A variable discretization method for general multiphase flow simulation in a producing hydrocarbon reservoir. For subsurface regions for which a regular or Voronoi computational mesh is suitable, a finite difference/finite volume method (“FDM”) is used to discretize numerical solution of the differential equations governing fluid flow (101). For subsurface regions with more complex geometries, a finite element method (“FEM”) is used. The invention combines FDM and FEM in a single computational framework (102). Mathematical coupling at interfaces between different discretization regions is accomplished by decomposing individual phase velocity into an averaged component and a correction term. The averaged velocity component may be determined from pressure and averaged capillary pressure and other properties based on the discretization method employed, while the velocity correction term may be computed using a multipoint flux approximation type method, which may be reduced to two-point flux approximation for simple grid and permeability fields.