Molecular dynamics and Enskog theory calculation of shock profiles in a dense hard sphere gas. (English) Zbl 0907.35101

Summary: Normal shock profiles in a dense hard sphere gas are obtained by solving numerically the Enskog kinetic equation. The results of the Enskog theory are compared with “exact” shock profiles obtained from molecular dynamics simulations. It is shown that, at least in the range of the flow parameters examined, the Enskog equation provides a remarkably good description of the shock propagation.


35Q35 PDEs in connection with fluid mechanics
76L05 Shock waves and blast waves in fluid mechanics
82C40 Kinetic theory of gases in time-dependent statistical mechanics
Full Text: DOI


[1] Enskog, D., Kinetische theorie, Svenska akad., 63, (1921) · JFM 47.0989.01
[2] Cercignani, C., Mathematical methods in kinetic theory, (1990), Plenum Press New York · Zbl 0726.76083
[3] Resibois, P.; DeLeener, M., Classical kinetic theory of fluids, (1977), J. Wiley & Sons
[4] Van Beijeren, H.; Ernst, M.H., The modified Enskog equation, Physica, 68, 437-456, (1973)
[5] Arkeryd, L.; Cercignani, C., Global existence in L1 for the Enskog equation and convergence of the solutions to solutions of the Boltzmann equation, J. stat. phys., 59, 845-867, (1990) · Zbl 0780.76066
[6] Bellomo, N.; Lachowicz, M.; Polewczac, J.; Toscani, G., Mathematical topics in non-linear kinetic theory II: the Enskog equation, (1991), World Scientific Singapore · Zbl 0733.76061
[7] Chapman, S.; Cowling, T.G., The mathematical theory of nonuniform gases, (1960), Cambridge University Press Cambridge · Zbl 0098.39702
[8] Leegwater, J.A.; van Beijren, H., Hydrodynamic correlation functions of hard-sphere fluids at short times, J. stat. phys., 57, 595, (1989)
[9] Frezzotti, A.; Sgarra, C., Numerical analysis of a shock wave solution of the Enskog equation …, J. stat. phys., 73, 193-207, (1993) · Zbl 1101.82335
[10] Alder, B.J.; Wainwright, T.E., Studies in molecular dynamics, J. chem. phys., 33, 5, 1439, (1960)
[11] Frezzotti, A., The propagation of shock waves in a dense gas according to Enskog theory, (), 455
[12] Landau, L.; Lifchitz, E., Physique théorique. tome VI: Mécanique des fluides, (), 284 · Zbl 0144.47605
[13] Carnahan, N.F.; Starling, K.E., J. chem. phys., 51, 635, (1969)
[14] Nordsieck, A.; Hicks, B., Monte Carlo evaluation of the Boltzmann collision integral, (), 695-710
[15] Aristov, V.V.; Tcheremissine, F.G., The conservative splitting method for solving the Boltzmann equation, USSR comp. math. phys., 20, 139, (1980)
[16] Holian, B.L.; Hoover, W.G.; Moran, B.; Straub, G.K., Shock-wave structure via non-equilibrium molecular dynamics and Navier-Stokes continuum mechanics, Phys. rev., 22A, 2798, (1980)
[17] Mareschal, M.; Salomon, E., Shock waves in gases using molecular dynamics and DSMC methods, Ttsp, 23, 281, (1994) · Zbl 0811.76034
[18] Allen, M.P.; Tildesley, D.J., Computer simulation of liquids, (1987), Clarendon Oxford · Zbl 0703.68099
[19] Alexander, F.J.; Garcia, A.L.; Alder, B.J., A consistent Boltzmann algorithm, Phys. rev. let., 74, 26, 5212, (1995)
[20] Bird, G.A., Molecular gas dynamics and the direct simulation of gas flows, (1994), Clarendon Oxford · Zbl 0709.76511
[21] López de Haro, M.; Garzó, V., On the Burnett equations for a dense monatomic hard-sphere gas, Physica A, 197, 98, (1993)
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. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.