On the sufficient conditions for the S-shaped Buckley-Leverett function
Classical Analysis and ODEs
2023-05-30 v2
Abstract
The flux function in the Buckley-Leverett equation, that is, the function characterizing the ratio of the relative mobility functions of the two phases, is considered. The common conjecture stating that any convex mobilities result in an S-shaped Buckley-Leverett function is analyzed and disproved by a counterexample. Additionally, sufficient conditions for the S-shaped Buckley-Leverett function are given. The class of functions satisfying those conditions is proven to be closed under multiplication. Some functions from known relative mobility models are confirmed to be in that class.
Keywords
Cite
@article{arxiv.2303.16803,
title = {On the sufficient conditions for the S-shaped Buckley-Leverett function},
author = {Nikita Rastegaev},
journal= {arXiv preprint arXiv:2303.16803},
year = {2023}
}