Entropy Stable Discontinuous Galerkin Methods for Balance Laws in Non-Conservative Form: Applications to the Euler Equations with Gravity
arXiv:2110.15920 · doi:10.1016/j.jcp.2022.111507
Abstract
In this work a non-conservative balance law formulation is considered that encompasses the rotating, compressible Euler equations for dry atmospheric flows. We develop a semi-discretely entropy stable discontinuous Galerkin method on curvilinear meshes using a generalization of flux differencing for numerical fluxes in fluctuation form. The method uses the skew-hybridized formulation of the element operators to ensure that, even in the presence of under-integration on curvilinear meshes, the resulting discretization is entropy stable. Several atmospheric flow test cases in one, two, and three dimensions confirm the theoretical entropy stability results as well as show the high-order accuracy and robustness of the method.
arXiv comment31 Pages, 13 figures
References in corpus (18)
- Split Form Nodal Discontinuous Galerkin Schemes with Summation-By-Parts Property for the Compressible Euler Equations
- Kinetic energy preserving and entropy stable finite volume schemes for compressible Euler and Navier-Stokes equations
- On discretely entropy conservative and entropy stable discontinuous Galerkin methods
- Relaxation Runge-Kutta Methods: Fully-Discrete Explicit Entropy-Stable Schemes for the Compressible Euler and Navier-Stokes Equations
- SpECTRE: A Task-based Discontinuous Galerkin Code for Relativistic Astrophysics
- An energy consistent discretization of the nonhydrostatic equations in primitive variables
- Well-Balanced Schemes for the Euler Equations with Gravitation: Conservative Formulation Using Global Fluxes
- Comparison of some Entropy Conservative Numerical Fluxes for the Euler Equations
- Efficient Exascale Discretizations: High-Order Finite Element Methods
- Astrophysical hydrodynamics with a high-order discontinuous Galerkin scheme and adaptive mesh refinement
- Entropy stable DGSEM for nonlinear hyperbolic systems in nonconservative form with application to two-phase flows
- Generalised Summation-by-Parts Operators and Variable Coefficients
- A Novel Averaging Technique for Discrete Entropy-Stable Dissipation Operators for Ideal MHD
- Entropy stable, robust and high-order DGSEM for the compressible multicomponent Euler equations
- On the robustness and performance of entropy stable discontinuous collocation methods for the compressible Navier-Stokes equations
- An entropy stable high-order discontinuous Galerkin spectral element method for the Baer-Nunziato two-phase flow model
- High-order accurate entropy stable nodal discontinuous Galerkin schemes for the ideal special relativistic magnetohydrodynamics
- Entropy stable discontinuous Galerkin methods for ten-moment Gaussian closure equations
Cited by in corpus (4)
- A discontinuous Galerkin spectral element method for a nonconservative compressible multicomponent flow model
- Structure-preserving approximations of the Serre-Green-Naghdi equations in standard and hyperbolic form
- An entropy stable discontinuous Galerkin method for the two-layer shallow water equations on curvilinear meshes
- Multiderivative time integration methods preserving nonlinear functionals via relaxation