4.4 Article

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

Journal

Publisher

WILEY-BLACKWELL
DOI: 10.1002/fld.2329

Keywords

multi-dimensional upwind; cross-wind diffusion; finite volume; positivity; discrete maximum principle; monotone; hyperbolic

Funding

  1. EPSRC [GR/S70968/01]
  2. Engineering and Physical Sciences Research Council [GR/S70968/01] Funding Source: researchfish

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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.

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