Nonexistence of Riemann solutions for a quadratic model derived from petroleum engineering
type: Item
instance of: scholarly article
title: Nonexistence of Riemann solutions for a quadratic model derived from petroleum engineering
zbMATH Open document ID: 1017.76095
DOI: 10.1016/S1468-1218(02)00004-4
author: Sunčica Čanić
published in: Nonlinear Analysis. Real World Applications
publication date: 2003-05-14T00:00:00Z
review text: This papgr shows that the viscous profile entropy criterion is too selective in reducing the number of solutions to guarantee existence of stable weak self-similar Riemann solution to conservation laws. The results presented by the author are a combination of analytical and numerical work. The theoretical ideas and techniques are derived from bifurcation theory of vector fieldd and from the theory of weak solutions of conservation laws. Numerical results are added when no theory is available. The studied model describes immiscible three-phase flows commonly encountered in petroleum reservoir engineering. The models consists of two equations describing conservation of mass for each fluid, combined with Darcy's force law.
Mathematics Subject Classification ID: 76T30
Mathematics Subject Classification ID: 76S05
Mathematics Subject Classification ID: 35Q35
zbMATH DE Number: 1910226
zbMATH Keywords: nonexistence
zbMATH Keywords: mass conservation
zbMATH Keywords: Darcy's law
zbMATH Keywords: viscous profile entropy criterion
zbMATH Keywords: self-similar Riemann solution
zbMATH Keywords: conservation laws
zbMATH Keywords: bifurcation
zbMATH Keywords: vector fieldd
zbMATH Keywords: weak solutions
zbMATH Keywords: immiscible three-phase flows
zbMATH Keywords: petroleum reservoir engineering
reviewed by: Yves Cherruault
MaRDI profile type: Publication
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full work available at URL: s1468-1218(02)00004-4
OpenAlex ID: W4246001661
description: scientific article; zbMATH DE number 1910226