Fluid Dynamics Research 38 (2006) 241 – 256 A stable moving-particle semi-implicit method for free surface flows B. Ataie-Ashtiani ∗ , Leila Farhadi Department of Civil Engineering, Sharif University of Technology, P.O. Box 11365-9313, Tehran, Iran Received 11 August 2004; received in revised form 30 August 2005; accepted 6 December 2005 Communicated by M. Oberlack Abstract In this paper, a mesh-less numerical approach is utilized to solve Euler’s equation that is the governing equation of the irrotational flow of ideal fluids. A fractional step method of discritization is applied which consists to split each time step in two steps. This numerical method is based on moving-particle semi-implicit method (MPS) for simulating incompressible inviscid flows with free surfaces. The motion of each particle is calculated through interactions with neighboring particles covered with the kernel function. There are limitations for getting a stable solution by MPS method. In this paper, various kernel functions are considered and applied to improve the stability of MPS method. Based on these studies a kernel function is introduced that improves the stability of MPS method. The numerical results of the model are in good agreement with experimental results. The applicability of this model to simulate hydraulic problems with free surface is shown through the solution of dam break problem. The present method is a very useful utility for solving problems with irregular free surface in hydraulic and coastal engineering when an accurate prediction of free water surface is required. © 2005 The Japan Society of Fluid Mechanics and Elsevier B.V. All rights reserved. Keywords: Numerical method; Free surface flow; Moving-particle semi-implicit method; Lagrangian approach 1. Introduction Free surface hydrodynamic flows are of significant industrial and environmental importance but are difficult to simulate because the surface boundary conditions are specified on an arbitrarily moving surface. ∗ Corresponding author. Fax: +98 21 601 4828. E-mail address: ataie@sharif.edu (B. Ataie-Ashtiani). 0169-5983/$30.00 © 2005 The Japan Society of Fluid Mechanics and Elsevier B.V. All rights reserved. doi:10.1016/j.fluiddyn.2005.12.002