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Meshless Upscaling Method and Its Application to a Fluid Flow in Porous Media
- Publisher: European Association of Geoscientists & Engineers
- Source: Conference Proceedings, ECMOR XII - 12th European Conference on the Mathematics of Oil Recovery, Sep 2010, cp-163-00003
- ISBN: 978-90-73781-89-4
Abstract
It is known that the two-point flux approximation, a numerical scheme used in reservoir simulators, has O(1) error when grids are not K-orthogonal. The multi-point flux approximations have found significant interest in the research community. However, non-physical oscillations can appear in the developed multi-point flux approximations when the anisotropy is really strong. In this paper, the meshless multi-point flux approximation (MMPFA) for general fluid flow in porous media is proposed. The MMPFA is based on a gradient approximation commonly used in meshless method and can be extended to include higher-order terms in the appropriate Taylor series. The MMPFA is combined with the mixed corrections which ensure linear completeness. The mixed correction utilizes Shepard Functions in combination with a correction to derivative approximations. Incompleteness of the kernel support combined with the lack of consistency of the kernel interpolation in conventional meshless method results in fuzzy boundaries. In corrected meshless method, the domain boundaries and field variables at the boundaries are approximated with the default accuracy of the method. The resulting normalized and corrected MMPFA scheme not only ensures first order consistency O(h) but also alleviates the particle deficiency (kernel support incompleteness) problem.