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The numerical simulation of two-dimensional fluid flow with strong shocks. (English) Zbl 0573.76057

The paper presents a comparison of numerical methods for simulating hydrodynamics - two-dimensional fluid flow with strong shocks. A substantial entropy production is defined as ”strong shocks”. In the case of shocks in air, Mach numbers of three and greater are used in the paper. The flow discontinuities that result due to strong shocks are treated using three approaches - artificial viscosity, blending of low- and high-order-accurate fluxes, and the use of nonlinear solutions to Riemann’s problem. Three test problems are used to illustrate the advantages and disadvantages of each approach. The paper restricts itself to the case of uniform, square computational zones in Cartesian coordinates.
Reviewer: S.Sankar

MSC:

76L05 Shock waves and blast waves in fluid mechanics
76M99 Basic methods in fluid mechanics

Software:

KRAKEN
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[1] Von Neumann, J.; Richtmyer, R. D., J. Appl. Phys., 21, 232 (1950) · Zbl 0037.12002
[2] Godunov, S. K., Mat. Sb., 47, 271 (1959)
[3] Courant, R.; Friedrichs, K. O., Supersonic Flow and Shock Waves (1948), Interscience: Interscience New York · Zbl 0041.11302
[4] Van Leer, B., J. Comput. Phys., 23, 276 (1977) · Zbl 0339.76056
[5] Van Leer, B., J. Comput. Phys., 32, 101 (1979) · Zbl 1364.65223
[6] Van Leer, B.; Woodward, P. R., (Proceedings, TICOM Conference. Proceedings, TICOM Conference, Austin, Texas (1979))
[7] Woodward, P. R.; Collela, P., (Lecture Notes in Physics No. 141 (1981), Springer-Verlag: Springer-Verlag New York/Berlin), 434
[9] Colella, P.; Woodward, P. R., The piecewise parabolic method (PPM) for gas-dynamcal simulations, J. Comput. Phys., 54 (1984) · Zbl 0531.76082
[10] Glimm, J., Comm. Pure Appl. Math., 18, 697 (1965) · Zbl 0141.28902
[11] Chorin, A. J., J. Comput. Phys., 22, 517 (1976) · Zbl 0354.65047
[12] Sod, G. A., J. Comput. Phys., 27, 1 (1978) · Zbl 0387.76063
[13] Colella, P., SIAM J. Sci. Statist. Comput., 3, 76 (1982) · Zbl 0502.76073
[14] Chorin, A. J., J. Comput. Phys., 25, 253 (1977) · Zbl 0403.65049
[15] Teng, Z.-H.; Liu, T.-P.; Chorin, A. J., SIAM J. Appl. Math., 42, 964 (1982) · Zbl 0502.76088
[17] Noh, W. F.; Gee, M.; Kramer, G., Lawrence Livermore National Laboratory Report UCID-18515 (1979)
[18] Gropp, W. D., SIAM J. Sci. Statist. Comput., 1, 191 (1980) · Zbl 0445.65096
[21] Woodward, P. R., Trade-offs in designing explicit hydrodynamics schemes for vector computers, (Rodrigue, G., Parallel Computation (1982), Academic Press: Academic Press New York)
[22] Eggleton, P., Mont. Not. Roy. Astron, Soc., 151, 351 (1971)
[23] Castor, J. I.; Davis, C. G.; Davison, D. K., Dynamical Zoning within a Lagrangian Mesh by Use of DYN, a Stellar Pulsation Code, (Los Alamos National Laboratory Report LA-66640 (1977))
[24] Winkler, K.-H. A., (Technical Report MPI-PAE/Astro 90 (1976), Max-Planck-Inst. Phys. Astrophys: Max-Planck-Inst. Phys. Astrophys Garching, West Germany)
[25] Tscharnuter, W. M.; Winkler, K.-H. A., Comput. Phys. Comm., 18, 171 (1979)
[26] Winkler, K.-H. A.; Newman, M. J., Astrophys. J., 238, 311 (1980)
[27] Dwyer, H. A.; Raiszadeh, F.; Otey, G., (Lecture Notes in Physics No. 141 (1981), Springer-Verlag: Springer-Verlag New York/Berlin), 170
[29] Gelinas, R. J.; Doss, S. K.; Miller, K., J. Comput. Phys., 40, 202 (1981) · Zbl 0482.65061
[30] Debar, R., Fundamentals of the KRAKEN Code, (E. O. Lawrence Livermore National Laboratory Report UCIR-760 (1974))
[31] Harten, A.; Zwas, G., J. Comput. Phys., 6, 568 (1972) · Zbl 0244.76033
[32] Boris, J. P.; Book, D. L., J. Comput. Phys., 11, 38 (1973) · Zbl 0251.76004
[33] Boris, J. P., Flux-Corrected Transport Modules for Solving Generalized Continuity Equations, N.R.L. Memorandum Report 3237 (1976)
[34] Zalesak, S. T., J. Comput. Phys., 31, 335 (1979) · Zbl 0416.76002
[35] Harten, A., The Method of Articial Compression, (AEC Research and Development Report C003077-50 (1974), New York University)
[37] Colella, P.; Glaz, H., Efficient Algorithms for the Solution of the Riemann Problem for Real Gases, Lawrence Berkeley Laboratory Report LBL-15776 (1983)
[38] Emery, A. E., J. Comput. Phys., 2, 306 (1968) · Zbl 0155.21102
[39] Ben-Dor, G.; Glass, I. I., J. Fluid Mech., 92, 459 (1979)
[40] Book, D.; Boris, J.; Kuhl, A.; Oran, E.; Picone, M.; Zalesak, S., (Lecture Notes in Physics No. 141 (1981), Springer-Verlag: Springer-Verlag New York/Berlin), 84
[41] Fursenko, A. A.; Golovizin, V. P.; Komissaruk, V. A.; Mende, N. P.; Zhmakin, A. I., Leningrad Physical-Technical Institute Report No. 709 (1981)
[42] Birkhoff, G.; MacDougall, D. P.; Pugh, E. M.; Taylor, G., J. Appl. Phys., 19, 563 (1948)
[43] MacCormack, R., (Lecture Notes in Physics No. 8 (1971), Springer-Verlag: Springer-Verlag New York/Berlin)
[44] Richtmyer, R. D.; Morton, K. W., Difference Methods for Initial Value Problems (1967), Interscience: Interscience New York · Zbl 0155.47502
[45] Lapidus, A., J. Comput. Phys., 2, 154 (1967) · Zbl 0152.44804
[46] Sutcliffe, W. G., BBC Hydrodynamics, E. O. Lawrence Livermore National Laboratory Report UCID-17013 (1973)
[47] Strang, G., SIAM J. Numer. Anal., 5, 506 (1968) · Zbl 0184.38503
[48] Ikeda, T.; Nakagawa, T., Math. Comp., 33, 1157 (1979) · Zbl 0497.65050
[49] Godunov, S. K.; Zabrodyn, A. W.; Prokopov, G. P., Zh. Vycisl. Mat. Fiz., 1, 1020 (1961)
[51] van Leer, B., On the Relation between the Upwind Differencing Schemes of Godunov, Engquist-Osher, and Roe, (ICASE Report No. 81-11 (1981)) · Zbl 0547.65065
[52] Osher, S.; Solomon, F., Math. Comp., 38, 339 (1982) · Zbl 0483.65055
[53] Harten, A.; Lax, P. D., SIAM J. Numer. Anal., 18, 289 (1981) · Zbl 0467.65038
[54] Roe, P. L., J. Comput. Phys., 43, 357 (1981) · Zbl 0474.65066
[55] Saltzman, J., (Courant Math. Res. DOE/ER/03077/174 (1982))
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