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) …

We review numerical methods for simulations of cosmic ray (CR) propagation on galactic
and larger scales. We present the development of algorithms designed for …

Partially ionized plasmas are found across the Universe in many different astrophysical
environments. They constitute an essential ingredient of the solar atmosphere, molecular …

This paper presents an overview and introduction to smoothed particle hydrodynamics and
magnetohydrodynamics in theory and in practice. Firstly, we give a basic grounding in the …

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 …

I thought that instead of the great number of precepts of which logic is composed, I would
have enough with the four following ones, provided that I made a firm and unalterable …

We describe a conservative, shock-capturing scheme for evolving the equations of general
relativistic magnetohydrodynamics. The fluxes are calculated using the Harten, Lax, & van …

The design and implementation of a new framework for adaptive mesh refinement
calculations are described. It is intended primarily for applications in astrophysical fluid …

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 …

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 …