Construction of high-order accurate shock-capturing finite difference schemes for unsteady shock waves

V. V. Ostapenko

Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki, Tome 40 (2000) no. 12, pp. 1857-1874

Bibliographie

[1] Lax P. D., Hyperbolic systems of conservation laws and the mathematicaltheory of shock waves, Soc. Industr. and Appl. Math., Philadelphia, 1972 | Zbl

[2] Rozhdestvenskii B. L., Yanenko N. N., Sistemy kvazilineinykh uravnenii, Nauka, M., 1978 | MR

[3] Le Veque R. J., Numerical methods of conservation laws, Birkhauser Verlag, Basel, Boston, 1992 | MR

[4] Voevodin A. F., Shugrin S. M., Metody resheniya odnomernykh evolyutsionnykh sistem, Nauka, Novosibirsk, 1993 | MR

[5] Lax P., Wendroff B., “Systems of conservation laws”, Communs Pure and Appl. Math., 13 (1960), 217–237 | DOI | MR | Zbl

[6] Goldin V. Ya., Kalitkin N. N., Shitova T. V., “Nelineinye raznostnye skhemy dlya giperbolicheskikh uravnenii”, Zh. vychisl. matem. i matem. fiz., 5:5 (1965), 938–944 | MR

[7] Rusanov V. V., “Raznostnye skhemy tretego poryadka tochnosti dlya skvoznogo rascheta razryvnykh reshenii”, Dokl. AN SSSR, 180:6 (1968), 1303–1305 | MR | Zbl

[8] Kolgan V. P., “Primenenie operatorov sglazhivaniya v raznostnykh skhemakh vysokogo poryadka tochnosti”, Zh. vychisl. matem. i matem. fiz., 18:5 (1978), 1340–1345 | MR | Zbl

[9] Van Leer B., “Toward the ultimate conservative difference scheme. V. A second-order sequel to Godunov's method”, J. Comput. Phys., 32:1 (1979), 101–136 | DOI | MR

[10] Kholodov A. S., “O postroenii raznostnykh skhem povyshennogo poryadka tochnosti dlya uravnenii giperbolicheskogo tipa”, Zh. vychisl. matem. i matem. fiz., 20:6 (1980), 1601–1620 | MR | Zbl

[11] Harten A., “High resolution schemes for hyperbolic conservation laws”, J. Comput. Phys., 49 (1983), 357–393 | DOI | MR | Zbl

[12] Harten A., Osher S., “Uniformly high-order accurate nonoscillatory schemes”, SIAM J. Numer. Analys., 24:2 (1987), 279–309 | DOI | MR | Zbl

[13] Tolstykh A. I., Kompaktnye raznostnye skhemy i ikh primenenie v zadachakh aerogidrodinamiki, Nauka, M., 1990 | MR

[14] Pinchukov V. I., “O postroenii monotonnykh skhem tipa prediktor-korrektor proizvolnogo poryadka approksimatsii”, Matem. modelirovanie, 3:9 (1991), 95–103 | MR | Zbl

[15] Dai W., Woodward P. R., “A second-order unsplit godunov scheme for two- and three-dimensional euler equations”, J. Comput. Phys., 134 (1997), 261–181 | DOI | MR

[16] Ostapenko V. V., “O approksimatsii zakonov sokhraneniya raznostnymi skhemami skvoznogo scheta”, Zh. vychisl. matem. i matem. fiz., 30:9 (1990), 1405–1417 | MR

[17] Ostapenko V. V., “O povyshenii poryadka slaboi approksimatsii zakonov sokhraneniya na razryvnykh resheniyakh”, Zh. vychisl. matem. i matem. fiz., 36:10 (1996), 146–157 | MR | Zbl

[18] Ostapenko V. V., “O skhodimosti raznostnykh skhem za frontom nestatsionarnoi udarnoi volny”, Zh. vychisl. matem. i matem. fiz., 37:10 (1997), 1201–1212 | MR | Zbl

[19] Casper J., Carpenter M. N., “Computational consideration for the simulation of shock-induced sound”, SIAN J. Sci. Comput., 19:1 (1998) | MR | Zbl

[20] Engquist B., Sjogreen B., “The convergence rate of finite difference schemes in the presence of shocks”, SIAM J. Numer. Analys., 35 (1998), 2464–2485 | DOI | MR | Zbl

[21] Hirsh R., “Higher order accurate difference solutions of a fluid mechanics problems by a compact differencing technique”, J. Comput. Phys., 19:1 (1975), 90–109 | DOI | MR | Zbl

[22] Ciment M., Leventhal S. H., Weinberg B. C., “The operator compact implicit method for parabolic equations”, J. Comput. Phys., 28:2 (1978), 135–166 | DOI | MR | Zbl

[23] Berger A. E., Solomon J. M., Ciment M. et al., “Generalized OCI schemes for boundary layer problems”, Math. Comput., 35:6 (1980), 695–731 | MR

[24] Ostapenko V. V., “Difference scheme of high accuracy in the area of influence of nonstationary shock”, Proc. Sec. Internat. Conf. “Finite-Difference Methods: Theory and Applic” (Minsk, Belarus. 1998), 3, 27–31 | MR

[25] Ostapenko V. V., “Raznostnaya skhema povyshennogo poryadka skhodimosti na nestatsionarnoi udarnoi volne”, Sibirskii zh. vychisl. matem., 2:1 (1999), 47–56 | MR | Zbl

[26] Ostapenko V. V., “O konechno-raznostnoi approksimatsii uslovii Gyugonio na fronte udarnoi volny, rasprostranyayuscheisya s peremennoi skorostyu”, Zh. vychisl. matem. i matem. fiz., 38:8 (1998), 1355–1367 | MR | Zbl

[27] Ostapenko V. V., “Approksimatsiya uslovii Gyugonio yavnymi konservativnymi raznostnymi skhemami na nestatsionarnykh udarnykh volnakh”, Sibirskii zh. vychisl. matem., 1:1 (1998), 77–88 | MR

[28] Ostapenko V. V., “O lokalnom vypolnenii zakonov sokhraneniya na fronte razmazannoi udarnoi volny”, Matem. modelirovanie, 2:7 (1990), 129–138 | MR | Zbl

[29] Ostapenko V. V., “O skhodimosti na udarnoi volne raznostnykh skhem skvoznogo scheta, invariantnykh otnositelno preobrazovaniya podobiya”, Zh. vychisl. matem. i matem. fiz., 26:11 (1986), 1661–1678 | MR | Zbl

[30] Ostapenko V. V., “Ob ekvivalentnykh opredeleniyakh ponyatiya konservativnosti dlya konechno-raznostnykh skhem”, Zh. vychisl. matem. i matem. fiz., 29:8 (1989), 1114–1128 | MR

[31] Belotserkovskii O. M., Byrkin A. P., Mazurov A. P., Tolstykh A. I., “Raznostnyi metod povyshennoi tochnosti dlya rascheta techenii vyazkogo gaza”, Zh. vychisl. matem. i matem. fiz., 22:6 (1982), 1480–1490 | MR

[32] Godunov S. K., “Raznostnyi metod chislennogo rascheta razryvnykh reshenii uravnenii gidrodinamiki”, Matem. sb., 47:3 (1959), 271–306 | MR | Zbl