Journal
JOURNAL OF COMPUTATIONAL PHYSICS
Volume 230, Issue 8, Pages 2997-3014Publisher
ACADEMIC PRESS INC ELSEVIER SCIENCE
DOI: 10.1016/j.jcp.2011.01.001
Keywords
Finite difference schemes; Compressible flows; Energy conservation; Split convective operators; Generalized curvilinear coordinates
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We discuss stabilization strategies for finite-difference approximations of the compressible Euler equations in generalized curvilinear coordinates that do not rely on explicit upwinding or filtering of the physical variables. Our approach rather relies on a skew-symmetric-like splitting of the convective derivatives, that guarantees preservation of kinetic energy in the semi-discrete, low-Mach-number limit. A locally conservative formulation allows efficient implementation and easy incorporation into existing compressible flow solvers. The validity of the approach is tested for benchmark flow cases, including the propagation of a cylindrical vortex, and the head-on collision of two vortex dipoles. The tests support high accuracy and superior stability over conventional central discretization of the convective derivatives. The potential use for DNS/LES of turbulent compressible flows in complex geometries is discussed. (C) 2011 Elsevier Inc. All rights reserved.
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