Analysis of a New Method for Computing the Flow of Miscible Fluids in a Porous Medium
John B. Bell, Gregory R. Shubin, Mary Fanett Wheeler · SIAM Journal on Numerical Analysis · 1985
Potempa, in his 1982 Ph.D dissertation, introduced a new numerical method for solving the equations describing multi-component single-phase flow in a porous medium. Potempa’s method has several desirable features including a substantial reduction of the “grid orientation” effect often observed with other methods. In thiss paper we show that for two-component, incompressible flow the method converges to the solution of the differential equation. We also show that this method is very close to a Galerkin procedure that incorporates a certain velocity- and mesh-dependent diffusion term. A corollary to the analysis demonstrates convergence for any piecewise-linear Galerkin procedure on a quasi-uniform mesh containing a mesh-dependent diffusion and satisfying a maximum principle.