GODUNOV-MIXED METHODS FOR ADVECTION-DIFFUSION EQUATIONS IN MULTIDIMENSIONS

Time-split methods for multidimetisional advection-diffusion equations are considered. In these methods, advection is approximated by a Godunov-type procedure, and diffusion is approximated by a low-order mixed finite element method. This approach is currently being used by a number of researchers to model fluid flow. A basic method is first outlined and analyzed, then three particular variations are discussed. The first variation uses an unsplit, higher-order Godunov method for modeling advection. In this approach, rectangular geometry and a CFL time step constraint are assumed. The second variation is a modification of the first which is fully second order in time. In the third approach, a method of characteristics is used to calculate the advective flux, and time steps larger than a CFL time step are allowed.