Dual-family viscous schock waves in n conservation laws with application to multi-phase flow in porous media
Alexei Mailybaev | Marchesin, Dan
Dual-family shock | viscous profile | conservation laws | sensitivity analysis | Riemann problem | multi-phase flow | porous medium
We consider shock waves satisfying the viscous profile criterion in general systems of n conservation laws. We study Si,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 Si,j shocks, which include the Rankine-Hugoniot conditions and additional equations resulting from the viscous profile requirement. Then we 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 Si,j shocks under change of problem parameters. All possible structures of solutions of the Riemann problems containing Si,j shocks and classical waves are described. As a physical application, all types of Si,j shocks with i > j are detected and studied in a family of models for multi-phase flow in porous media.