Efficient Entropy Stable Gauss Collocation Methods
Copyright policy )Efficient Entropy Stable Gauss Collocation Methods
The construction of high order entropy stable collocation schemes on quadrilateral and hexahedral elements has relied on the use of Gauss-Legendre-Lobatto collocation points and their equivalence with summation-by-parts (SBP) finite difference operators. In this work, we show how to efficiently generalize the construction of semi-discretely entropy stable schemes on tensor product elements to Gauss points and generalized SBP operators. Numerical experiments suggest that the use of Gauss points significantly improves accuracy on curved meshes.
Accepted to SISC
- Rice University United States
Compressible Navier-Stokes equations, high order, Numerical Analysis (math.NA), Euler equations, compressible Euler, nonlinear conservation laws, hyperbolic, Hyperbolic conservation laws, Finite difference methods for initial value and initial-boundary value problems involving PDEs, FOS: Mathematics, Finite element, Rayleigh-Ritz and Galerkin methods for initial value and initial-boundary value problems involving PDEs, Mathematics - Numerical Analysis, Stability and convergence of numerical methods for initial value and initial-boundary value problems involving PDEs, entropy, Spectral, collocation and related methods for initial value and initial-boundary value problems involving PDEs, discontinuous Galerkin
Compressible Navier-Stokes equations, high order, Numerical Analysis (math.NA), Euler equations, compressible Euler, nonlinear conservation laws, hyperbolic, Hyperbolic conservation laws, Finite difference methods for initial value and initial-boundary value problems involving PDEs, FOS: Mathematics, Finite element, Rayleigh-Ritz and Galerkin methods for initial value and initial-boundary value problems involving PDEs, Mathematics - Numerical Analysis, Stability and convergence of numerical methods for initial value and initial-boundary value problems involving PDEs, entropy, Spectral, collocation and related methods for initial value and initial-boundary value problems involving PDEs, discontinuous Galerkin
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