Morris, M. I.; Ball, R. C. Renormalization of miscible flow functions. (English) Zbl 0708.76133 J. Phys. A, Math. Gen. 23, No. 19, 4199-4209 (1990). Summary: We present a numerical renormalization study of two-phase, viscous fingering flow in a uniform two-dimensional porous medium. Iterating our procedure gives the effective flow parametrization appropriate to successively larger scales and enables us to compute flow functions that can be used to simulate kilometre-sized oil reservoirs, starting from functions appropriate to 10cm core samples. We parametrize the local flow in terms of the fractional and total flows across a block as functions of the average composition and pressure gradient across the block. From numerical simulations on a fine grid, we measure the corresponding flow functions for larger blocks: these show only limited statistical scatter and so allow us to define a renormalization. We discuss the range of physically significant fractional flow and total mobility functions, and find evidence for non-trivial fixed point behaviour of these functions in the fingering instability regime. MSC: 76S05 Flows in porous media; filtration; seepage 76T99 Multiphase and multicomponent flows Keywords:numerical renormalization study of two-phase, viscous fingering flow; uniform two-dimensional porous medium; fractional flow; total mobility functions; fingering instability regime PDFBibTeX XMLCite \textit{M. I. Morris} and \textit{R. C. Ball}, J. Phys. A, Math. Gen. 23, No. 19, 4199--4209 (1990; Zbl 0708.76133) Full Text: DOI