Dynamically Adaptive Godunov Schemes with Renormalization in Reservoir Simulation

Abstract

Abstract Simulation of unstable flow pr.cesses requires the use of both accurate and efficient techniques. Accurate results have been obtained efficiently for flow in a uniform permeability field, by using a higher order Godunov scheme combined with dynamic grid adaptivity. Application of the adaptiye higher order scheme to unstable flows resuiting from a randomly varying permeability field is described here. Use of dynamic grids with varying levels of refinement demands an adaptive definition of the permeability field. Effective permeabilities of coarsened grid blocks are defined by local cell renormalization. High resolution results are obtained together with large savings in computer time.