An Upwind Generalized Finite Difference Method for Meshless Solution of Two-phase Porous Flow Equations

This paper makes the first attempt to apply newly developed upwind GFDM for the meshless solution of two-phase porous flow equations. In the presented method, meshless nodes are flexibly collocated to characterize the computational domain, instead of complicated mesh generation, and the computational domain is divided into overlapping sub-domains centered on each node. Combining with moving least square approximation and local Taylor expansion, derivatives of oil-phase pressure at the central node are approximated by a generalized difference scheme of nodal pressure in the local subdomain. By introducing the upwind scheme of phase permeability, fully implicit nonlinear discrete equations of the immiscible two-phase porous flow are obtained and solved by Newton iteration method with automatic differentiation technology, to avoid the additional computational cost and possible computational instability caused by sequentially coupled scheme. The upwind GFDM with the fully implicit nonlinear solver given in this paper may provide a critical reference for developing a general-purpose meshless numerical simulator for porous flow.