The ideal MHD equations are a central model in astrophysics, and their solution relies upon
stable numerical schemes. We present an implementation of a new method, which …

A standard paradigm for the existence of solutions in fluid dynamics is based on the
construction of sequences of approximate solutions or approximate minimizers. This …

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 …

We develop a new second-order flux globalization based path-conservative central-upwind
(PCCU) scheme for rotating shallow water magnetohydrodynamic equations. The new …

Modern astrophysical simulations aim to accurately model an ever-growing array of physical
processes, including the interaction of fluids with magnetic fields, under increasingly …

We construct an unconventional divergence preserving discretization of updated
Lagrangian ideal magnetohydrodynamics (MHD) over simplicial grids. The cell-centered …

The high-accuracy solution of the MHD equations is of great interest in various fields of
physics, mathematics, and engineering. Higher-order DG schemes offer low dissipation and …

We develop a new second-order unstaggered semidiscrete path-conservative central-
upwind (PCCU) scheme for ideal and shallow water magnetohydrodynamics (MHD) …

In this article, we consider the Chew, Goldberger and Low (CGL) plasma flow equations,
which is a set of nonlinear, non-conservative hyperbolic PDEs modeling anisotropic plasma …

We deal with the discretization of generalized transient advection problems for differential
forms on bounded spatial domains. We pursue an Eulerian method of lines approach with …