A Dynamically Adaptive Higher Order Godunov Scheme in Two Dimensions for Reservoir Simulation

Current reservoir simulators are generally inefficient due to the use of low order accurate schemes on regular grids. The numerical diffusion inherent in the singlepoint upstream weighting scheme can cause large errors in the predicted solutions, which can only be removed by the use of fine grids with many grid blocks. The aim of this work is to develop a method which can produce results of high order accuracy efficiently. A high order Godunov scheme is combined with grid adaptivity, where grid blocks are inserted in highly active regions of the flow field thereby concentrating the computational effort where it is most needed. The results presented demonstrate the benefits of the method in reservoir simu lation. The superiority of the adaptive high order scheme over that of the first order scheme is demonstrated. The quality of the results obtained by the adap tive scheme is comparable with those of the standard scheme, while great savings in computer time are obtained. The adaptive high order scheme also uses less computer time than the corresponding adaptive low order scheme.