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High Order Weighted Essentially Nonoscillatory Schemes for Convection Dominated Problems

SIAM Review, ISSN 0036-1445, 3/2009, Volume 51, Issue 1, pp. 82 - 126

High order accurate weighted essentially nonoscillatory (WENO) schemes are relatively new but have gained rapid popularity in numerical solutions of hyperbolic...

Conservation laws | Shock discontinuity | Interpolation | Shock waves | Approximation | Mathematical discontinuity | Hamilton Jacobi equation | Polynomials | Stencils | Galerkin methods | Survey and Review | Computational fluid dynamics | Hyperbolic partial differential equations | Semiconductor device simulation | Computational astronomy and astrophysics | Convection dominated problems | Traffic flow models | Weighted essentially nonoscillatory (WENO) scheme | Computational biology | computational biology | MATHEMATICS, APPLIED | computational fluid dynamics | traffic flow models | HAMILTON-JACOBI EQUATIONS | weighted essentially nonoscillatory (WENO) scheme | SHALLOW-WATER EQUATIONS | computational astronomy and astrophysics | SHOCK-CAPTURING SCHEMES | DIFFERENCE WENO SCHEMES | DIRECT NUMERICAL-SIMULATION | hyperbolic partial differential equations | NAVIER-STOKES EQUATIONS | convection dominated problems | DISCONTINUOUS GALERKIN METHODS | FLAME TRANSFER-FUNCTIONS | semiconductor device simulation | HYPERBOLIC CONSERVATION-LAWS | FINITE-VOLUME SCHEMES | Heat | Astrophysics | Differential equations, Partial | Analysis | Convection | Studies | Accuracy | Partial differential equations | Applied mathematics | Approximations

Conservation laws | Shock discontinuity | Interpolation | Shock waves | Approximation | Mathematical discontinuity | Hamilton Jacobi equation | Polynomials | Stencils | Galerkin methods | Survey and Review | Computational fluid dynamics | Hyperbolic partial differential equations | Semiconductor device simulation | Computational astronomy and astrophysics | Convection dominated problems | Traffic flow models | Weighted essentially nonoscillatory (WENO) scheme | Computational biology | computational biology | MATHEMATICS, APPLIED | computational fluid dynamics | traffic flow models | HAMILTON-JACOBI EQUATIONS | weighted essentially nonoscillatory (WENO) scheme | SHALLOW-WATER EQUATIONS | computational astronomy and astrophysics | SHOCK-CAPTURING SCHEMES | DIFFERENCE WENO SCHEMES | DIRECT NUMERICAL-SIMULATION | hyperbolic partial differential equations | NAVIER-STOKES EQUATIONS | convection dominated problems | DISCONTINUOUS GALERKIN METHODS | FLAME TRANSFER-FUNCTIONS | semiconductor device simulation | HYPERBOLIC CONSERVATION-LAWS | FINITE-VOLUME SCHEMES | Heat | Astrophysics | Differential equations, Partial | Analysis | Convection | Studies | Accuracy | Partial differential equations | Applied mathematics | Approximations

Journal Article

SIAM Journal on Scientific Computing, ISSN 1064-8275, 2018, Volume 40, Issue 2, pp. A903 - A928

In this paper, we design a new type of high order finite volume weighted essentially nonoscillatory (WENO) schemes to solve hyperbolic conservation laws on...

Finite volume scheme | Weighted essentially nonoscillatory scheme | High order accuracy | Triangular mesh | Steady state problem | MATHEMATICS, APPLIED | EFFICIENT IMPLEMENTATION | high order accuracy | TETRAHEDRAL MESHES | weighted essentially nonoscillatory scheme | ENO SCHEMES | finite volume scheme | SHOCK-CAPTURING SCHEMES | CONSTRUCTION | triangular mesh | SYSTEMS | steady state problem | LIMITERS | UNSTRUCTURED MESHES | HYPERBOLIC CONSERVATION-LAWS | CENTRAL WENO SCHEMES

Finite volume scheme | Weighted essentially nonoscillatory scheme | High order accuracy | Triangular mesh | Steady state problem | MATHEMATICS, APPLIED | EFFICIENT IMPLEMENTATION | high order accuracy | TETRAHEDRAL MESHES | weighted essentially nonoscillatory scheme | ENO SCHEMES | finite volume scheme | SHOCK-CAPTURING SCHEMES | CONSTRUCTION | triangular mesh | SYSTEMS | steady state problem | LIMITERS | UNSTRUCTURED MESHES | HYPERBOLIC CONSERVATION-LAWS | CENTRAL WENO SCHEMES

Journal Article

SIAM Journal on Numerical Analysis, ISSN 0036-1429, 1/2012, Volume 50, Issue 2, pp. 544 - 573

We design arbitrarily high-order accurate entropy stable schemes for systems of conservation laws. The schemes, termed TeCNO schemes, are based on two main...

Conservation laws | Shallow water equations | Essentially non oscillatory schemes | Approximation | Scalars | Entropy | Mathematical vectors | Mathematical functions | Euler equations | High-order accuracy | Entropy stability | Sign property | ENO reconstruction | NUMERICAL VISCOSITY | MATHEMATICS, APPLIED | entropy stability | EFFICIENT IMPLEMENTATION | NAVIER-STOKES EQUATIONS | high-order accuracy | CONVERGENCE | DIFFERENCE APPROXIMATIONS | FINITE-ELEMENT-METHOD | sign property

Conservation laws | Shallow water equations | Essentially non oscillatory schemes | Approximation | Scalars | Entropy | Mathematical vectors | Mathematical functions | Euler equations | High-order accuracy | Entropy stability | Sign property | ENO reconstruction | NUMERICAL VISCOSITY | MATHEMATICS, APPLIED | entropy stability | EFFICIENT IMPLEMENTATION | NAVIER-STOKES EQUATIONS | high-order accuracy | CONVERGENCE | DIFFERENCE APPROXIMATIONS | FINITE-ELEMENT-METHOD | sign property

Journal Article

SIAM Journal on Numerical Analysis, ISSN 0036-1429, 2015, Volume 53, Issue 4, pp. 1833 - 1856

High-order temporal discretizations for hyperbolic conservation laws have historically been formulated as either a method of lines (MOL) or a Lax-Wendroff...

Hyperbolic conservation laws | Weighted essentially nonoscillatory | Lax-Wendroff | Finite difference methods | MATHEMATICS, APPLIED | GENERALIZED RIEMANN PROBLEM | EFFICIENT IMPLEMENTATION | HYPERBOLIC SYSTEMS | WENO SCHEMES | finite difference methods | weighted essentially nonoscillatory | HIGH-ORDER | SHOCK-CAPTURING SCHEMES | RUNGE-KUTTA SCHEMES | hyperbolic conservation laws | SCALAR CONSERVATION-LAWS | ADER SCHEMES | CHARACTERISTIC GALERKIN METHODS

Hyperbolic conservation laws | Weighted essentially nonoscillatory | Lax-Wendroff | Finite difference methods | MATHEMATICS, APPLIED | GENERALIZED RIEMANN PROBLEM | EFFICIENT IMPLEMENTATION | HYPERBOLIC SYSTEMS | WENO SCHEMES | finite difference methods | weighted essentially nonoscillatory | HIGH-ORDER | SHOCK-CAPTURING SCHEMES | RUNGE-KUTTA SCHEMES | hyperbolic conservation laws | SCALAR CONSERVATION-LAWS | ADER SCHEMES | CHARACTERISTIC GALERKIN METHODS

Journal Article

International Journal for Numerical Methods in Fluids, ISSN 0271-2091, 01/2013, Volume 71, Issue 2, pp. 185 - 207

In this paper, the efficient application of high‐order weighted essentially nonoscillatory (WENO) reconstruction to the subsonic and transonic engineering...

shock capturing | RANS | weighted essentially nonoscillatory | compressible flow | high order | engineering problems | WENO SCHEMES | PHYSICS, FLUIDS & PLASMAS | COMPUTER SCIENCE, INTERDISCIPLINARY APPLICATIONS | MATHEMATICS, INTERDISCIPLINARY APPLICATIONS | MECHANICS | TURBULENCE | FLOWS | HYPERBOLIC CONSERVATION-LAWS

shock capturing | RANS | weighted essentially nonoscillatory | compressible flow | high order | engineering problems | WENO SCHEMES | PHYSICS, FLUIDS & PLASMAS | COMPUTER SCIENCE, INTERDISCIPLINARY APPLICATIONS | MATHEMATICS, INTERDISCIPLINARY APPLICATIONS | MECHANICS | TURBULENCE | FLOWS | HYPERBOLIC CONSERVATION-LAWS

Journal Article

SIAM Journal on Scientific Computing, ISSN 1064-8275, 2012, Volume 34, Issue 2, pp. A627 - A658

To easily generalize the maximum-principle-satisfying schemes for scalar conservation laws in [X. Zhang and C.-W. Shu, J. Comput. Phys., 229 (2010), pp....

Finite volume scheme | Incompressible flow | Strong stability preserving time discretization | Convection diffusion equations | High order accuracy | Maximum principle | Weighted essentially nonoscillatory scheme | Navier-Stokes equations | MATHEMATICS, APPLIED | EFFICIENT IMPLEMENTATION | high order accuracy | strong stability preserving time discretization | incompressible flow | weighted essentially nonoscillatory scheme | convection diffusion equations | POSITIVITY | maximum principle | finite volume scheme

Finite volume scheme | Incompressible flow | Strong stability preserving time discretization | Convection diffusion equations | High order accuracy | Maximum principle | Weighted essentially nonoscillatory scheme | Navier-Stokes equations | MATHEMATICS, APPLIED | EFFICIENT IMPLEMENTATION | high order accuracy | strong stability preserving time discretization | incompressible flow | weighted essentially nonoscillatory scheme | convection diffusion equations | POSITIVITY | maximum principle | finite volume scheme

Journal Article

SIAM Journal on Numerical Analysis, ISSN 0036-1429, 1/2013, Volume 51, Issue 2, pp. 864 - 893

This study proposes modified essentially nonoscillatory (ENO) schemes that can improve the performance of the classical ENO schemes. The key ideas of our...

Conservation laws | Linear systems | Interpolation | Essentially non oscillatory schemes | Advection | Approximation | Scalars | Polynomials | Evaluation points | Stencils | Hyperbolic conservation laws | Exponential polynomials | Flux function | ENO scheme | Approximation order | SHOCK-CAPTURING SCHEMES | MATHEMATICS, APPLIED | interpolation | EFFICIENT IMPLEMENTATION | hyperbolic conservation laws | exponential polynomials | flux function | approximation order | HIGH-ORDER | ENO-SCHEMES | Mathematical analysis | Mathematical models | Computational efficiency | Smoothness

Conservation laws | Linear systems | Interpolation | Essentially non oscillatory schemes | Advection | Approximation | Scalars | Polynomials | Evaluation points | Stencils | Hyperbolic conservation laws | Exponential polynomials | Flux function | ENO scheme | Approximation order | SHOCK-CAPTURING SCHEMES | MATHEMATICS, APPLIED | interpolation | EFFICIENT IMPLEMENTATION | hyperbolic conservation laws | exponential polynomials | flux function | approximation order | HIGH-ORDER | ENO-SCHEMES | Mathematical analysis | Mathematical models | Computational efficiency | Smoothness

Journal Article

SIAM Journal on Numerical Analysis, ISSN 0036-1429, 8/1991, Volume 28, Issue 4, pp. 907 - 922

Hamilton-Jacobi (H-J) equations are frequently encountered in applications, e.g., in control theory and differential games. H-J equations are closely related...

Viscosity | Conservation laws | Mathematical procedures | Essentially non oscillatory schemes | Mathematical discontinuity | Approximation | Hamilton Jacobi equation | Entropy | Control theory | Cauchy problem | SHOCK-CAPTURING SCHEMES | MATHEMATICS, APPLIED | ESSENTIALLY NONOSCILLATORY SCHEMES | HAMILTON-JACOBI EQUATIONS | EFFICIENT IMPLEMENTATION

Viscosity | Conservation laws | Mathematical procedures | Essentially non oscillatory schemes | Mathematical discontinuity | Approximation | Hamilton Jacobi equation | Entropy | Control theory | Cauchy problem | SHOCK-CAPTURING SCHEMES | MATHEMATICS, APPLIED | ESSENTIALLY NONOSCILLATORY SCHEMES | HAMILTON-JACOBI EQUATIONS | EFFICIENT IMPLEMENTATION

Journal Article

Computers and Fluids, ISSN 0045-7930, 2010, Volume 39, Issue 2, pp. 197 - 214

Freestream and vortex preservation properties of a weighted essentially nonoscillatory scheme (WENO) and a weighted compact nonlinear scheme (WCNS) on...

COMPUTER SCIENCE, INTERDISCIPLINARY APPLICATIONS | MECHANICS | FINITE-DIFFERENCE SCHEMES | RESOLUTION | COMPACT NONLINEAR SCHEMES | ESSENTIALLY NONOSCILLATORY SCHEMES | ACCURACY

COMPUTER SCIENCE, INTERDISCIPLINARY APPLICATIONS | MECHANICS | FINITE-DIFFERENCE SCHEMES | RESOLUTION | COMPACT NONLINEAR SCHEMES | ESSENTIALLY NONOSCILLATORY SCHEMES | ACCURACY

Journal Article

International Journal for Numerical Methods in Fluids, ISSN 0271-2091, 07/2013, Volume 72, Issue 8, pp. 811 - 845

After several years of planning, the 1st International Workshop on High‐Order CFD Methods was successfully held in Nashville, Tennessee, on January 7–8, 2012,...

CFD | High‐order methods | High-order methods | ACCURATE | FINITE-DIFFERENCE SCHEMES | ELEMENT-METHOD | PHYSICS, FLUIDS & PLASMAS | RESOLUTION | ESSENTIALLY NONOSCILLATORY SCHEMES | ACOUSTICS | RUNGE-KUTTA SCHEMES | COMPUTER SCIENCE, INTERDISCIPLINARY APPLICATIONS | MATHEMATICS, INTERDISCIPLINARY APPLICATIONS | MECHANICS | NAVIER-STOKES EQUATIONS | UNSTRUCTURED GRIDS | COMPUTATIONAL FLUID-DYNAMICS | Reproduction | Numerical analysis | Computational fluid dynamics | Meetings | Fluid flow | Workshops | Mathematical models | Offices

CFD | High‐order methods | High-order methods | ACCURATE | FINITE-DIFFERENCE SCHEMES | ELEMENT-METHOD | PHYSICS, FLUIDS & PLASMAS | RESOLUTION | ESSENTIALLY NONOSCILLATORY SCHEMES | ACOUSTICS | RUNGE-KUTTA SCHEMES | COMPUTER SCIENCE, INTERDISCIPLINARY APPLICATIONS | MATHEMATICS, INTERDISCIPLINARY APPLICATIONS | MECHANICS | NAVIER-STOKES EQUATIONS | UNSTRUCTURED GRIDS | COMPUTATIONAL FLUID-DYNAMICS | Reproduction | Numerical analysis | Computational fluid dynamics | Meetings | Fluid flow | Workshops | Mathematical models | Offices

Journal Article

Journal of Computational and Applied Mathematics, ISSN 0377-0427, 03/2019, Volume 349, pp. 379 - 389

In this work we introduce and analyze a new nonlinear subdivision scheme based on a nonlinear blending between Chaikin’s subdivision rules and the linear...

Linear and nonlinear subdivision schemes | Harten’s multiresolution | Harten's multiresolution | MATHEMATICS, APPLIED | ESSENTIALLY NONOSCILLATORY SCHEMES | STABILITY

Linear and nonlinear subdivision schemes | Harten’s multiresolution | Harten's multiresolution | MATHEMATICS, APPLIED | ESSENTIALLY NONOSCILLATORY SCHEMES | STABILITY

Journal Article

Journal of Computational Physics, ISSN 0021-9991, 12/2016, Volume 326, pp. 780 - 804

Finite difference WENO schemes have established themselves as very worthy performers for entire classes of applications that involve hyperbolic conservation...

Conservation laws | Finite difference | Higher order Godunov schemes | Hyperbolic systems | WENO | TRIANGULAR MESHES | FINITE-DIFFERENCE SCHEMES | RECONSTRUCTION | IMPLEMENTATION | ESSENTIALLY NONOSCILLATORY SCHEMES | PHYSICS, MATHEMATICAL | SHOCK-CAPTURING SCHEMES | COMPUTER SCIENCE, INTERDISCIPLINARY APPLICATIONS | TURBULENCE | UNSTRUCTURED MESHES | HYPERBOLIC CONSERVATION-LAWS | NUMERICAL-SIMULATION | Environmental law

Conservation laws | Finite difference | Higher order Godunov schemes | Hyperbolic systems | WENO | TRIANGULAR MESHES | FINITE-DIFFERENCE SCHEMES | RECONSTRUCTION | IMPLEMENTATION | ESSENTIALLY NONOSCILLATORY SCHEMES | PHYSICS, MATHEMATICAL | SHOCK-CAPTURING SCHEMES | COMPUTER SCIENCE, INTERDISCIPLINARY APPLICATIONS | TURBULENCE | UNSTRUCTURED MESHES | HYPERBOLIC CONSERVATION-LAWS | NUMERICAL-SIMULATION | Environmental law

Journal Article

Computers and Fluids, ISSN 0045-7930, 01/2010, Volume 39, Issue 1, pp. 60 - 76

In this paper, we propose a new unified family of arbitrary high order accurate explicit one-step finite volume and discontinuous Galerkin schemes on...

DISCONTINUOUS GALERKIN SCHEMES | SOUND GENERATION | MIXING LAYER | COMPUTER SCIENCE, INTERDISCIPLINARY APPLICATIONS | MECHANICS | NONLINEAR HYPERBOLIC SYSTEMS | ELEMENT METHOD | ESSENTIALLY NONOSCILLATORY SCHEMES | CONSERVATION-LAWS | NUMERICAL-SIMULATION | FINITE-VOLUME SCHEMES | FLOW

DISCONTINUOUS GALERKIN SCHEMES | SOUND GENERATION | MIXING LAYER | COMPUTER SCIENCE, INTERDISCIPLINARY APPLICATIONS | MECHANICS | NONLINEAR HYPERBOLIC SYSTEMS | ELEMENT METHOD | ESSENTIALLY NONOSCILLATORY SCHEMES | CONSERVATION-LAWS | NUMERICAL-SIMULATION | FINITE-VOLUME SCHEMES | FLOW

Journal Article

Journal of Applied Mathematics, ISSN 1110-757X, 2014, Volume 2014, pp. 1 - 13

The paper constructs a class of simple high-accurate schemes (SHA schemes) with third order approximation accuracy in both space and time to solve linear...

MATHEMATICS, APPLIED | ESSENTIALLY NONOSCILLATORY SCHEMES | MONOTONICITY | SYSTEMS | HIGH-ORDER | DIFFERENCE SCHEME | Conservation laws | Problems | Boundary conditions | Accuracy | Models | Finite element analysis | Approximation | Mathematical analysis | Oscillations | Flux | Mathematical models | Fluxes

MATHEMATICS, APPLIED | ESSENTIALLY NONOSCILLATORY SCHEMES | MONOTONICITY | SYSTEMS | HIGH-ORDER | DIFFERENCE SCHEME | Conservation laws | Problems | Boundary conditions | Accuracy | Models | Finite element analysis | Approximation | Mathematical analysis | Oscillations | Flux | Mathematical models | Fluxes

Journal Article

SIAM Journal on Scientific Computing, ISSN 1064-8275, 05/2000, Volume 21, Issue 6, pp. 2126 - 2143

In this paper, we present a weighted ENO (essentially nonoscillatory) scheme to approximate the viscosity solution of the Hamilton Jacobi equation: phi(t) + H...

weighted ENO | VISCOSITY SOLUTIONS | MATHEMATICS, APPLIED | shape-from-shading | EFFICIENT IMPLEMENTATION | level set | ENO | Hamilton jacobi equation | ESSENTIALLY NONOSCILLATORY SCHEMES

weighted ENO | VISCOSITY SOLUTIONS | MATHEMATICS, APPLIED | shape-from-shading | EFFICIENT IMPLEMENTATION | level set | ENO | Hamilton jacobi equation | ESSENTIALLY NONOSCILLATORY SCHEMES

Journal Article

Journal of Computational Physics, ISSN 0021-9991, 2010, Volume 229, Issue 23, pp. 8918 - 8934

We construct uniformly high order accurate discontinuous Galerkin (DG) schemes which preserve positivity of density and pressure for Euler equations of...

Hyperbolic conservation laws | Finite volume scheme | Discontinuous Galerkin method | Essentially non-oscillatory scheme | Gas dynamics | Positivity preserving | Compressible Euler equations | High order accuracy | Weighted essentially non-oscillatory scheme | EFFICIENT IMPLEMENTATION | ESSENTIALLY NONOSCILLATORY SCHEMES | PHYSICS, MATHEMATICAL | NUMBER ASTROPHYSICAL JETS | COMPUTER SCIENCE, INTERDISCIPLINARY APPLICATIONS | HIGH-RESOLUTION SCHEMES | SYSTEMS | HYPERBOLIC CONSERVATION-LAWS | NUMERICAL-SIMULATION | FINITE-ELEMENT METHOD | Construction | Discretization | Mathematical analysis | Mathematical models | Euler equations | Density | Galerkin methods | Preserving

Hyperbolic conservation laws | Finite volume scheme | Discontinuous Galerkin method | Essentially non-oscillatory scheme | Gas dynamics | Positivity preserving | Compressible Euler equations | High order accuracy | Weighted essentially non-oscillatory scheme | EFFICIENT IMPLEMENTATION | ESSENTIALLY NONOSCILLATORY SCHEMES | PHYSICS, MATHEMATICAL | NUMBER ASTROPHYSICAL JETS | COMPUTER SCIENCE, INTERDISCIPLINARY APPLICATIONS | HIGH-RESOLUTION SCHEMES | SYSTEMS | HYPERBOLIC CONSERVATION-LAWS | NUMERICAL-SIMULATION | FINITE-ELEMENT METHOD | Construction | Discretization | Mathematical analysis | Mathematical models | Euler equations | Density | Galerkin methods | Preserving

Journal Article

Journal of Computational Physics, ISSN 0021-9991, 2010, Volume 229, Issue 9, pp. 3091 - 3120

We construct uniformly high order accurate schemes satisfying a strict maximum principle for scalar conservation laws. A general framework (for arbitrary order...

Hyperbolic conservation laws | Finite volume scheme | Discontinuous Galerkin method | Incompressible flow | Essentially non-oscillatory scheme | Strong stability preserving time discretization | High order accuracy | Maximum principle | Passive convection equation | Weighted essentially non-oscillatory scheme | TIME DISCRETIZATIONS | EFFICIENT IMPLEMENTATION | ESSENTIALLY NONOSCILLATORY SCHEMES | MODEL | PHYSICS, MATHEMATICAL | SHOCK-CAPTURING SCHEMES | COMPUTER SCIENCE, INTERDISCIPLINARY APPLICATIONS | HIGH-RESOLUTION SCHEMES | EULER EQUATIONS | Environmental law | Conservation laws | Construction | Discretization | Mathematical analysis | Preserves | Scalars | Mathematical models

Hyperbolic conservation laws | Finite volume scheme | Discontinuous Galerkin method | Incompressible flow | Essentially non-oscillatory scheme | Strong stability preserving time discretization | High order accuracy | Maximum principle | Passive convection equation | Weighted essentially non-oscillatory scheme | TIME DISCRETIZATIONS | EFFICIENT IMPLEMENTATION | ESSENTIALLY NONOSCILLATORY SCHEMES | MODEL | PHYSICS, MATHEMATICAL | SHOCK-CAPTURING SCHEMES | COMPUTER SCIENCE, INTERDISCIPLINARY APPLICATIONS | HIGH-RESOLUTION SCHEMES | EULER EQUATIONS | Environmental law | Conservation laws | Construction | Discretization | Mathematical analysis | Preserves | Scalars | Mathematical models

Journal Article

Annual Review of Fluid Mechanics, ISSN 0066-4189, 01/2011, Volume 43, Issue 1, pp. 163 - 194

We review numerical methods for direct numerical simulation (DNS) and large-eddy simulation (LES) of turbulent compressible flow in the presence of shock...

energy conservation | shock-capturing schemes | numerical dissipation | shock waves | FINITE-DIFFERENCE SCHEMES | HIGH-ORDER-ACCURATE | PHYSICS, FLUIDS & PLASMAS | ESSENTIALLY NONOSCILLATORY SCHEMES | SHOCK-TURBULENCE INTERACTION | SHOCK/BOUNDARY-LAYER INTERACTION | RUNGE-KUTTA SCHEMES | MECHANICS | NAVIER-STOKES EQUATIONS | LARGE-EDDY SIMULATION | NONLINEAR HYPERBOLIC SYSTEMS | IMMERSED BOUNDARY METHOD | Shock waves | Turbulence | Numerical analysis | Analysis | Research | Eddies | Properties | Simulation methods | Methods | Turbulent flow | Computational fluid dynamics | Nonlinearity | Mathematical models | Entropy

energy conservation | shock-capturing schemes | numerical dissipation | shock waves | FINITE-DIFFERENCE SCHEMES | HIGH-ORDER-ACCURATE | PHYSICS, FLUIDS & PLASMAS | ESSENTIALLY NONOSCILLATORY SCHEMES | SHOCK-TURBULENCE INTERACTION | SHOCK/BOUNDARY-LAYER INTERACTION | RUNGE-KUTTA SCHEMES | MECHANICS | NAVIER-STOKES EQUATIONS | LARGE-EDDY SIMULATION | NONLINEAR HYPERBOLIC SYSTEMS | IMMERSED BOUNDARY METHOD | Shock waves | Turbulence | Numerical analysis | Analysis | Research | Eddies | Properties | Simulation methods | Methods | Turbulent flow | Computational fluid dynamics | Nonlinearity | Mathematical models | Entropy

Journal Article

Journal of Computational Physics, ISSN 0021-9991, 02/2017, Volume 331, pp. 90 - 107

High-order numerical methods that satisfy a discrete analog of the entropy inequality are uncommon. Indeed, no proofs of nonlinear entropy stability currently...

Weighted essentially nonoscillatory (WENO) schemes | The Navier–Stokes equations | Entropy stability | Summation-by-parts (SBP) operators | Spectral collocation methods | NUMERICAL-METHODS | NONLINEAR CONSERVATION-LAWS | FORM | The Navier-Stokes equations | DISCONTINUOUS GALERKIN METHOD | PHYSICS, MATHEMATICAL | COMPUTER SCIENCE, INTERDISCIPLINARY APPLICATIONS | COMPUTATIONAL FLUID-DYNAMICS | SYSTEMS | CONVERGENCE | UNSTRUCTURED MESHES | WENO LIMITERS | Fluid dynamics | Compressibility | Computational fluid dynamics | Numerical methods | Fluid flow | Entropy | Spectra | Navier Stokes equations | Finite element method | Collocation | Mathematical analysis | Collocation methods | Finite element analysis | Dimensional stability | Navier-Stokes equations

Weighted essentially nonoscillatory (WENO) schemes | The Navier–Stokes equations | Entropy stability | Summation-by-parts (SBP) operators | Spectral collocation methods | NUMERICAL-METHODS | NONLINEAR CONSERVATION-LAWS | FORM | The Navier-Stokes equations | DISCONTINUOUS GALERKIN METHOD | PHYSICS, MATHEMATICAL | COMPUTER SCIENCE, INTERDISCIPLINARY APPLICATIONS | COMPUTATIONAL FLUID-DYNAMICS | SYSTEMS | CONVERGENCE | UNSTRUCTURED MESHES | WENO LIMITERS | Fluid dynamics | Compressibility | Computational fluid dynamics | Numerical methods | Fluid flow | Entropy | Spectra | Navier Stokes equations | Finite element method | Collocation | Mathematical analysis | Collocation methods | Finite element analysis | Dimensional stability | Navier-Stokes equations

Journal Article