Nonexistence of Riemann solutions for a quadratic model derived from petroleum engineering
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.
scientific article; zbMATH DE number 1910226
scientific article