×

Front tracking for gas dynamics. (English) Zbl 0577.76068

Summary: Front tracking is an adaptive computational method in which a lower dimensional moving grid is fitted to and follows the dynamical evolution of distinguished waves in a fluid flow. The method takes advantage of known analytic solutions, derived from the Rankine-Hugoniot relations, for idealized discontinuities. In this paper the method is applied to the Euler equations describing compressible gas dynamics. The main thrust here is validation of the front tracking method: we present results on a series of test problems for which comparison answers can be obtained by independent methods.

MSC:

76N15 Gas dynamics (general theory)
76L05 Shock waves and blast waves in fluid mechanics
76G25 General aerodynamics and subsonic flows
PDFBibTeX XMLCite
Full Text: DOI

References:

[1] Ben-Artzi, M.; Falcovitz, J., J. Comput. Phys., 55, 1-32 (1984)
[2] Colella, P.; Woodward, P., J. Comput. Phys., 54 (1984)
[3] Courant, R.; Friedrichs, K., Supersonic Flow and Shock Waves (1948), Interscience: Interscience New York · Zbl 0041.11302
[4] Deschambault, R.; Glass, I., J. Fluid Mech., 131, 27-57 (1983)
[5] Emmons, H., Fundamentals of Gas Dynamics (1958), Princeton Univ. Press: Princeton Univ. Press Princeton, N.J
[6] Glaz, H.; Liu, T.-P., The asymptotic analysis of wave interactions and numerical calculations of transonic nozzle flow (1982), preprint
[7] Glimm, J.; Isaacson, E.; Lindquist, B.; McBryan, O.; Yaniv, S., (Frontiers in Applied Mathematics, Vol. 1 (1983), SIAM: SIAM Philadelphia), 137-160
[8] Glimm, J.; Lindquist, B.; McBryan, O.; Padmanabhan, L., (Frontiers in Applied Mathematics, Vol. 1 (1983), SIAM: SIAM Philadelphia), 107-135
[9] Glimm, J.; Lindquist, B.; McBryan, O.; Plohr, B.; Yaniv, S., (Proceedings, Seventh SPE Symposium on Petroleum Reservoir Simulation (1983))
[10] Glimm, J.; Marchesin, D.; McBryan, O., J. Comput. Phys., 39, 179-200 (1981)
[11] Glimm, J.; Marshall, G.; Plohr, B., Adv. Appl. Math., 5, No. 1, 1-30 (1984)
[14] Guckenheimer, J., Arch. Rational Mech. Anal., 59, No. 3, 281-291 (1975)
[15] Krasny, R., A Numerical Study of Kelvin-Helmholtz Instability by the Point Vortex Method, (Thesis (1984), Department of Mathematics, University of California: Department of Mathematics, University of California Berkeley)
[18] Marshall, G.; Plohr, B., J. Comput. Phys., 56, 410 (1985)
[19] Moretti, G., Thoughts and Afterthoughts about Shock Computations, (Report No. PIBAL-72-37 (1972), Polytechnic Institute of Brooklyn)
[20] Plohr, B.; Glimm, J.; McBryan, O., (Chandra, J.; Flaherty, J., Lecture Notes in Engineering, Vol. 3 (1983), Springer-Verlag: Springer-Verlag New York), 180-191
[21] Richtmyer, R.; Morton, K., Difference Methods for Initial Value Problems (1967), Interscience: Interscience New York · Zbl 0155.47502
[22] Smoller, J., Shock Waves and Reaction-Diffusion Equations (1982), Springer-Verlag: Springer-Verlag New York
[23] Sod, G., J. Fluid Mech., 83, 785-794 (1977)
[24] Wagner, D., SIAM J. Math. Anal., 14, No. 3, 534-559 (1983)
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.