This paper presents a computational scheme for compressible magnetohydrodynamics
(MHD). The scheme is based on the same elements that make up many modern …

In this paper we design a class of numerical schemes that are higher-order extensions of the
weighted essentially non-oscillatory (WENO) schemes of G.-S. Jiang and C.-W. Shu (1996) …

Seven schemes to maintain the∇· B= 0 constraint numerically are compared. All these
algorithms can be combined with shock-capturing Godunov type base schemes. They fall …

As computational astrophysics comes under pressure to become a precision science, there
is an increasing need to move to high accuracy schemes for computational astrophysics …

The equations of magnetohydrodynamics (MHD) have been formulated as a hyperbolic
system of conservation laws. In that form it becomes possible to use higher order Godunov …

In this paper a new, simple and universal formulation of the HLLEM Riemann solver (RS) is
proposed that works for general conservative and non-conservative systems of hyperbolic …

This article considers stabilized finite element and finite volume discretization techniques for
systems of conservation laws. Using newly developed techniques in entropy symmetrization …

An approximate Riemann solver is developed for the governing equations of ideal
magnetohydrodynamics (MHD). The Riemann solver has an eight-wave structure, where …

We present a high-order accurate weighted essentially non-oscillatory (WENO) finite
difference scheme for solving the equations of ideal magnetohydrodynamics (MHD). This …

While working on an adaptive mesh refinement (AMR) scheme for divergence-free
magnetohydrodynamics (MHD), Balsara discovered a unique strategy for the reconstruction …