This paper focuses on flux-continuous general tensor pressure equation approximation for strongly anisotropic media. Earlier methods have focused on single-parameter pointwise schemes which are effective for smaller anisotropy ratios. However they have conditional M-matrices depending on the strength of the tensor cross-terms. For strongly anisotropic full tensor cases, the methods can yield pressure solutions with severe spurious oscillations. The spurious oscillations are shown to be caused by decoupling on both structured and unstructured grids. Flow results and convergence tests confirm the decoupling theory.

Anisotropic flux-continuous full pressure continuity formulations are presented. The formulations lead to improved discretization schemes for the complete range of elliptic tensors. The new schemes are shown to be positive definite, have quasi-positive M-matrices for full-tensor fields with large anisotropy ratios, and compute well resolved solutions that are essentially free of spurious oscillations.

Anisotropic Darcy-flux schemes are presented on structured, unstructured and anisotropy favoring grids. The methods are applied to a range of geological test cases and grid-types including arbitrarily high anisotropy ratio in two and three dimensions.

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