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This paper makes the first attempt to apply newly developed upwind GFDM forthe meshless solution of two-phase porous flow equations. In the presentedmethod, node cloud is used to flexibly discretize the computational domain,instead of complicated mesh generation. Combining with moving least squareapproximation and local Taylor expansion, spatial derivatives of oil-phasepressure at a node are approximated by generalized difference operators in thelocal influence domain of the node. By introducing the first-order upwindscheme of phase relative permeability, and combining the discrete boundaryconditions, fully-implicit GFDM-based nonlinear discrete equations of theimmiscible two-phase porous flow are obtained and solved by the nonlinearsolver based on the Newton iteration method with the automatic differentiation,to avoid the additional computational cost and possible computationalinstability caused by sequentially coupled scheme. Two numerical examples areimplemented to test the computational performances of the presented method.Detailed error analysis finds the two sources of the calculation error, roughlystudies the convergence order thus find that the low-order error of GFDM makesthe convergence order of GFDM lower than that of FDM when node spacing issmall, and points out the significant effect of the symmetry or uniformity ofthe node collocation in the node influence domain on the accuracy ofgeneralized difference operators, and the radius of the node influence domainshould be small to achieve high calculation accuracy, which is a significantdifference between the studied hyperbolic two-phase porous flow problem and theelliptic problems when GFDM is applied.

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