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Shock simulation by the particle method SPH. (English) Zbl 0572.76059
The particle method SPH (smoothed particle hydrodynamics), which can be derived from the exact equations of motion by multiplying each term by an appropriately chosen kernel and then integrating over the given domain, is applied to one-dimensional shock tube problems. The basic idea is to use a new kind of artificial viscosity in order to get a satisfactory shock simulation, since standard artificial viscosities like bulk viscosity or von Neumann-Richtmyer viscosity lead to under- and overshooting effects or smearing of the shock front. It is further shown that a super Gaussian interpolating kernel with fourth-order errors gives significantly better shock resolutions than the standard Gaussian kernel with second-order errors. Numerical results are given and compared with those obtained by G. A. Sod [ibid. 27, 1-31 (1978; Zbl 0387.76063)] and B. van Leer [ibid. 32, 101-136 (1979)].
Reviewer: R.H.W.Hoppe

76L05 Shock waves and blast waves in fluid mechanics
76M99 Basic methods in fluid mechanics
Full Text: DOI
[1] Gingold, R.A.; Monaghan, J.J., Mon. not. roy. astron. soc., 181, 375-389, (1977)
[2] Gingold, R.A.; Monaghan, J.J., J. comput. phys., 46, 429-453, (1982)
[3] Hockney, R.W.; Eastwood, J.W., Computer simulation using particles, (1981), McGraw-Hill New York · Zbl 0662.76002
[4] Marder, B.M., Math. comp., 29, 434, (1975)
[5] Monaghan, J.J., SIAM. J. sci. statist. comput., 3, 422, (1982)
[6] Roache, P.J., Computational fluid dynamics, (1975), Hermosa Pub Albuquerque · Zbl 0306.76001
[7] Sod, G.A., J. comput. phys., 27, 1-31, (1978)
[8] Van Leer, B., J. comput. phys., 32, 101-136, (1979)
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