Asymptotic analysis of coupled problems for compressible flows
We consider a two-dimensional coupled transmission problem with the conservation laws for compressible viscous flows, where in a subdomain of the flow-field domain the terms modelling the viscosity and heat conductivity effects are strongly dominated by the convective part. In order to approximate the physical solution, we construct a reduced problem including the Navier-Stokes/Euler coupling of equations. An asymptotic analysis based on singular perturbation theory includes vector-valued boundary layer functions which are used in order to establish transmission conditions at the artificial interface and to improve the solution of the reduced coupled problem. We present numerical results confirming our asymptotic analysis, and an application associated with magneto-plasma-dynamic (MPD) flows.
KeywordsMach Number Asymptotic Analysis Compressible Flow Transmission Condition Couple Problem
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