7 papers · 1 filter
Limiter-based fully-discrete entropy stable explicit DG schemes for ideal MHD equations
Yuchang Liu, Yan Jiang, Zheng Sun
We propose a class of high-order fully-discrete entropy stable (ES) explicit discontinuous Galerkin (DG) solvers for the compressible ideal magnetohydrodynamics (MHD) equations. Ou…
A bound-preserving oscillation-eliminating discontinuous Galerkin method with operator splitting for solving Kapila's five-equation model
Jia-Jun Zou, Yu-Chang Liu, Fan Zhang +3
This paper proposes a robust operator-splitting discontinuous Galerkin (DG) framework to overcome the severe stiffness-induced instabilities in simulating compressible two-phase fl…
A limiter-based approach to construct high-order fully-discrete entropy stable explicit DG schemes for hyperbolic conservation laws
Yuchang Liu, Wei Guo, Yan Jiang +1
This paper presents a class of novel high-order fully-discrete entropy stable (ES) discontinuous Galerkin (DG) schemes with explicit time discretization. The proposed methodology e…
Structure-preserving nodal DG method for Euler equations with gravity II: general equilibrium states
Yuchang Liu, Wei Guo, Yan Jiang +1
We develop an entropy-stable nodal discontinuous Galerkin (DG) scheme for the Euler equations with gravity, which is also well-balanced with respect to general equilibrium solution…
Structure-preserving nodal DG method for the Euler equations with gravity: well-balanced, entropy stable, and positivity preserving
Yuchang Liu, Wei Guo, Yan Jiang +1
We propose an entropy stable and positivity preserving discontinuous Galerkin (DG) scheme for the Euler equations with gravity, which is also well-balanced for hydrostatic equilibr…
A globally divergence-free entropy stable nodal DG method for conservative ideal MHD equations
Yuchang Liu, Wei Guo, Yan Jiang +1
We propose an arbitrarily high-order globally divergence-free entropy stable nodal discontinuous Galerkin (DG) method to directly solve the conservative form of the ideal MHD equat…