Entropy stable discontinuous Galerkin methods for ten-moment Gaussian closure equations

Lax-Wendroff flux reconstruction method for hyperbolic conservation laws

“…This is a smooth convergence test from [7] and requires no limiter. The domain is taken to be Ω = [−0.5, 0.5] and the potential for source terms (19) The solutions are computed at 𝑡 = 0.5 and the convergence results for variable 𝜌 and 𝑝 11 are shown in Figure 1 where optimal convergence rates are seen.…”

Entropy stable discontinuous Galerkin schemes for the special relativistic hydrodynamics equations

“…In [21], authors have presented a framework for entropy stable DG schemes based on the SBP property. This framework has been applied to various hyperbolic systems in [15,26,47].…”

Entropy Stable Discontinuous Galerkin Methods for Balance Laws in Non-Conservative Form: Applications to the Euler Equations with Gravity

“…Most entropy stable DG schemes are constructed assuming exact integration in time, and Ranocha et al [45] achieved fully discrete entropy-stability using relaxation Runge-Kutta time integrators. Entropy-stable DG schemes have been constructed for many systems of nonlinear conservation and balance laws, such as the shallow water equations [61], the compressible multi-component Euler equations [47], special relativistic ideal magneto-hydrodynamics [20], and the ten-moment Gaussian closure equations [6]. However, many equations of physical interest do not conform to the standard balance law form and require extensions of the basic entropystability framework.…”