ABSTRACT
This chapter briefly summarizes the equations used by global space weather models and points out the various approximations used by the various codes. It uses Block Adaptive-Tree Solar-Wind Roe-Type Upwind (BATS-R-US) multiphysics extended magnetohydrodynamics (MHD) model and SWMF to illustrate the various techniques. The chapter discusses the validation of global space weather codes, the transition to operational space weather forecasting, and the recent efforts to incorporate improved physics in the next-generation models. The richness of spatial and temporal scales represents a fundamental challenge in modeling space weather. The commonly used approximation in global space weather codes is single-fluid MHD. A simpler approximation of the MHD equations assumes that the random motion of the particles is tied to the magnetic field lines. The most exciting new feature of the space weather modeling framework/Geospace operational model is its ability to forecast regional space weather conditions. The current-generation space weather models use either numerical dissipation or some empirical resisitivity models to establish reconnection.
