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STABILIZED, MULTISCALE, AND MULTIPHYSICS METHODS IN FLUID MECHANICS

Three-Dimensional Edge-Based SUPG Computation of Inviscid Compressible Flows With YZβ Shock-Capturing

[+] Author and Article Information
Lucia Catabriga

Department of Computer Science, Federal University of Espírito Santo, Avenida Fernando Ferrari 514, Vitória, ES 29075-910, Brazilluciac@inf.ufes.br

Denis A. F. de Souza

Laboratory for Computational Methods in Engineering (LAMCE), Federal University of Rio de Janeiro, P.O. Box 68506, Rio de Janeiro, RJ 21945-970, Brazildenis@lamce.coppe.ufrj.br

Alvaro L. G. A. Coutinho

Department of Civil Engineering-COPPE and Center for Parallel Computations, Federal University of Rio de Janeiro, P.O. Box 68506, Rio de Janeiro, RJ 21945-970, Brazilalvaro@nacad.ufrj.br

Tayfun E. Tezduyar

Mechanical Engineering, Rice University, MS 321, 6100 Main Street, Houston, TX 77005tezduyar@rice.edu

J. Appl. Mech 76(2), 021208 (Jan 15, 2009) (7 pages) doi:10.1115/1.3062968 History: Received July 08, 2008; Revised August 28, 2008; Published January 15, 2009

The streamline-upwind/Petrov–Galerkin (SUPG) formulation of compressible flows based on conservation variables, supplemented with shock-capturing, has been successfully used over a quarter of a century. In this paper, for inviscid compressible flows, the YZβ shock-capturing parameter, which was developed recently and is based on conservation variables only, is compared with an earlier parameter derived based on the entropy variables. Our studies include comparing, in the context of these two versions of the SUPG formulation, computational efficiency of the element- and edge-based data structures in iterative computation of compressible flows. Tests include 1D, 2D, and 3D examples.

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Copyright © 2009 by American Society of Mechanical Engineers
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Figures

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Figure 1

1D shock tube. Mesh.

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Figure 2

1D shock tube. Solutions at t=0.2. (a) Density, (b) velocity, and (c) pressure.

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Figure 3

2D flow in a channel with a step. Mesh until x1=0.7.

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Figure 4

2D flow in a channel with a step. Density obtained with δ91. (a) t=0.3, (b) t=0.6, and (c) t=1.2.

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Figure 5

2D flow in a channel with a step. Density obtained with νSHOC. (a) t=0.3, (b) t=0.6, and (c) t=1.2.

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Figure 6

2D flow in a channel with a step. Distribution of δ91. (a) t=0.3, (b) t=0.6, and (c) t=1.2.

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Figure 7

2D flow in a channel with a step. Distribution of νSHOC. (a) t=0.3, (b) t=0.6, and (c) t=1.2.

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Figure 8

3D flow around a sphere. Dimensions of the problem domain. The cylinder is located at x1=8.

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Figure 9

3D flow around a sphere. Mesh.

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Figure 10

3D flow around a sphere. Density obtained with δ91.

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Figure 11

3D flow around a sphere. Density obtained with νSHOC.

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