Review on the local weak form-based meshless method (MLPG): Developments and Applications in Ocean Engineering

This paper reviews the developments and applications of meshfree method based on MLPG (Meshless Local Petrov Galerkin) in ocean engineering, primarily from the work carried out at IIT Madras and City, University of London, UK. Apart from discussing the various stages in the model development, this paper will also reports its applications to small amplitude waves, wave overtopping and breaking, porous layers, long wave run-up, vegetation, floating bodies in waves, wave interaction with elastic structure and two phase flow modelling. Generally, the Navier - Stokes equation will lead to numerical dissipation for long distance propagations and increase in computational time. In order to avoid this, one needs to look for a physics based approach. One of the successfully implemented approaches in MLPG was by coupling with fully nonlinear potential flow theory (FNPT), either one-way or two-way. In this paper, we bring out the advantages and implementation issues of MLPG. The paper also discuss the relationship with ISPH/MPS methods and some concepts that are adopted in both formulations. The paper ends with the key challenges and future directions in the development of the numerical method.