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

This chapter is intended to provide a review of the current state of the art modeling in the field of computational magnetohydrodynamics<IndexTerm ID="ITerm1"> (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.