Standard reservoir simulation schemes employ single-point upstream weighting for approximation of the con-vective fluxes when multiple phases or components are present. These schemes introduce both coordinate-line numerical diffusion and crosswind diffusion into the solution that is grid and geometry dependent. Families of locally conservative cell-based multidimensional upwind schemes that reduce both directional and crosswind diffusion are presented for convective flow approximation in porous media. The schemes are coupled with full-tensor Darcy flux approximations and handle general flow situations involving counter current gravity flows and systems of hyperbolic equations.

Characteristic vector upwind approximations are proposed and compared with the classical upstream weighting upwind schemes for the case of gravity segregated flows. When dealing with systems of hyperbolic equations, characteristic wave decomposition upwind is used in combination with different limiting strategies involving conservative, primitive and characteristic variables. Alternate wave vector tracing approximations are proposed based on phase velocities and characteristic velocities and comparisons are presented. The cell-based multidimensional formulations are designed for unstructured grids and are constructed such that are stable subject to conditions on the tracing direction and satisfy a local maximum principle that ensures solutions are free of spurious oscillations.

Benefits of the resulting schemes are demonstrated for gravity segregated flows involving three component two phase flow systems. The cell based multidimensional schemes are shown to effectively reduce crosswind diffusion, leading to improved resolution of concentration and saturation fronts.

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