Numerically simulating magnetohydrodynamics (MHD) poses notable challenges, including
the suppression of spurious oscillations near discontinuities (eg, shocks) and preservation of …

This paper is devoted to the design and analysis of some structure-preserving finite element
schemes for the magnetohydrodynamics (MHD) system. The main feature of the method is …

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 …

In the numerical simulation of ideal magnetohydrodynamics (MHD), kee** the pressure
and density always positive is essential for both physical considerations and numerical …

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 …

Ideal magnetohydrodynamic (MHD) equations consist of a set of nonlinear hyperbolic
conservation laws, with a divergence-free constraint on the magnetic field. Neglecting this …

Ideal MHD equations arise in many applications such as astrophysical plasmas and space
physics, and they consist of a system of nonlinear hyperbolic conservation laws. The exact …

This paper develops novel and robust central discontinuous Galerkin (CDG) schemes of
arbitrarily high-order accuracy for special relativistic magnetohydrodynamics (RMHD) with a …

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