Analysis of a New Method for Computing the Flow of Miscible Fluids in a Porous Medium

Autor:	John B. Bell, Mary F. Wheeler, Gregory R. Shubin
Rok vydání:	1985
Předmět:	Numerical Analysis Computational Mathematics Maximum principle Flow (mathematics) Differential equation Incompressible flow Applied Mathematics Numerical analysis Mathematical analysis Diffusion (business) Galerkin method Porous medium Mathematics
Zdroj:	SIAM Journal on Numerical Analysis. 22:1041-1050
ISSN:	1095-7170 0036-1429
DOI:	10.1137/0722062
Popis:	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.
Databáze:	OpenAIRE
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