Cross flow tensors and finite volume approximation with by deferred correction Original Research Article

A general framework for full tensor finite volume schemes is presented along with properties of the schemes that in turn provide motivation for a deferred correction scheme. The approach is illustrated by writing a general nine node discretization as a five-node scheme plus a residual term involving the extra nodes. A possible solution procedure involves solving the standard five-node matrix problem to yield an initial solution, then re-solving the problem with the residual determined by the first iterate of the pressure field, relaxation using the pressure from the previous IMPES time step is also examined. Stability of the inner iteration is considered and strategies are discussed. This method is coupled with a higher order Godunov scheme for integrating the convective components of the flow equations. Results presented include two phase flow examples with full tensor fields and serve to demonstrate the potential of the method.