A pseudo two point flux approximation for general, Non-orthogonal quadrilateral grids with improved monotonicity

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    Abstract

    Multi-Point Flux Approximations (MPFA) have enjoyed wide credence in recent years for their ability to solve the elliptic pressure equation on non K-orthogonal grids. While it is well known that Two Point Flux Approximations (TPFA) lead to a O (1) velocity error on non K-orthogonal grids, MPFA schemes suffer from monotonicity issues and nonphysical oscillations can be present in the pressure solution for highly anisotropic media. In this work we combine the formalism of MPFA and TPFA together. The result is a two point flux approximation, cell-centered finite volume method that uses two points to approximate the flux through a grid interface while at the same time treats general grids and full permeability tensors rigorously. The two points, however, will generally not coincide with centroids of the two cells sharing the grid interface, and hence we are naming this novel technique "pseudo-TPFA method", or pTPFA for short. The pressure value at each of these two points is interpolated by the pressures of one cell center and one vertex of the grid. To eliminate pressures of grid vertices from the flux expression, our recently enhanced multipoint flux approximation (eMPFA) formulation is used to approximate pressure values at grid vertices using cell-center pressures. Extensive numerical experiments are performed to test monotonicity and convergence properties of the pseudo-TPFA method. For highly anisotropic media, pressure solutions of the pseudo-TPFA method do not display spurious oscillations and has much better monotonicity properties over conventional MPFA-O methods. Moreover, MPFA-O methods are known to be affected by the grids used while the pseudo-TPFA method is only slightly grid-dependent. Finally we demonstrate that the pseudo-TPFA method reproduces linear pressure fields and has comparable convergence properties to MPFA-O method.

    Original languageBritish English
    Title of host publication15th European Conference on the Mathematics of Oil Recovery, ECMOR 2016
    ISBN (Electronic)9462821933, 9789462821934
    StatePublished - 2016
    Event15th European Conference on the Mathematics of Oil Recovery, ECMOR 2016 - Amsterdam, Netherlands
    Duration: 29 Aug 20161 Sep 2016

    Publication series

    Name15th European Conference on the Mathematics of Oil Recovery, ECMOR 2016

    Conference

    Conference15th European Conference on the Mathematics of Oil Recovery, ECMOR 2016
    Country/TerritoryNetherlands
    CityAmsterdam
    Period29/08/161/09/16

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