An overview of grid-based numerical methods used in relativistic hydrodynamics (RHD) and
magnetohydrodynamics (RMHD) is presented. Special emphasis is put on a comprehensive …

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 …

A new multi-state Harten–Lax–van Leer (HLL) approximate Riemann solver for the ideal
magnetohydrodynamic (MHD) equations is developed based on the assumption that the …

We perform three-dimensional simulations of magnetorotational supernovae using a
progenitor star with two different initial magnetic field strengths of 1010 and 1012 G in the …

We present a first 3D magnetohydrodynamic (MHD) simulation of oxygen, neon, and carbon
shell burning in a rapidly rotating core-collapse supernova progenitor. We also run a purely …

In this work we present a general strategy for constructing multidimensional HLLE Riemann
solvers, with particular attention paid to detailing the two-dimensional HLLE Riemann solver …

In this paper we present a genuinely two-dimensional HLLC Riemann solver. On logically
rectangular meshes, it accepts four input states that come together at an edge and outputs …

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 …

The goal of this paper is to formulate genuinely multidimensional HLL and HLLC Riemann
solvers for unstructured meshes by extending our prior papers on the same topic for logically …

The purpose of this paper is twofold. First, the application of high-order methods in
combination with the popular HLLC Riemann solver demonstrates that the grid-aligned …