This paper develops high-order accurate well-balanced (WB) energy stable (ES) finite
difference schemes for multi-layer (the number of layers M⩾ 2) shallow water equations …

This paper proposes high-order accurate well-balanced (WB) energy stable (ES) adaptive
moving mesh finite difference schemes for the shallow water equations (SWEs) with non-flat …

This paper extends the high-order entropy stable (ES) adaptive moving mesh finite
difference schemes developed in Duan and Tang (2022) to the two-and three-dimensional …

This paper develops the genuinely multidimensional HLL Riemann solver for the two-
dimensional special relativistic hydrodynamic equations on Cartesian meshes and studies …

An entropy stable scheme based on adaptive unstructured meshes for solving ideal
magnetohydrodynamic (MHD) equations is proposed. Firstly, a semi-discrete finite volume …

An adaptive moving mesh finite difference scheme is developed for tokamak magneto-
hydrodynamic (MHD) simulations, based on the CLT code (S. Wang and ZW Ma, Phys …

In this paper, a high-order direct arbitrary Lagrangian-Eulerian (ALE) discontinuous Galerkin
(DG) scheme is developed for compressible fluid flows in two-dimensional (2D) Cartesian …

All the existing entropy stable (ES) schemes for relativistic hydrodynamics (RHD) in the
literature were restricted to the ideal equation of state (EOS), which however is often a poor …

This article proposes entropy stable discontinuous Galerkin schemes (DG) for two-fluid
relativistic plasma flow equations. These equations couple the flow of relativistic fluids via …

We develop a fast-running smooth adaptive meshing (SAM) algorithm for dynamic
curvilinear mesh generation, which is based on a fast solution strategy of the time …