Ewing, R. E.; Heinemann, R. F.; Koebbe, J. V.; Prasad, U. S. Velocity weighting techniques for fluid displacement problems. (English) Zbl 0631.76113 Comput. Methods Appl. Mech. Eng. 64, 137-151 (1987). Many very difficult problems arise in the numerical simulation of multiphase or multicomponent fluid flow through porous media. In order to illustrate the numerical difficulties and certain remedies in a simple context, the flow of only two incompressible fluids will be discussed in this paper. In the miscible displacement prototype, the two fluids will be assumed to mix completely to form one flowing phase with two components (called solvent and oil). In this case dispersion of the components is quite important and should be modeled and resolved if possible. In the prototype, when the fluids do not mix but flow together as separate phases, dispersion is assumed to be negligible, while the nonlinear interference between the phases is important and must be modeled carefully. For simplicity of exposition only these two prototypes will be considered. These models are both basically of convection- diffusion type with convection being the dominant process. A goal of this paper is to present techniques for controlling numerical dispersion and grid orientation problems which can be incorporated fairly easily into existing codes. The ideas arise from some of the mixed finite element and method of characteristics techniques. The techniques are intended to treat both miscible and immiscible displacements and to work efficiently even when fairly coarse grids are used. Cited in 1 Document MSC: 76S05 Flows in porous media; filtration; seepage 76T99 Multiphase and multicomponent flows 76M99 Basic methods in fluid mechanics Keywords:miscible displacement; convection-diffusion; numerical dispersion; grid orientation problems; mixed finite element; method of characteristics techniques; immiscible displacements PDFBibTeX XMLCite \textit{R. E. Ewing} et al., Comput. 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