Dual-Family Viscous Shock Waves in n Conservation Laws with Application to Multi-Phase Flow in Porous Media |
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Authors: | Dan Marchesin Alexei A Mailybaev |
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Institution: | (1) Instituto Nacional de Matemática Pura e Aplicada – IMPA, Estrada Dona Castorina 110, 22460-320 Rio de Janeiro, RJ, Brazil;(2) Institute of Mechanics, Moscow State Lomonosov University, Michurinsky pr. 1, 119192 Moscow, Russia |
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Abstract: | We consider shock waves satisfying the viscous profile criterion in general systems of n conservation laws. We study S
i, j
dual-family shock waves, which are associated with a pair of characteristic families i and j. We explicitly introduce defining equations relating states and speeds of S
i, j
shocks, which include the Rankine–Hugoniot conditions and additional equations resulting from the viscous profile requirement.
We then develop a constructive method for finding the general local solution of the defining equations for such shocks and
derive formulae for the sensitivity analysis of S
i, j
shocks under change of problem parameters. All possible structures of solutions to the Riemann problems containing S
i, j
shocks and classical waves are described. As a physical application, all types of S
i, j
shocks with i>j are detected and studied in a family of models for multi-phase flow in porous media. |
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Keywords: | |
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