Numerical Solutions of One-Pressure Models in Multifluid Flows

Flows of a mixture of several fluids can be described by one-pressure models; their formulation is formally simple, and their efficiency has been recognized. But from the mathematical viewpoint they present severe peculiarities: they are not hyperbolic, appear to be ill posed, and are in nonconserva...

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Bibliographic Details
Published in:SIAM journal on numerical analysis 1995-08, Vol.32 (4), p.1139-1154
Main Authors: Berger, Fabienne, Colombeau, Jean-Francois
Format: Article
Language:English
Subjects:
Ambiguity
Approximation
Cauchy problem
Computational methods in fluid dynamics
Difference and functional equations, recurrence relations
Energy
Exact sciences and technology
Fluid dynamics
Fluids
Fundamental areas of phenomenology (including applications)
Gases
Infinitesimals
Liquids
Mathematical functions
Mathematical methods in physics
Mathematics
Multiphase and particle-laden flows
Nonhomogeneous flows
Numerical analysis
Numerical analysis. Scientific computation
Numerical approximation and analysis
Ordinary and partial differential equations, boundary value problems
Physics
Sciences and techniques of general use
Shock waves
State law
State laws
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Summary:Flows of a mixture of several fluids can be described by one-pressure models; their formulation is formally simple, and their efficiency has been recognized. But from the mathematical viewpoint they present severe peculiarities: they are not hyperbolic, appear to be ill posed, and are in nonconservative form, so they show ambiguous products of distributions in case of shock waves. A resolution of these ambiguities is proposed. It gives jump conditions similar to the classical Rankine-Hugoniot jump conditions of conservative systems. This resolution attempts to solve the Riemann problem and then the Cauchy problem by Godunov type schemes, following nonconservative techniques initiated by A. Y. Le Roux and collaborators.
ISSN:0036-1429
1095-7170
DOI:10.1137/0732052