A meshless multi-point flux approximation method

Abstract

In this paper, the meshless multi-point flux approximation (MMPFA) for general fluid flow in porous media is presented. 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. The MMPFA method can be used to model three-dimensional miscible flow in porous media with complex geometry and general anisotropic permeability distributions. To illustrate the performance of the MMPFA, a modelling of a single phase fluid flow in fully anisotropic porous media is presented.