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Incompressible SPH method based on Rankine source solution for violent water wave simulation

Ma, Q., Zheng, X. and Duan, W.Y. (2014). Incompressible SPH method based on Rankine source solution for violent water wave simulation. Journal of Computational Physics, 276, pp. 291-314. doi: 10.1016/


With wide applications, the smoothed particle hydrodynamics method (abbreviated as SPH) has become an important numerical tool for solving complex flows, in particular those with a rapidly moving free surface. For such problems, the incompressible Smoothed Particle Hydrodynamics (ISPH) has been shown to yield better and more stable pressure time histories than the traditional SPH by many papers in literature. However, the existing ISPH method directly approximates the second order derivatives of the functions to be solved by using the Poisson equation. The order of accuracy of the method becomes low, especially when particles are distributed in a disorderly manner, which generally happens for modelling violent water waves. This paper introduces a new formulation using the Rankine source solution. In the new approach to the ISPH, the Poisson equation is first transformed into another form that does not include any derivative of the functions to be solved, and as a result, does not need to numerically approximate derivatives. The advantage of the new approach without need of numerical approximation of derivatives is obvious, potentially leading to a more robust numerical method. The newly formulated method is tested by simulating various water waves, and its convergent behaviours are numerically studied in this paper. Its results are compared with experimental data in some cases and reasonably good agreement is achieved. More importantly, numerical results clearly show that the newly developed method does need less number of particles and so less computational costs to achieve the similar level of accuracy, or to produce more accurate results with the same number of particles compared with the traditional SPH and existing ISPH when it is applied to modelling water waves.

Publication Type: Article
Additional Information: NOTICE: this is the author’s version of a work that was accepted for publication in Journal of Computational Physics. Changes resulting from the publishing process, such as editing, structural formatting, and other quality control mechanisms may not be reflected in this document. Changes may have been made to this work since it was submitted for publication. A definitive version was published in Journal of Computational Physics, 276, 1st November 2014; 10.1016/
Publisher Keywords: Meshless method; SPH; ISPH; ISPH_R; Free surface flow; Wave impact; Violent water waves
Subjects: T Technology > TA Engineering (General). Civil engineering (General)
Departments: School of Mathematics, Computer Science & Engineering
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