Time stepping along characteristics with incomplete iteration for a Galerkin approximation of miscible displacement in porous media. (English) Zbl 0594.76087

Russell, Thomas F.

SIAM J. Numer. Anal. 22, 970-1013 (1985).

In this paper miscible displacement of one incompressible fluid by another in a porous medium is modeled by a nonlinear coupled system of two partial differential equations. The solution algorithm proposed uses a standard Galerkin procedure for pressures and a combination of Galerkin procedure and method of characteristics for concentration. Convergence rates for the proposed algorithms are discussed in detail. The author indicates that numerical the results obtained (which are published elsewhere) show that larger time steps are appropriate with this scheme, and that the approximations exhibit improved qualitative behavior.

Reviewer: M.Aral

MSC:

76S05	Flows in porous media; filtration; seepage
76M99	Basic methods in fluid mechanics
65C20	Probabilistic models, generic numerical methods in probability and statistics

Keywords:

miscible displacement; nonlinear coupled system of two partial differential equations; standard Galerkin procedure for pressures; Galerkin procedure; method of characteristics for concentration; Convergence rates