Journal of Applied Mathematics
Volume 2011 (2011), Article ID 793653, 16 pages
Research Article

Development of a Particle Interaction Kernel Function in MPS Method for Simulating Incompressible Free Surface Flow

1Department of Engineering Science and Ocean Engineering, National Taiwan University, Taipei, 10617, Taiwan
2Taida Institute of Mathematical Science (TIMS), National Taiwan University, Taipei, 10617, Taiwan
3Center for Quantum Science and Engineering (CQSE), National Taiwan University, Taipei, 10617, Taiwan

Received 3 December 2010; Accepted 2 January 2011

Academic Editor: Zhangxin Chen

Copyright © 2011 Tony W. H. Sheu et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


We aimed to derive a kernel function that accounts for the interaction among moving particles within the framework of particle method. To predict a computationally more accurate moving particle solution for the Navier-Stokes equations, kernel function is a key to success in the development of interaction model. Since the smoothed quantity of a scalar or a vector at a spatial location is mathematically identical to its collocated value provided that the kernel function is chosen to be the Dirac delta function, our guideline is to derive the kernel function that is closer to the delta function as much as possible. The proposed particle interaction model using the newly developed kernel function will be validated through the two investigated Navier-Stokes problems which have either the semianalytical or the benchmark solutions.