For solving time-dependent convection-dominated partial differential equations (PDEs),
which arise frequently in computational physics, high order numerical methods, including …

We construct a local Lax–Friedrichs type positivity-preserving flux for compressible Navier–
Stokes equations, which can be easily extended to multiple dimensions for generic forms of …

In this paper, we are interested in constructing a scheme solving compressible Navier–
Stokes equations, with desired properties including high order spatial accuracy …

In this paper, we design high-order bound-preserving discontinuous Galerkin (DG) methods
for multicomponent chemically reacting flows. In this problem, the density and pressure are …

We consider solving a generalized Allen-Cahn equation coupled with a passive convection
for a given incompressible velocity field. The numerical scheme consists of the first order …

In this paper, we construct a positivity-preserving high order accurate finite volume hybrid
Hermite Weighted Essentially Non-oscillatory (HWENO) scheme for compressible Navier …

In this paper, we develop bound-preserving discontinuous Galerkin (DG) methods for the
coupled system of compressible miscible displacement problems. We consider the problem …

In this paper, we construct bound-preserving interior penalty discontinuous Galerkin (IPDG)
methods with a second-order implicit pressure explicit concentration (SIPEC) time marching …

For the initial value problem of scalar conservation laws, a bound-preserving property is
desired for numerical schemes in many applications. Traditional methods to enforce a …

In this paper, we develop high-order bound-preserving (BP) discontinuous Galerkin (DG)
methods for the coupled system of compressible miscible displacements on triangular …