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High order conservative finite difference scheme for variable density low Mach number turbulent flows

Desjardins, Olivier and Blanquart, Guillaume and Balarac, Guillaume and Pitsch, Heinz (2008) High order conservative finite difference scheme for variable density low Mach number turbulent flows. Journal of Computational Physics, 227 (15). pp. 7125-7159. ISSN 0021-9991. doi:10.1016/

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The high order conservative finite difference scheme of Morinishi et al. [Y. Morinishi, O.V. Vasilyev, T. Ogi, Fully conservative finite difference scheme in cylindrical coordinates for incompressible flow simulations, J. Comput. Phys. 197 (2004) 686] is extended to simulate variable density flows in complex geometries with cylindrical or cartesian non-uniform meshes. The formulation discretely conserves mass, momentum, and kinetic energy in a periodic domain. In the presence of walls, boundary conditions that ensure primary conservation have been derived, while secondary conservation is shown to remain satisfactory. In the case of cylindrical coordinates, it is desirable to increase the order of accuracy of the convective term in the radial direction, where most gradients are often found. A straightforward centerline treatment is employed, leading to good accuracy as well as satisfactory robustness. A similar strategy is introduced to increase the order of accuracy of the viscous terms. The overall numerical scheme obtained is highly suitable for the simulation of reactive turbulent flows in realistic geometries, for it combines arbitrarily high order of accuracy, discrete conservation of mass, momentum, and energy with consistent boundary conditions. This numerical methodology is used to simulate a series of canonical turbulent flows ranging from isotropic turbulence to a variable density round jet. Both direct numerical simulation (DNS) and large eddy simulation (LES) results are presented. It is observed that higher order spatial accuracy can improve significantly the quality of the results. The error to cost ratio is analyzed in details for a few cases. The results suggest that high order schemes can be more computationally efficient than low order schemes.

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URLURL TypeDescription DOIArticle
Blanquart, Guillaume0000-0002-5074-9728
Additional Information:Copyright © 2008 Elsevier. Received 18 September 2007; revised 11 March 2008; accepted 13 March 2008. Available online 28 March 2008. The authors wish to express their gratitude to Mr. Ed Knudsen for his immense help in the development of the code used for the simulations in this paper. We are also thankful to Mr. Shashank and Dr. Vincent Moureau for their fruitful comments on a draft of this manuscript. We also gratefully acknowledge funding by NASA and by the DOE through the ASC program.
Funding AgencyGrant Number
Department of Energy (DOE)UNSPECIFIED
Subject Keywords:High order scheme; Finite difference scheme; Low Mach number; Variable density; Energy conservation; Conservative scheme; Cylindrical coordinates; Boundary conditions; DNS; LES
Issue or Number:15
Record Number:CaltechAUTHORS:20091008-132109270
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Official Citation:Olivier Desjardins, Guillaume Blanquart, Guillaume Balarac, Heinz Pitsch, High order conservative finite difference scheme for variable density low Mach number turbulent flows, Journal of Computational Physics, Volume 227, Issue 15, 20 July 2008, Pages 7125-7159, ISSN 0021-9991, (
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:16219
Deposited By: George Porter
Deposited On:09 Oct 2009 15:22
Last Modified:08 Nov 2021 23:25

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