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 …

This review aims at providing an up-to-date status and a general introduction to the subject
of the numerical study of energetic particle acceleration and transport in turbulent …

In simulations of magnetohydrodynamic (MHD) processes the violation of the divergence
constraint causes severe stability problems. In this paper we develop and test a new …

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 …

In this paper we describe a community toolkit which is designed to provide parallel support
with adaptive mesh capability for a large and important class of computational models, those …

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 …

We present Phantom, a fast, parallel, modular, and low-memory smoothed particle
hydrodynamics and magnetohydrodynamics code developed over the last decade for …

A new code for astrophysical magnetohydrodynamics (MHD) is described. The code has
been designed to be easily extensible for use with static and adaptive mesh refinement. It …