We develop structure-preserving methods for the compressible Euler equations with gravity in vector-invariant form and potential temperature as a prognostic variable within the flux-differencing discontinuous Galerkin spectral element method (DGSEM) framework. By discretizing the nonconservative terms as symmetric and antisymmetric products, we derive two-point numerical fluxes that conserve both the thermodynamic entropy and the total energy. Moreover, we design an entropy-stable numerical flux that is well-balanced for both isothermal and isentropic background states. All properties are shown to carry over to the high-order DGSEM on general curvilinear meshes. Several numerical examples confirm the theoretical findings and show the robustness and accuracy of the scheme for use in modern dynamical cores for atmospheric flows.
We study a thermal Maxwell-Stefan-Navier-Stokes system modelling miscible mixtures under a quasi-incompressibility constraint. The system consists of the conservation laws for mass and momentum, and the balance law for entropy, which is preferred over the balance law for energy because it facilitates the development of...
Boris D. Andrews, Aaron Baier-Reinio, Aaron Brunk et al.· 0 citations
We propose a class of high-order fully-discrete entropy stable (ES) explicit discontinuous Galerkin (DG) solvers for the compressible ideal magnetohydrodynamics (MHD) equations. Our main theoretical contribution is the introduction of a novel generalized-path-decomposition framework for MHD equations in Godunov's symme...
Yu-Chang Liu, Yan Jiang, Zheng Sun· 2 citations· ⚡1
We propose a mixed finite element discretisation for the incompressible Navier-Stokes equations that preserves the evolution laws of both energy and enstrophy, in a stronger sense than previous discretisations. In two dimensions, the evolution law for enstrophy only permits dissipation for thermodynamically isolated sy...
Boris D. Andrews, Matin Shams, Patrick E. Farrell· 0 citations
This paper develops skew-symmetric formulations and energy stable finite difference schemes for the reactive Euler and reactive Navier--Stokes equations. By introducing suitable transformed variables, we rewrite the governing equations into skew-symmetric forms and obtain continuous energy estimates by standard integra...
We develop and analyze a structure-preserving discretization for the coupled Stokes–Biot equations. The method is based on a fully-mixed formulation and computes directly the fluid and poroelastic stresses and the Darcy velocity. The scheme employs equal-order polynomial approximations for all unknowns, yet exhibits lo...
I. Yotov, L. Zhao· ESAIM: Mathematical Modellin...· 0 citations
The aim of the present study is to develop discontinuous Galerkin and nonconforming finite-element methods for solving the 2D advection-diffusion equation. The discrete formulations are stabilized by means of a family of numerical fluxes and the dispersion relations are constructed via a Fourier/stability analysis. The...
D. L. Le Roux· 0 citations
We use cookies to run the site and, with your consent, for analytics and to show ads.
See our Cookie Policy.
