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High Order Weighted Essentially Nonoscillatory Schemes for Convection Dominated Problems

SIAM review, ISSN 1095-7200, 02/2009, 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 partial differential equations (PDEs...

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 | Physical Sciences | Mathematics | Mathematics, Applied | Science & Technology | 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 | Physical Sciences | Mathematics | Mathematics, Applied | Science & Technology | Heat | Astrophysics | Differential equations, Partial | Analysis | Convection | Studies | Accuracy | Partial differential equations | Applied mathematics | Approximations

Journal Article

Book

SIAM journal on scientific computing, ISSN 1095-7197, 01/2018, Volume 40, Issue 2, pp. A903 - A928

In this paper, we design a new type of high order finite volume weighted essentially nonoscillatory (WENO...

Finite volume scheme | Weighted essentially nonoscillatory scheme | High order accuracy | Triangular mesh | Steady state problem | Physical Sciences | Mathematics | Mathematics, Applied | Science & Technology

Finite volume scheme | Weighted essentially nonoscillatory scheme | High order accuracy | Triangular mesh | Steady state problem | Physical Sciences | Mathematics | Mathematics, Applied | Science & Technology

Journal Article

SIAM journal on numerical analysis, ISSN 1095-7170, 01/2012, Volume 50, Issue 2, pp. 544 - 573

We design arbitrarily high-order accurate entropy stable schemes for systems of conservation laws...

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 | Physical Sciences | Mathematics | Mathematics, Applied | Science & Technology

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 | Physical Sciences | Mathematics | Mathematics, Applied | Science & Technology

Journal Article

SIAM journal on numerical analysis, ISSN 1095-7170, 08/1991, Volume 28, Issue 4, pp. 907 - 922

.... In this paper high-order essentially nonoscillatory (ENO) schemes for H-J equations are investigated, which yield uniform high-order accuracy in smooth regions and sharply resolve discontinuities in the derivatives...

Viscosity | Conservation laws | Mathematical procedures | Essentially non oscillatory schemes | Mathematical discontinuity | Approximation | Hamilton Jacobi equation | Entropy | Control theory | Cauchy problem | Physical Sciences | Mathematics | Mathematics, Applied | Science & Technology

Viscosity | Conservation laws | Mathematical procedures | Essentially non oscillatory schemes | Mathematical discontinuity | Approximation | Hamilton Jacobi equation | Entropy | Control theory | Cauchy problem | Physical Sciences | Mathematics | Mathematics, Applied | Science & Technology

Journal Article

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

.... Indeed, no proofs of nonlinear entropy stability currently exist for high-order weighted essentially nonoscillatory (WENO...

Weighted essentially nonoscillatory (WENO) schemes | The Navier–Stokes equations | Entropy stability | Summation-by-parts (SBP) operators | Spectral collocation methods | Physical Sciences | Computer Science, Interdisciplinary Applications | Technology | Physics, Mathematical | Computer Science | Physics | Science & Technology | Fluid dynamics | Compressibility | Computational fluid dynamics | Numerical methods | Fluid flow | Entropy | Spectra | Navier Stokes equations | Finite element method | 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 | Physical Sciences | Computer Science, Interdisciplinary Applications | Technology | Physics, Mathematical | Computer Science | Physics | Science & Technology | Fluid dynamics | Compressibility | Computational fluid dynamics | Numerical methods | Fluid flow | Entropy | Spectra | Navier Stokes equations | Finite element method | Mathematical analysis | Collocation methods | Finite element analysis | Dimensional stability | Navier-Stokes equations

Journal Article

SIAM journal on numerical analysis, ISSN 0036-1429, 12/1998, Volume 35, Issue 6, pp. 2147 - 2168

We present a general procedure to convert schemes which are based on staggered spatial grids into nonstaggered schemes...

Conservation laws | High resolution | Essentially non oscillatory schemes | Approximation | Blasts | Mach reflection | Boundary conditions | Mathematics | Grants | Upwind schemes | Hyperbolic conservation laws | Central schemes | Staggered grids | Physical Sciences | Mathematics, Applied | Science & Technology

Conservation laws | High resolution | Essentially non oscillatory schemes | Approximation | Blasts | Mach reflection | Boundary conditions | Mathematics | Grants | Upwind schemes | Hyperbolic conservation laws | Central schemes | Staggered grids | Physical Sciences | Mathematics, Applied | Science & Technology

Journal Article

International journal for numerical methods in fluids, ISSN 0271-2091, 01/2013, Volume 71, Issue 2, pp. 185 - 207

SUMMARY
In this paper, the efficient application of high‐order weighted essentially nonoscillatory (WENO...

shock capturing | RANS | weighted essentially nonoscillatory | compressible flow | high order | engineering problems | Mathematics, Interdisciplinary Applications | Physical Sciences | Computer Science, Interdisciplinary Applications | Physics, Fluids & Plasmas | Technology | Computer Science | Mechanics | Mathematics | Physics | Science & Technology

shock capturing | RANS | weighted essentially nonoscillatory | compressible flow | high order | engineering problems | Mathematics, Interdisciplinary Applications | Physical Sciences | Computer Science, Interdisciplinary Applications | Physics, Fluids & Plasmas | Technology | Computer Science | Mechanics | Mathematics | Physics | Science & Technology

Journal Article

1990, 65

Book

International journal for numerical methods in fluids, ISSN 1097-0363, 2009, Volume 63, Issue 1, pp. 1 - n/a

.... It comprises a finite volume (FV) discretization using semi‐discrete, non‐staggered central schemes for colocated variables prescribed on a mesh of polyhedral cells that have an arbitrary number of faces...

Navier–Stokes equations | supersonic jet | biconic | forward‐facing step | polyhedral | central schemes | semi‐discrete | finite volume | compressible viscous flows | hypersonic flows | Forward-facing step | Navier-stokes equations | Polyhedral | Supersonic jet | Compressible viscous flows | Hypersonic flows | Semi-discrete | Biconic | Finite volume | Central schemes | Mathematics, Interdisciplinary Applications | Physical Sciences | Computer Science, Interdisciplinary Applications | Physics, Fluids & Plasmas | Technology | Computer Science | Mechanics | Mathematics | Physics | Science & Technology | Interpolation | Computational fluid dynamics | Mathematical analysis | High speed | Solvers | Mathematical models | Constraining | Navier-Stokes equations

Navier–Stokes equations | supersonic jet | biconic | forward‐facing step | polyhedral | central schemes | semi‐discrete | finite volume | compressible viscous flows | hypersonic flows | Forward-facing step | Navier-stokes equations | Polyhedral | Supersonic jet | Compressible viscous flows | Hypersonic flows | Semi-discrete | Biconic | Finite volume | Central schemes | Mathematics, Interdisciplinary Applications | Physical Sciences | Computer Science, Interdisciplinary Applications | Physics, Fluids & Plasmas | Technology | Computer Science | Mechanics | Mathematics | Physics | Science & Technology | Interpolation | Computational fluid dynamics | Mathematical analysis | High speed | Solvers | Mathematical models | Constraining | Navier-Stokes equations

Journal Article

SIAM journal on scientific computing, ISSN 1095-7197, 01/2002, Volume 24, Issue 2, pp. 480 - 506

We present the first fourth-order central scheme for two-dimensional hyperbolic systems of conservation laws...

Nonoscillatory schemes | Central weighted essentially nonoscillatory reconstruction | Central difference schemes | High-order accuracy | Weighted essentially nonoscillatory reconstruction | Hyperbolic systems | Physical Sciences | Mathematics | Mathematics, Applied | Science & Technology

Nonoscillatory schemes | Central weighted essentially nonoscillatory reconstruction | Central difference schemes | High-order accuracy | Weighted essentially nonoscillatory reconstruction | Hyperbolic systems | Physical Sciences | Mathematics | Mathematics, Applied | Science & Technology

Journal Article

SIAM journal on numerical analysis, ISSN 0036-1429, 2015, Volume 53, Issue 4, pp. 1833 - 1856

.... In particular, we construct a new class of conservative finite difference methods by applying weighted essentially nonoscillatory (WENO...

Hyperbolic conservation laws | Weighted essentially nonoscillatory | Lax-Wendroff | Finite difference methods | Physical Sciences | Mathematics | Mathematics, Applied | Science & Technology

Hyperbolic conservation laws | Weighted essentially nonoscillatory | Lax-Wendroff | Finite difference methods | Physical Sciences | Mathematics | Mathematics, Applied | Science & Technology

Journal Article

Journal of computational physics, ISSN 0021-9991, 01/2002, Volume 175, Issue 1, pp. 108 - 127

High-order accurate weighted essentially nonoscillatory (WENO) schemes have recently been developed for finite difference and finite volume methods both in structured and in unstructured meshes...

Weighted essentially nonoscillatory | Stability | High-order accuracy | Shock calculation | Negative weights | Physical Sciences | Computer Science, Interdisciplinary Applications | Technology | Physics, Mathematical | Computer Science | Physics | Science & Technology

Weighted essentially nonoscillatory | Stability | High-order accuracy | Shock calculation | Negative weights | Physical Sciences | Computer Science, Interdisciplinary Applications | Technology | Physics, Mathematical | Computer Science | Physics | Science & Technology

Journal Article

Journal of computational physics, ISSN 0021-9991, 07/2014, Volume 269, pp. 355 - 385

In [8], the authors have designed a new fifth-order WENO finite-difference scheme (named WENO-η...

WENO-[formula omitted] | WENO-Z | Weighted essentially non-oscillatory | Smoothness indicators | High order accuracy | WENO-η | WENO-Zη

WENO-[formula omitted] | WENO-Z | Weighted essentially non-oscillatory | Smoothness indicators | High order accuracy | WENO-η | WENO-Zη

Journal Article

SIAM journal on numerical analysis, ISSN 1095-7170, 01/2014, Volume 52, Issue 5, pp. 2335 - 2355

... (WENO) schemes that the parameter ε occurring in the smoothness indicators of the scheme should be chosen proportional to the square of the mesh size, h2, to achieve the optimal order of accuracy...

Conservation laws | Essentially non oscillatory schemes | Mathematical discontinuity | Approximation | Critical points | Polynomials | Convection diffusion equation | Chronological order | Stencils | Observed choices | Weighted essentially nonoscillatory schemes | Order reduction | Accuracy analysis | Physical Sciences | Mathematics | Mathematics, Applied | Science & Technology | Reconstruction | Discontinuity | Accuracy | Mathematical models | Smoothness | Time integration | Optimization | Convergence

Conservation laws | Essentially non oscillatory schemes | Mathematical discontinuity | Approximation | Critical points | Polynomials | Convection diffusion equation | Chronological order | Stencils | Observed choices | Weighted essentially nonoscillatory schemes | Order reduction | Accuracy analysis | Physical Sciences | Mathematics | Mathematics, Applied | Science & Technology | Reconstruction | Discontinuity | Accuracy | Mathematical models | Smoothness | Time integration | Optimization | Convergence

Journal Article

SIAM journal on scientific computing, ISSN 1095-7197, 01/2005, Volume 27, Issue 3, pp. 995 - 1013

... (weighted essentially nonoscillatory) methodology as limiters for the RKDG (Runge-Kutta discontinuous Galerkin) methods...

High-order accuracy | Runge-Kutta discontinuous Galerkin method | Weighted essentially nonoscillatory finite volume scheme | Limiters | Physical Sciences | Mathematics | Mathematics, Applied |

High-order accuracy | Runge-Kutta discontinuous Galerkin method | Weighted essentially nonoscillatory finite volume scheme | Limiters | Physical Sciences | Mathematics | Mathematics, Applied |