Abstract
We construct exact (1+1)-dimensional solutions (space x, time t), in the presence of a purely reflecting well, for both the four velocity discrete Boltzmann model and the Broadwell model. These exact solutions, sums of two similarity shock waves, are positive for x≥0, t≥0.
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References
CornilleH., J. Phys. A20, 1973 (1987); J. Math. Phys. 28, 1567 (1987); Phys. Let. A125, 253 (1987); J. Stat. Phys. 48, 789 (1987); C. R. Acad. Sci. 304, 1091 (1987); Saclay Spht/87-104, J. Math. Phys. (1988). Cabannes, H. and Tiem, D. M., C. R. Acad. Sci. 304, 29 (1987); Complex Systems 1, 574 (1987).
Cornille, H., J. Phys. A20, L1063 (1987); Saclay Spht/87, 88-31, J. Stat. Phys. (1988).
Bobylev, A., Math. Congress Warsaw (1987); Wick, J., Math. Meth. Appl. Sci. 6, 515 (1984); Platkowski, J., Mécan. Théor. Appl. 4, 555 (1985).
HarrisS., J. Math. Phys. 8, 2407 (1967); Gatignol, R., Lecture Notes in Physics 36, Springer, Berlin, 1975; T.T.S.P. 16, 837 (1987); Frisch, U., d'Humieres, D., Hasslacher, B., Lallemand, P., Pomeau, Y., and Rivet, J. P., Complex Systems 1, 648 (1987) and references therein.
BroadwellJ. E., Phys. Fluids 7, 1243 (1964); Tartar, L., Séminaire Goulaouic-Schwartz 1 (1975); Beale, J. T., Commun. Math. Phys. 102, 217 (1985).
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Cornille, H. Exact solutions for the discrete Boltzmann models with specular reflection. Lett Math Phys 16, 245–250 (1988). https://doi.org/10.1007/BF00398961
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DOI: https://doi.org/10.1007/BF00398961