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Evaluation of an energy relaxation method for the simulation of unsteady, viscous, real gas flows
Author(s) -
Bongiovanni Emmanuel,
Ern Alexandre,
GlinskyOlivier Nathalie
Publication year - 2004
Publication title -
international journal for numerical methods in fluids
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.938
H-Index - 112
eISSN - 1097-0363
pISSN - 0271-2091
DOI - 10.1002/fld.728
Subject(s) - discretization , mechanics , finite volume method , relaxation (psychology) , shock tube , computational fluid dynamics , shock (circulatory) , navier–stokes equations , compressibility , physics , perfect gas , finite element method , real gas , mathematics , thermodynamics , shock wave , mathematical analysis , medicine , psychology , social psychology
This study investigates a new energy relaxation method designed to capture the dynamics of unsteady, viscous, real gas flows governed by the compressible Navier–Stokes equations. We focus on real gas models accounting for inelastic molecular collisions and yielding temperature‐dependent heat capacities. The relaxed Navier–Stokes equations are discretized using a mixed finite volume/finite element method and a high‐order time integration scheme. The accuracy of the energy relaxation method is investigated on three test problems of increasing complexity: the advection of a periodic set of vortices, the interaction of a temperature spot with a weak shock, and finally, the interaction of a reflected shock with its trailing boundary layer in a shock tube. In all cases, the method is validated against benchmark solutions and the numerical errors resulting from both discretization and energy relaxation are assessed independently. Copyright © 2004 John Wiley & Sons, Ltd.