THE APPLICATION OF SPECTRAL METHODS IN SIMULATING COMPRESSIBLE FLUID AND MAGNETOFLUID TURBULENCE

We consider the requirements a computational method must meet for the simulation of compressible hydrodynamic and magnetohydrodynamic (MHD) turbulence. After reviewing the properties which make spectral (Galerkin) and pseudospectral methods particularly useful for incompressible turbulence simulations, we consider how well these methods carry over to the compressible case. Major obstacles exist in formulating algorithms using the Galerkin method. In spite of the presence of aliasing errors, the pseudospectral method can be used to write algorithms that conserve a number of important global quantities. Accordingly, we suggest pseudospectral forms for a polytropic MHD model. Finally, a pseudospectral algorithm for the ideal gas MHD model is suggested. This algorithm conserves energy in terms of the dynamical fluid variables and not, as is common practice, due to a separate energy equation written in conservative form.