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

A finite-volume method is developed for simulating the mixing of turbulent flows at
transcritical conditions. Spurious pressure oscillations associated with fully conservative …

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 …

A new second-order method for approximating the compressible Euler equations is
introduced. The method preserves all the known invariant domains of the Euler system …

We introduce an approximation technique for nonlinear hyperbolic systems with sources that
is invariant domain preserving. The method is discretization-independent provided …

Solutions to many partial differential equations satisfy certain bounds or constraints. For
example, the density and pressure are positive for equations of fluid dynamics, and in the …

Discontinuous Galerkin (DG) methods combine features in finite element methods (weak
formulation, finite dimensional solution and test function spaces) and in finite volume …

In this paper, we present convergence analysis of high-order finite element based methods,
in particular, we focus on a discontinuous Galerkin scheme using summation-by-parts …

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 develop a fully conservative, positivity-preserving, and entropy-bounded
discontinuous Galerkin scheme for simulating the multicomponent, chemically reacting …