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STABILIZED, MULTISCALE, AND MULTIPHYSICS METHODS IN FLUID MECHANICS

# Computation of Inviscid Supersonic Flows Around Cylinders and Spheres With the V-SGS Stabilization and $YZβ$ Shock-Capturing

[+] Author and Article Information
Franco Rispoli

Dipartimento di Meccanica e Aeronautica, Università degli Studi di Roma “La Sapienza,” Via Eudossiana 18, I-00184 Roma, Italyfranco.rispoli@uniroma1.it

Rafael Saavedra

Departamento de Ingeneria Mecánica-Electrica, Universidad de Piura, Avenida Ramón Mugica 131, Piura, Perúrsaavedr@udep.edu.pe

Filippo Menichini

Dipartimento di Meccanica e Aeronautica, Università degli Studi di Roma “La Sapienza,” Via Eudossiana 18, I-00184 Roma, Italyf.menichini@dma.ing.uniroma1.it

Tayfun E. Tezduyar

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

J. Appl. Mech 76(2), 021209 (Jan 26, 2009) (6 pages) doi:10.1115/1.3057496 History: Received November 21, 2007; Revised July 09, 2008; Published January 26, 2009

## Abstract

The $YZβ$ shock-capturing technique was introduced originally for use in combination with the streamline-upwind/Petrov–Galerkin (SUPG) formulation of compressible flows in conservation variables. It is a simple residual-based shock-capturing technique. Later it was also combined with the variable subgrid scale (V-SGS) formulation of compressible flows in conservation variables and tested on standard 2D test problems. The V-SGS method is based on an approximation of the class of SGS models derived from the Hughes variational multiscale method. In this paper, we carry out numerical experiments with inviscid supersonic flows around cylinders and spheres to evaluate the performance of the $YZβ$ shock-capturing combined with the V-SGS method. The cylinder computations are carried out at Mach numbers 3 and 8, and the sphere computations are carried out at Mach number 3. The results compare well to those obtained with the $YZβ$ shock-capturing combined with the SUPG formulation, which were shown earlier to compare very favorably to those obtained with the well established OVERFLOW code.

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## Figures

Figure 1

2D flow around a cylinder. Structured mesh with 4096 quadrilateral elements and 4225 nodes.

Figure 2

2D flow around a cylinder at M=3 Mach number. Computed with bM=2 and bR=0.

Figure 3

2D flow around a cylinder at M=3 Mach number. Computed with bM=1 and bR=0.

Figure 4

2D flow around a cylinder at M=3 Mach number. Computed with bM=1, bR=1, and ρsca=ρ2.

Figure 5

2D flow around a cylinder at M=8 Mach number. Computed with bM=2 and bR=0.

Figure 6

2D flow around a cylinder at M=8 Mach number. Computed with bM=1 and bR=0.

Figure 7

2D flow around a cylinder at M=8 Mach number. Computed with bM=1, bR=1, and ρsca=ρ2.

Figure 8

3D flow around a sphere. Block-structured mesh with 52,896 hexahedral elements and 56,760 nodes.

Figure 9

3D flow around a sphere at M=3 Mach number. Computed with bM=1 and bR=0.

Figure 10

3D flow around a sphere at M=3 Mach number. Computed with bM=1, bR=0, and bF=1.

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