2019/06/16 by Koondanibha Mitra, Mitra, Koondanibha, Tobias Köppl +9
Computer Science · Engineering · Mathematics · #65N12 #65N15 #65N30 #78M34 #Advanced Mathematical Modeling in Engineering #Advanced Numerical Methods in Computational Mathematics #Dynamical Systems (math.DS) #FOS: Mathematics #Fluid Dynamics and Thin Films #math.DS #msc:65N12 #msc:65N15 #msc:65N30 #msc:78M34
paper · pdf · doi:10.48550/arxiv.1906.08134
openalex publication_date 2019/06/16 · arxiv created 2019/06/20 · arxiv updated 2019/06/21 · openalex created_date 2019/06/27 · openalex updated_date 2026/07/28
In this work, we study the behaviour of saturation fronts for two phase flow through a long homogeneous porous column. In particular, the model includes hysteresis and dynamic effects in the capillary pressure and hysteresis in the permeabilities. The analysis uses travelling wave approximation. Entropy solutions are derived for Riemann problems that are arising in this context. These solutions belong to a much broader class compared to the standard Oleinik solutions, where hysteresis and dynamic effects are neglected. The relevant cases are examined and the corresponding solutions are categorized. They include non-monotone profiles, multiple shocks and self-developing stable saturation plateaus. Numerical results are presented that illustrate the mathematical analysis. Finally, we compare experimental results with our theoretical findings.