The solutions of the Riemann problem for a hyperbolic system modeling polymer flooding with hysteresis
type: Item
instance of: scholarly article
title: The solutions of the Riemann problem for a hyperbolic system modeling polymer flooding with hysteresis
zbMATH Open document ID: 0876.35074
author: K. M. Furati
published in: Journal of Mathematical Analysis and Applications
publication date: 1997-10-22T00:00:00Z
review text: The author derives a model describing two phase flow with hysteresis in porous media, in which the phases consist of water containing a dissolved polymer, and oil. For a constant concentration of polymer, the model reduces to a Buckley-Leverett equation with hysteresis. In the general case, the model consists of a nonstrictly hyperbolic system of three conservation laws concerning the saturation of water, the concentration of polymer and the hysteresis parameter -- denoted by \(\pi\) -- with a double-valued flux function, the branches of which are called primary and secondary. The author then distinguishes between six wave families, which are either stationary waves, primary or secondary Buckley-Leverett waves, primary, secondary, or \(\pi-\)field contact discontinuities. By means of these waves, he solves the Riemann problem in all possible cases.
Mathematics Subject Classification ID: 35L65
Mathematics Subject Classification ID: 76S05
zbMATH DE Number: 1005580
zbMATH Keywords: two phase flow
zbMATH Keywords: nonstrictly hyperbolic system
zbMATH Keywords: Buckley-Leverett equation
MaRDI profile type: Publication
full work available at URL: jmaa.1997.5222
OpenAlex ID: W1978336669
cites work: The Solution of the Riemann Problem for a Hyperbolic System of Conservation Laws Modeling Polymer Flooding
cites work: A system of non-strictly hyperbolic conservation laws arising in elasticity theory
cites work: Q3028637
cites work: Q3274322
cites work: The Riemann Problem for Longitudinal Motion in an Elastic-Plastic Bar
DOI: 10.1006/JMAA.1997.5222
description: scientific article; zbMATH DE number 1005580