Accuracy of Bhatnagaar-Gross-Krook scheme in solving laminar viscous flow problems

This paper describes the development of a gas-kinetic solver to compute laminar viscous flows in two-space dimensions via a finite difference approach. The convection flux terms of the Navier–Stokes equations are discretized by a semidiscrete finite difference method. The resulting inviscid flux fun...

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Main Authors:	Omar, Ashraf Ali E., Ong, Jiunn Chit, Asrar, Waqar, Ismail, Ahmad Faris
Format:	Article
Language:	English
Published:	The American Institute of Aeronautics and Astronautics (AIAA) 2009
Subjects:	TJ Mechanical engineering and machinery
Online Access:	http://irep.iium.edu.my/1215/ http://irep.iium.edu.my/1215/ http://irep.iium.edu.my/1215/1/Accuracy_of_Bhatnagaar.pdf

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recordtype	eprints
spelling	iium-12152011-12-14T04:17:38Z http://irep.iium.edu.my/1215/ Accuracy of Bhatnagaar-Gross-Krook scheme in solving laminar viscous flow problems Omar, Ashraf Ali E. Ong, Jiunn Chit Asrar, Waqar Ismail, Ahmad Faris TJ Mechanical engineering and machinery This paper describes the development of a gas-kinetic solver to compute laminar viscous flows in two-space dimensions via a finite difference approach. The convection flux terms of the Navier–Stokes equations are discretized by a semidiscrete finite difference method. The resulting inviscid flux function is then determined by a numerical scheme that is based on the Bhatnagaar–Gross–Krook model of the approximate collisional Boltzmann equation. The scheme is based on the direct splitting of the inviscid flux function with inclusion of particle collisions in the transport process. As for the diffusion flux terms, they are discretized by a second-order central difference scheme. The cell interface values required by the gas-kinetic scheme are reconstructed to higher-order spatial accuracy via the monotone upstream-centered schemes for conservation laws variable interpolation method. Anexplicit-type time integration method known as the modified fourth-order Runge–Kutta is employed for computing steady-state solutions. In the numerical case studies, the results obtained from the flux vector splitting Bhatnagaar–Gross–Krook scheme are compared with available experimental data, analytical solutions, the results from upwind schemes, and the results from central difference scheme to verify the accuracy and robustness of the gas-kinetic solver. The tests have shown that the Bhatnagaar–Gross–Krook scheme is able to resolve the shear layer, the shock structure, and the flow accurately as the results compare favorably with the available experimental and analytical data. The American Institute of Aeronautics and Astronautics (AIAA) 2009-04 Article PeerReviewed application/pdf en http://irep.iium.edu.my/1215/1/Accuracy_of_Bhatnagaar.pdf Omar, Ashraf Ali E. and Ong, Jiunn Chit and Asrar, Waqar and Ismail, Ahmad Faris (2009) Accuracy of Bhatnagaar-Gross-Krook scheme in solving laminar viscous flow problems. AIAA Journal, 47 (4). pp. 885-892. ISSN 0001-1452 http://www.aiaa.org/content.cfm?pageid=318&volume=47&issue=4&pubid=2&paperid=35247
repository_type	Digital Repository
institution_category	Local University
institution	International Islamic University Malaysia
building	IIUM Repository
collection	Online Access
language	English
topic	TJ Mechanical engineering and machinery
spellingShingle	TJ Mechanical engineering and machinery Omar, Ashraf Ali E. Ong, Jiunn Chit Asrar, Waqar Ismail, Ahmad Faris Accuracy of Bhatnagaar-Gross-Krook scheme in solving laminar viscous flow problems
description	This paper describes the development of a gas-kinetic solver to compute laminar viscous flows in two-space dimensions via a finite difference approach. The convection flux terms of the Navier–Stokes equations are discretized by a semidiscrete finite difference method. The resulting inviscid flux function is then determined by a numerical scheme that is based on the Bhatnagaar–Gross–Krook model of the approximate collisional Boltzmann equation. The scheme is based on the direct splitting of the inviscid flux function with inclusion of particle collisions in the transport process. As for the diffusion flux terms, they are discretized by a second-order central difference scheme. The cell interface values required by the gas-kinetic scheme are reconstructed to higher-order spatial accuracy via the monotone upstream-centered schemes for conservation laws variable interpolation method. Anexplicit-type time integration method known as the modified fourth-order Runge–Kutta is employed for computing steady-state solutions. In the numerical case studies, the results obtained from the flux vector splitting Bhatnagaar–Gross–Krook scheme are compared with available experimental data, analytical solutions, the results from upwind schemes, and the results from central difference scheme to verify the accuracy and robustness of the gas-kinetic solver. The tests have shown that the Bhatnagaar–Gross–Krook scheme is able to resolve the shear layer, the shock structure, and the flow accurately as the results compare favorably with the available experimental and analytical data.
format	Article
author	Omar, Ashraf Ali E. Ong, Jiunn Chit Asrar, Waqar Ismail, Ahmad Faris
author_facet	Omar, Ashraf Ali E. Ong, Jiunn Chit Asrar, Waqar Ismail, Ahmad Faris
author_sort	Omar, Ashraf Ali E.
title	Accuracy of Bhatnagaar-Gross-Krook scheme in solving laminar viscous flow problems
title_short	Accuracy of Bhatnagaar-Gross-Krook scheme in solving laminar viscous flow problems
title_full	Accuracy of Bhatnagaar-Gross-Krook scheme in solving laminar viscous flow problems
title_fullStr	Accuracy of Bhatnagaar-Gross-Krook scheme in solving laminar viscous flow problems
title_full_unstemmed	Accuracy of Bhatnagaar-Gross-Krook scheme in solving laminar viscous flow problems
title_sort	accuracy of bhatnagaar-gross-krook scheme in solving laminar viscous flow problems
publisher	The American Institute of Aeronautics and Astronautics (AIAA)
publishDate	2009
url	http://irep.iium.edu.my/1215/ http://irep.iium.edu.my/1215/ http://irep.iium.edu.my/1215/1/Accuracy_of_Bhatnagaar.pdf
first_indexed	2023-09-18T20:08:25Z
last_indexed	2023-09-18T20:08:25Z
_version_	1777407314377048064

Accuracy of Bhatnagaar-Gross-Krook scheme in solving laminar viscous flow problems

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