A number of problems in compuational MHD require that the temperature is accurately resolved in low plasma beta. If shocks are present this means that the usual Riemann based approach is not always appropriate. At Warwick we have developed staggered grid Lagrangian remap codes to deal with this problem. These give about the same shock resolution as Riemann based algorithms but accurately determine the plasma teperature. Such codes are routinely used to study MHD shocks and reconnection in the Solar corona and non-linear MHD wave propagation problems in general. For problems where only weak non-linearities are important, such as wave coupling and MHD turbulence, we have written high order finite different codes.
These Lagranigian remap-codes are currently being externeded into full ALE code for MHD in Cartesian and (r-z) geometry