We present a novel quasi-conservative arbitrary high order accurate ADER (Arbitrary-
Derivative) discontinuous Galerkin method allowing to efficiently use a non-conservative …

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 …

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

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 …

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 …

This paper develops high-order accurate, well-balanced (WB), and positivity-preserving (PP)
finite volume schemes for shallow water equations on adaptive moving structured meshes …

This paper develops the high-order entropy stable (ES) finite difference schemes for multi-
dimensional compressible Euler equations with the van der Waals equation of state (EOS) …

In this paper, a direct arbitrary Lagrangian-Eulerian (ALE) discontinuous Galerkin (DG)
scheme is proposed for simulating compressible multi-material flows on the adaptive …