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We consider a finite volume method for flow simulations in an anisotropic porous medium in the presence of a well. The hydraulic head varies logarithmically and its gradient changes rapidly in the well vicinity. Thus, the use of standard numerical schemes results in a completely wrong total well flux and an inaccurate hydraulic head. In this article we propose two finite volume methods to model the well singularity in an anisotropic medium. The first method significantly reduces the total well flux error, but the hydraulic head is still not even first-order accurate. The second method gives a second-order accurate hydraulic head and at least first-order accurate total well flux.

Finite Volume Methods for Well-Driven Flows in Anisotropic Porous Media