION | FLOW SIMULATION | Gas utilities | Analysis | Aerospace engineering

Journal Article

Journal of scientific computing, ISSN 0885-7474, 09/2017, Volume 72, Issue 3, pp. 957 - 985

In this paper we intend to establish fast numerical approaches to solve a class of initial-boundary problem of time-space fractional convection-diffusion...

NONLINEAR SOURCE-TERM | MESHLESS METHOD | ADVECTION-DISPERSION EQUATION | APPROXIMATIONS | Fast Fourier transform | COMPACT EXPONENTIAL SCHEME | Krylov subspace method | HIGH-ORDER | Fractional convection-diffusion equation | Toeplitz matrix | FINITE-VOLUME METHOD | NUMERICAL-SOLUTION | VARIABLE-COEFFICIENTS | COLLOCATION METHOD | Shifted Grunwald discretization | Circulant preconditioner | Fractional convection–diffusion equation | Computational Mathematics and Numerical Analysis | 65H18 | Theoretical, Mathematical and Computational Physics | Mathematics | Shifted Grünwald discretization | 15A51 | Algorithms | Mathematical and Computational Engineering | 65F15 | MATHEMATICS, APPLIED

NONLINEAR SOURCE-TERM | MESHLESS METHOD | ADVECTION-DISPERSION EQUATION | APPROXIMATIONS | Fast Fourier transform | COMPACT EXPONENTIAL SCHEME | Krylov subspace method | HIGH-ORDER | Fractional convection-diffusion equation | Toeplitz matrix | FINITE-VOLUME METHOD | NUMERICAL-SOLUTION | VARIABLE-COEFFICIENTS | COLLOCATION METHOD | Shifted Grunwald discretization | Circulant preconditioner | Fractional convection–diffusion equation | Computational Mathematics and Numerical Analysis | 65H18 | Theoretical, Mathematical and Computational Physics | Mathematics | Shifted Grünwald discretization | 15A51 | Algorithms | Mathematical and Computational Engineering | 65F15 | MATHEMATICS, APPLIED

Journal Article