Mathematical modeling and numerical study of viscous fingering

Abstract

The main goal of the thesis is to simulate and analyze non-linear partial differential equations effeciently in Matlab. Immiscible displacement of oil by water in porous media is simulated and analyzed in Matlab. We visualized different scenarios in two dimensions by using the MRST toolbox. Multiple initial states were used on various mesh sizes and we determined optimal grid sizes to converge to the correct number of fingers. We examined the stability of viscous fingering theoretically and numerically with the help of automatic differentiation. We showed general results about the instability of the base state and determined the relationship between the growth rate and the number of fingers. We conducted a theoretical introduction of dimension splitting which could provide even faster and better results for the stability.