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2012 A Stabilized Incompressible SPH Method by Relaxing the Density Invariance Condition
Mitsuteru Asai, Abdelraheem M. Aly, Yoshimi Sonoda, Yuzuru Sakai
J. Appl. Math. 2012(SI07): 1-24 (2012). DOI: 10.1155/2012/139583


A stabilized Incompressible Smoothed Particle Hydrodynamics (ISPH) is proposed to simulate free surface flow problems. In the ISPH, pressure is evaluated by solving pressure Poisson equation using a semi-implicit algorithm based on the projection method. Even if the pressure is evaluated implicitly, the unrealistic pressure fluctuations cannot be eliminated. In order to overcome this problem, there are several improvements. One is small compressibility approach, and the other is introduction of two kinds of pressure Poisson equation related to velocity divergence-free and density invariance conditions, respectively. In this paper, a stabilized formulation, which was originally proposed in the framework of Moving Particle Semi-implicit (MPS) method, is applied to ISPH in order to relax the density invariance condition. This formulation leads to a new pressure Poisson equation with a relaxation coefficient, which can be estimated by a preanalysis calculation. The efficiency of the proposed formulation is tested by a couple of numerical examples of dam-breaking problem, and its effects are discussed by using several resolution models with different particle initial distances. Also, the effect of eddy viscosity is briefly discussed in this paper.


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Mitsuteru Asai. Abdelraheem M. Aly. Yoshimi Sonoda. Yuzuru Sakai. "A Stabilized Incompressible SPH Method by Relaxing the Density Invariance Condition." J. Appl. Math. 2012 (SI07) 1 - 24, 2012.


Published: 2012
First available in Project Euclid: 17 October 2012

zbMATH: 1244.76101
MathSciNet: MR2927256
Digital Object Identifier: 10.1155/2012/139583

Rights: Copyright © 2012 Hindawi

Vol.2012 • No. SI07 • 2012
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