A Nonlinear Correction FV Scheme for Near-Well Regions

Kramarenko, Vasily K.; Nikitin, Kirill D.; Vassilevski, Yuri

doi:10.1007/978-3-319-57394-6_53

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2018

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“…to split flux in the well vicinity into a linear part and a part that is due to the influence of the well. The NWC scheme is further generalized in [9,10] for polyhedral grids and arbitrary wells. This correction changes only the approximation of one-sided linear fluxes, but use the same logic for their combining as the non-linear multi-point scheme.…”

Section: Introductionmentioning

confidence: 99%

Non-linear multi-point flux approximation in the near-well region

Dotlić¹,

Pokorni²,

Pušić³

et al. 2018

Filomat

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We consider non-linear multi-point flux approximations (MPFA) scheme for flow simulations in a model of anisotropic porous medium that includes wells. The hydraulic head varies logarithmically and its gradient changes rapidly in the well vicinity. Due to this strong non-linearity of the near-well flow, use of the MPFA scheme in the near well region results in a completely wrong total well flux and an inaccurate hydraulic head distribution. In this article we propose correction of the MPFA scheme. The outcome is a scheme that is second-order accurate even in the well vicinity for anisotropic medium. Solution obtained with this scheme respects minimum and maximum principle, and also, it is non-oscillating.

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Section: Introductionmentioning

confidence: 99%