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On the stability and dissipation of wall boundary conditions for compressible flows
Author(s) -
Lamarque N.,
Porta M.,
Nicoud F.,
Poinsot T.
Publication year - 2009
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.2060
Subject(s) - stability (learning theory) , boundary (topology) , dissipation , boundary value problem , neumann boundary condition , compressibility , dirichlet boundary condition , mechanics , dirichlet distribution , mathematical analysis , matrix (chemical analysis) , term (time) , mathematics , physics , materials science , computer science , thermodynamics , machine learning , composite material , quantum mechanics
Abstract Characteristic formulations for boundary conditions have demonstrated their effectiveness to handle inlets and outlets, especially to avoid acoustic wave reflections. At walls, however, most authors use simple Dirichlet or Neumann boundary conditions, where the normal velocity (or pressure gradient) is set to zero. This paper demonstrates that there are significant differences between characteristic and Dirichlet methods at a wall and that simulations are more stable when using walls modelled with a characteristic wave decomposition. The derivation of characteristic methods yields an additional boundary term in the continuity equation, which explains their increased stability. This term also allows to handle the two acoustic waves going towards and away from the wall in a consistent manner. Those observations are confirmed by stability matrix analysis and one‐ and two‐dimensional simulations of acoustic modes in cavities. Copyright © 2009 John Wiley & Sons, Ltd.