Control Volume Approximation of Degenerate Two-Phase Porous Flows
Thomas J. Murphy, Noel J. Walkington · SIAM Journal on Numerical Analysis · 2019
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.