International Journal of Computational Engineering ScienceVol. 04, No. 04, pp. 853-868 (2003) No AccessAN ACCURATE SCHEME FOR GAS DYNAMICAL CALCULATIONSMAHMOOD K. MAWLOOD, WAQAR ASRAR, ASHRAF A. OMAR, and MEGAT M. H. M. AHMADMAHMOOD K. MAWLOODDepartment of Aerospace Engineering, Faculty of Engineering, Universiti Putra Malaysia, 43400 UPM, Serdang, Selangor D. E., Malaysia Search for more papers by this author , WAQAR ASRARDepartment of Mechanical Engineering, Faculty of Engineering, International Islamic University Malaysia, Jalan Gombak, 53100 Kuala Lumpur, MalaysiaCorresponding author. Search for more papers by this author , ASHRAF A. OMARDepartment of Mechanical Engineering, Faculty of Engineering, International Islamic University Malaysia, Jalan Gombak, 53100 Kuala Lumpur, Malaysia Search for more papers by this author , and MEGAT M. H. M. AHMADDepartment of Mechanical and Manufacturing Engineering, Faculty of Engineering, Universiti Putra Malaysia, 43400 UPM, Serdang, Selangor D. E., Malaysia Search for more papers by this author https://doi.org/10.1142/S1465876303002209Cited by:0 PreviousNext AboutSectionsPDF/EPUB ToolsAdd to favoritesDownload CitationsTrack CitationsRecommend to Library ShareShare onFacebookTwitterLinked InRedditEmail AbstractAn accurate numerical method is developed for computing inviscid flows containing discontinuities. The method is based on flux vector splitting (FVS) and a third-order accurate upwind-biased compact finite-difference scheme. Two different flux splitting techniques, namely, the kinetic flux vector splitting (KFVS) and van Leer's flux splitting, are used to solve one-dimensional gas dynamics test problems. The idea of total variation diminishing (TVD) is employed to suppress spurious numerical oscillations. The stability and high-order accuracy of the scheme are shown.Keywords:High-Order Compact SchemesTotal Variation DiminishingEuler EquationsRunge-Kutta Methods References C. W. Shu, SIAM. J. Sci. Statist. Comput. 9, 1073 (1988). Crossref, Google Scholar S. Gottlieb and C. W. Shu, ICASE Report No. 2000-15, 2000 . Google ScholarS. K. Lele, J. Comp. Phys. 103, 16 (1992), DOI: 10.1016/0021-9991(92)90324-R. Crossref, Google ScholarJ. A. Ekaterinaris, J. Comp. Phys. 156, 272 (1999), DOI: 10.1006/jcph.1999.6360. Crossref, Google ScholarJ. A. Ekaterinaris, AIAA J. 38, 1594 (2000), DOI: 10.2514/2.1142. Crossref, Google ScholarM. R. Visbal and D. V. Gaitonde, AIAA J. 10, 358 (1999). Google ScholarX. Deng and H. Maekawa, J. Comp. Phys. 130, 77 (1997), DOI: 10.1006/jcph.1996.5553. Crossref, Google ScholarP. L. Roe, J. Comp. Phys. 43, 357 (1981), DOI: 10.1016/0021-9991(81)90128-5. Crossref, Google Scholar Hartenet al., J. Comp. Phys. 71, 231 (1987), DOI: 10.1016/0021-9991(87)90031-3. Crossref, Google Scholar Cockburn and C. W. Shu, SIAM J. Numer. Analy. 31, 607 (1994), DOI: 10.1137/0731033. Crossref, Google ScholarN. A. Adams and K. Shariff, J. Comp. Phys. 127, 27 (1996), DOI: 10.1006/jcph.1996.0156. Crossref, Google Scholar Fu and Y. Ma, J. Comp. Phys. 134, 1 (1997), DOI: 10.1006/jcph.1996.5492. Crossref, Google ScholarX. Zhong, J. Comp. Phys. 144, 662 (1998), DOI: 10.1006/jcph.1998.6010. Crossref, Google ScholarK. S. Ravichandran, J. Comp. Phys. 130, 161 (1997), DOI: 10.1006/jcph.1996.5561. Crossref, Google ScholarM. H. Carpenter and D. Gotlieb, J. Comp. Phys. 108, 272 (1993), DOI: 10.1006/jcph.1993.1182. Crossref, Google ScholarJ. L. Steger and R. F. Warming, J. Comp. Phys. 40, 263 (1981), DOI: 10.1016/0021-9991(81)90210-2. Crossref, Google ScholarB. Van Leer, Lecture Notes in Physics 170 (1982) p. 507. Google ScholarS. M. Deshpande and P. S. Kulkarni, Computers Math. Applic. 35, 75 (1998), DOI: 10.1016/S0898-1221(97)00259-9. Crossref, Google Scholar Hirsch , Numerical Computation of Internal and External Flows, Vol. 2: Computational Methods for Inviscid and Viscous Flows ( John Wiley & Sons , UK , 1990 ) . Google ScholarG. A. Sod, J. Comp. Phys. 27, 1 (1978), DOI: 10.1016/0021-9991(78)90023-2. Crossref, Google ScholarC. W. Shu and S. Osher, J. Comp. Phys. 83, 32 (1989), DOI: 10.1016/0021-9991(89)90222-2. Crossref, Google Scholar FiguresReferencesRelatedDetails Recommended Vol. 04, No. 04 Metrics History Revised 26 May 2003 KeywordsHigh-Order Compact SchemesTotal Variation DiminishingEuler EquationsRunge-Kutta MethodsPDF download