Douglas, Jim jun.; Roberts, Jean E. Numerical methods for a model for compressible miscible displacement in porous media. (English) Zbl 0537.76062 Math. Comput. 41, 441-459 (1983). The authors derive a nonlinear parabolic system for single-phase, miscible displacement of one compressible fluid by another in a porous medium under the assumption that no volume change results from the mixing of the components and that a pressure-density relation exists for each component in a form that is independent of mixing implying that fluids are in the liquid state. They analyse two numerical schemes for approximating the solution of a two component system only for concentration of fluid and pressure using a parabolic Galerkin procedure for the concentration equation for both the schemes but a parabolic Galerkin procedure for the first scheme and a parabolic mixed finite element technique for the second numerical scheme for the pressure equation. It is claimed that the two procedures used for the two-component model can easily be generalized to treat an n-component model. The formulations and analysis are new and are of great interest to people working in ’numerical analysis’ and ’petroleum engineering’. [This is an abridged version, the complete review is available on demand.] Reviewer: H.K.Verma Cited in 2 ReviewsCited in 79 Documents MSC: 76S05 Flows in porous media; filtration; seepage 76T99 Multiphase and multicomponent flows 76M99 Basic methods in fluid mechanics 76N10 Existence, uniqueness, and regularity theory for compressible fluids and gas dynamics Keywords:mixing without volume change; nonlinear parabolic system; single-phase, miscible displacement; pressure-density relation; parabolic Galerkin procedure; concentration equation; parabolic mixed finite element technique; pressure equation; n-component model; petroleum engineering PDFBibTeX XMLCite \textit{J. Douglas jun.} and \textit{J. E. Roberts}, Math. Comput. 41, 441--459 (1983; Zbl 0537.76062) Full Text: DOI