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Restoring particle consistency in smoothed particle hydrodynamics. (English) Zbl 1329.76285
Summary: Though the smoothed particle hydrodynamics (SPH) method has been widely applied to different areas, it is associated with some inherent numerical problems. One notable problem is the particle inconsistency that results from the particle approximation process and can lead to low approximation accuracy. In this paper, the particle inconsistency problem is investigated and some methods to improve the particle inconsistency are discussed. A new approach is proposed to restore the particle consistency. The new approach retains the conventional non-negative smoothing function instead of reconstructing a new smoothing function. A series of numerical studies have been carried out to verify the performance of the new approach. It is found the new approach can successfully restore the particle consistency and can therefore significantly improve the approximation accuracy.

76M28 Particle methods and lattice-gas methods
74S30 Other numerical methods in solid mechanics (MSC2010)
Full Text: DOI
[1] Belytschko, T.; Krongauz, Y.; Organ, D.; Fleming, M.; Krysl, P., Meshless methods: an overview and recently developments, Comput. methods appl. mech. engrg., 139, 3-47, (1996) · Zbl 0891.73075
[2] Bonet, J.; Kulasegaram, S., Correction and stabilization of smoothed particle hydrodynamics method with applications in metal forming simulations, Internat. J. numer. methods engrg., 47, 1189-1214, (2000) · Zbl 0964.76071
[3] Chen, J.K.; Beraun, J.E.; Carney, T.C., A corrective smoothed particle method for boundary value problems in heat conduction, Internat. J. numer. methods engrg., 46, 231-252, (1999) · Zbl 0941.65104
[4] Cleary, P.W., Modelling confined multi-material heat and mass flows using SPH, Appl. math. modelling, 22, 981-993, (1998)
[5] Dilts, G.A., Moving least square particle hydrodynamics i: consistency and stability, Internat. J. numer. methods engrg., 44, 1115-1155, (1999) · Zbl 0951.76074
[6] D.A. Fulk, A Numerical Analysis of Smoothed Particle Hydrodynamics, Ph.D. Thesis, Air Force Institute of Technology, 1994
[7] Gingold, R.A.; Monaghan, J.J., Smoothed particle hydrodynamics: theory and application to non-spherical stars, Monthly notices roy. astronom. soc., 181, 375-389, (1977) · Zbl 0421.76032
[8] Johnson, G.R.; Stryk, R.A.; Beissel, S.R., SPH for high velocity impact computations, Comput. methods appl. mech. engrg., 139, 347-373, (1996) · Zbl 0895.76069
[9] Liu, G.R.; Liu, M.B., Smoothed particle hydrodynamics—A meshfree particle method, (2003), World Scientific Singapore · Zbl 1046.76001
[10] Liu, M.B.; Liu, G.R.; Lam, K.Y., Investigations into water mitigations using a meshless particle method, Shock waves, 12, 3, 181-195, (2002)
[11] Liu, M.B.; Liu, G.R.; Lam, K.Y., Constructing smoothing functions in smoothed particle hydrodynamics with applications, J. comput. appl. math., 155, 2, 263-284, (2003) · Zbl 1065.76167
[12] Liu, M.B.; Liu, G.R.; Lam, K.Y.; Zong, Z., Computer simulation of the high explosive explosion using SPH methodology, Comput. fluids, 32, 3, 305-322, (2003) · Zbl 1009.76525
[13] Liu, M.B.; Liu, G.R.; Zong, Z.; Lam, K.Y., Smoothed particle hydrodynamics for numerical simulation of underwater explosions, Comput. mech., 30, 2, 106-118, (2003) · Zbl 1128.76352
[14] Lucy, L.B., Numerical approach to testing the fission hypothesis, Astronom. J., 82, 1013-1024, (1977)
[15] Matlab, Partial differential equation toolbox, (1996), The MathWorks Inc
[16] Monaghan, J.J., Smoothed particle hydrodynamics, Annual rev. astronom. astrophys., 30, 543-574, (1992)
[17] Monaghan, J.J., Simulating free surface flow with SPH, J. comput. phys., 110, 399-406, (1994) · Zbl 0794.76073
[18] J.P. Morris, Analysis of Smoothed Particle Hydrodynamics with Applications, Ph.D. Thesis, Monash University, 1996
[19] Randles, P.W.; Libersky, L.D., Smoothed particle hydrodynamics some recent improvements and applications, Comput. methods appl. mech. engrg., 138, 375-408, (1996) · Zbl 0896.73075
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