MHD Modeling: Aims, Usage, Scales Assessed, Caveats, Codes

Abstract

This chapter is intended to provide a review of the current state of the art modeling in the field of computational magnetohydrodynamics (MHD). The equations of MHD are first derived starting from a kinetic description and its applicability in terms of temporal and spatial scales are discussed. The chapter then focuses on Godunov-type methods which have became widespread over last decades, owing to their ability to describe high-Mach number flows and discontinuities. These schemes lean on a conservative formulation of the equations and on the solution of the Riemann problem at cell interfaces. Such flows are often encountered in astrophysical environments such as supernovae remnants, pulsar wind nebulae and relativistic jets. Finally, advanced modeling using adaptive mesh refinement techniques is also described together with an example application. 9.1 Overview Matter in the visible universe exists for the most part in the form of a plasma, that is, a collection of charge particles and the electromagnetic fields generated from them. An exact description of a plasma that requires knowledge of every particle position at all times is unattainable, except for extremely simple situations. Instead, different levels of approximation can be adopted that are sufficiently accurate to capture the essential dynamics of the system at the scale of interest. As it is often the case, the same phenomenon may be described using different viewpoints, each modeling a limited range of behavior (Bellan 2006). The price to pay for choosing one method or the other is measured by the amount of information that one is willing to sacrifice in order to provide an acceptable description of the system at the desired spatial and temporal scales and for which the chosen model is appropriate. Stated roughly, the larger the spatial scale one of the system, the less the wealth of information one is able to cope with. Since, as we shall see, a A. Mignone