Multi‐dimensional wave‐oriented upwind schemes with reduced cross‐wind diffusion for flow in porous media

Single‐point upstream weighting schemes remain the reservoir simulation standard for integrating the convective components of the subsurface flow equations. While single‐point upstream weighting is attractive due to simplicity and small stencil, the accompanying first‐order error can contribute to a large amount of grid‐dependent numerical diffusion which smooths the numerical solution. New upwind schemes are introduced for reservoir simulation that significantly reduce cross‐wind diffusion, retain a local flux approximation with local conservation, and are free of spurious oscillations.