For compressible flow simulations involving both turbulence and shockwaves, the
competing requirements render it challenging to develop high-order numerical methods …

In this paper, a high-order semi-implicit (SI) asymptotic preserving (AP) and divergence-free
finite difference weighted essentially nonoscillatory (WENO) scheme is proposed for …

Several advances have been reported in the recent literature on divergence-free finite
volume schemes for Magnetohydrodynamics (MHD). Almost all of these advances are …

This paper proposes and analyzes arbitrarily high-order discontinuous Galerkin (DG) and
finite volume methods which provably preserve the positivity of density and pressure for the …

Due to the prevalence of magnetic fields in astrophysical environments,
magnetohydrodynamic (MHD) simulation has become a basic tool for studying astrophysical …

We propose a second-order accurate semi-implicit and well-balanced finite volume scheme
for the equations of ideal magnetohydrodynamics including gravitational source terms. The …

The density and pressure are positive physical quantities in magnetohydrodynamics (MHD).
Design of provably positivity-preserving (PP) numerical schemes for ideal compressible …

Numerical schemes provably preserving the positivity of density and pressure are highly
desirable for ideal magnetohydrodynamics (MHD), but the rigorous positivity-preserving …

We propose a simple modification of standard weighted essentially non-oscillatory (WENO)
finite volume methods for Cartesian grids, which retains the full spatial order of accuracy of …

Abstract We present a Finite Volume scheme for solving Maxwell's equations coupled to
magnetized multi-fluid plasma equations for reactive and collisional partially ionized flows …