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. Copyright (C) 2010 John Wiley & Sons, Ltd.