Dan Marchesin

TL;DR: In this article, a front tracking method was used to calculate fluid interface discontinuities in a coarse grid. But this method is not suitable for solving the problem of petroleum reservoir simulation.

TL;DR: In this paper, a mathematical model for deep bed filtration containing two empirical parameters is proposed. But, given pressure drop data in seawater coreflood laboratory experiments, the authors prove that given pressure difference between the core inlet and the core outlet, the problem of determining the formation damage coefficient is an inverse problem that determines only a combination of these two parameters, rather than each of them.

TL;DR: Transitional shock waves are discontinuous solutions that possess viscous profiles but do not conform to the Lax characteristic criterion; they are sensitive to the precise form of the physical viscosity.

TL;DR: In this paper, the authors used the random choice method to compute the oil-water interface for two dimensional porous media equations and showed that it is a correct numerical procedure for this problem even in the highly fingered case.