Title: EVALUATION OF GAS-KINETIC SCHEMES FOR SOLVING 1D INVISCID COMPRESSIBLE FLOW PROBLEMS
Abstract: International Journal of Computational Engineering ScienceVol. 04, No. 04, pp. 829-851 (2003) No AccessEVALUATION OF GAS-KINETIC SCHEMES FOR SOLVING 1D INVISCID COMPRESSIBLE FLOW PROBLEMSJIUNN CHIT ONG, ASHRAF ALI OMAR, and WAQAR ASRARJIUNN CHIT ONGDepartment of Aerospace Engineering, Faculty of Engineering, University Putra Malaysia, 43400, Serdang, Selangor, D.E., Malaysia Search for more papers by this author , ASHRAF ALI OMARDepartment of Aerospace Engineering, Faculty of Engineering, University Putra Malaysia, 43400, Serdang, Selangor, D.E., Malaysia Search for more papers by this author , and WAQAR ASRARDepartment of Mechanical Engineering, Faculty of Engineering, International Islamic University Malaysia, Jalan Gombak, 53100 Kuala Lumpur, Malaysia Search for more papers by this author https://doi.org/10.1142/S1465876303002192Cited by:5 PreviousNext AboutSectionsPDF/EPUB ToolsAdd to favoritesDownload CitationsTrack CitationsRecommend to Library ShareShare onFacebookTwitterLinked InRedditEmail AbstractIn this paper, two classes of gas-kinetic schemes are investigated for one-dimensional compressible inviscid flow, namely, the Kinetic Flux Vector Splitting (KFVS) scheme and the Bhatnagar-Gross-Krook (BGK) scheme. Second-order high-resolution scheme for both methods are also developed for calculating flows containing discontinuities. This is achieved by means of reconstructing the initial data via Monotone Upstream-Centered Schemes for Conservation Laws (MUSCL) approach. The Total Variation Diminishing (TVD) shock capturing properties of these second-order schemes are achieved through the use of non-linear limiters. In addition, a multistage TVD Runge-Kutta method is employed for the time integration of the finite volume gas-kinetic scheme. Exclusive consideration is focused on the BGK scheme, which yields a better numerical result in comparison with the KFVS scheme. Three typical one-dimensional inviscid flow problems containing shocks, namely, steady flow in a divergent nozzle, the unsteady shock tube problem, and two interacting blast waves problem are analyzed numerically with the gas-kinetic schemes. Numerical results from the first-order and second-order gas-kinetic schemes are presented and compared with the exact solutions. Other computed results such as those from the Steger-Warming's Flux Vector Splitting scheme, Roe's Flux Difference Splitting scheme, MacCormack's scheme, and high-order compact Van Leer's Flux Splitting Scheme are also presented as comparisons to the gas-kinetic schemes. In addition, the effects of grid sizes on the numerical results of the gas-kinetic schemes are also investigated.Keywords:Gas-kinetic schemesHigh-resolution schemeMUSCL approachcompressible inviscid flow References C. Hirsch , The Numerical Computation of Internal and External Flows 2 ( John Wiley & Sons , 1990 ) . Google Scholar K. Xu, "Entropy Analysis of Kinetic Flux Vector Splitting Schemes for the Compressible Euler Equations", ICASE Report, 99-5, 1999 . Google Scholar K. 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Mahmood et al. , A High-Order Shock Capturing Scheme for Inviscid Flows , 2nd World Engineering Congress Sarawak ( 2002 ) . Google ScholarP. Woodward and P. Colella, J. Comput. Phys. 54, 115 (1984), DOI: 10.1016/0021-9991(84)90142-6. Crossref, Google Scholar FiguresReferencesRelatedDetailsCited By 5Accuracy of Bhatnagaar-Gross-Krook Scheme in Solving Laminar Viscous Flow ProblemsAshraf A. Omar, Ong J. Chit, Waqar Asrar and Ahmad F. Ismail1 Apr 2009 | AIAA Journal, Vol. 47, No. 4Finite difference gas-kinetic BGK scheme for compressible inviscid flow computationAshraf A. Omar, Ong J. Chit, Lim J. Hsuh and Waqar Asrar1 Mar 2008 | International Journal of Computational Fluid Dynamics, Vol. 22, No. 3Hypersonic Flow Simulation by the Gas-Kinetic Bhatnagar-Gross-Krook SchemeOng J. Chit, Ashraf A. Omar, Waqar Asrar and Zairil A. Zaludin1 Jul 2005 | AIAA Journal, Vol. 43, No. 7Implicit Gas-Kinetic Bhatnagar-Gross-Krook Scheme for Compressible FlowsOng Jiunn Chit, Ashraf Ali Omar, Waqar Asrar and Megat Mohammad Hamdan1 Jul 2004 | AIAA Journal, Vol. 42, No. 7Development of Gas-Kinetic BGK Scheme for Two-Dimensional Compressible Inviscid FlowsOng Chit, Ashraf Omar, Waqar Asrar and Megat Hamdan19 June 2004 Recommended Vol. 04, No. 04 Metrics History Received 30 August 2002 Revised 16 April 2003 KeywordsGas-kinetic schemesHigh-resolution schemeMUSCL approachcompressible inviscid flowPDF download
Publication Year: 2003
Publication Date: 2003-12-01
Language: en
Type: article
Indexed In: ['crossref']
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Cited By Count: 10
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