CONTROL VOLUME APPROXIMATION OF DEGENERATE TWO-PHASE POROUS FLOWS

摘要

Implicit Euler approximations of the equations governing the porous flow of two immiscible incompressible fluids are shown to be the Euler-Lagrange equations of a convex function. Tools from convex analysis are then used to develop robust fully discrete algorithms for their numerical approximation. Existence and uniqueness of solutions to control volume approximations are established.