FEM and MLPG Methods for Simulating Nonlinear Water Waves
by
Q.W. Ma
School of Engineering and Mathemetical Science, City University, Northampton Square, London, EC1V 0HB, UK

A finite element method (FEM) to simulate nonlinear water waves has been developed and applied successfully to modelling various problems including monochromatic, bichromatic and irregular progressive waves, sloshing waves in moving tanks and interactions between waves and structures [1-3]. However, its successes rely on good meshes. Those meshes may become over-distorted during simulation. To overcome over-distortion, they must be regenerated every time step or very several time steps. However, the dissipation can not be avoided due to re-meshing. If complicated unstructured meshes are used, re-meshing may take a lot of CPU time.

Effort has been made to develop an approach based on meshless local Petrove-Galerkin (MLPG) method [4]. The main idea of the approach is that: using a set of nodes to represent the fluid particles in the flow domain; defining a circle sub-domain (called integration sub-domain) for each node; deriving a weak form of differential equations over each of all the integration sub-domains; approximating unknown variables in term of a weight function which is then inserted into the weak form to form a set of algebraic equations. Preliminary results show that this method may be a good alternative to FEM.

In this paper, comparison between these two methods will be made to identify the advantages and disadvantages of MLPG method relative to FEMs and also to validate the results obtained by the new developed method using the published data and analytical solutions. More details will be presented in the conference.

Reference [1] Ma, Q.W., Wu, G.X. & Eatock Taylor, R., 2001, "Finite element simulation of fully nonlinear interaction between vertical cylinders and steep waves--part 1 methodology and numerical procedure", Int. J. Numer. Meth. Fluids, Vol. 36, pp. 265-285.

[2] Ma, Q.W., Wu, G.X. & Eatock Taylor, R., 2001, "Finite element simulation of fully nonlinear interaction between vertical cylinders and steep waves--part 2 numerical results and validation", Int. J. Numer. Meth. Fluids, Vol. 36, pp. 265-285.

[3] Wu, G.X., Ma, Q.W and Eatock Taylor R. 1998, "Numerical simulation of sloshing waves based on finite element method", Applied Ocean Research, Vol. 20, pp. 337-355.

[4] Ma, Q.W., 2004, "Simulation of Non-Linear Water Waves Using Meshless Local Petrov-Galerkin (MLPG) Method", Proceedings of 10th International Workshop for Water Waves and Floating Bodies, 28/31 March 2004, Cortona, Italy.

Date received: March 1, 2004

Copyright © 2004 by the author(s). The author(s) of this document and the organizers of the conference have granted their consent to include this abstract in Atlas Conferences Inc. Document # cakt-90.