A higher-order Godunov scheme coupled with dynamic local grid refinement for flow in a porous medium

Abstract

Today's reservoir simulators are generally inefficient due to the use of low-order accurate schemes in space and time on regular grids. The numerical diffusion inherent in the single-point upstream weighting scheme can cause large errors in the numerical solutions, which can only be removed by the use of very fine uniform grids with many grid blocks. The aim of this work is to develop a method which can produce physically reliable and accurate results efficiently. A higher-order Godunov scheme is coupled with dynamic grid adaptivity, where grid blocks are inserted in highly active regions of the flow field and removed from regions of inactivity, thereby concentrating the computational effort where it is most needed. The quality of results computed by the adaptive higher-order scheme are comparable with those computed by the higher-order scheme on a uniform grid, globally refined to the level of the finest adaptive grid zones, while great savings in computer time are obtained. The adaptive high-order scheme is vastly superior compared to the first-order scheme on a uniform or adaptive grid. The results presented demonstrate the benefits of the method in reservoir simulation.