Modified SFDI for Fully NonlinearWave Simulation
Guochun Xu, S Yan and Q.W. Ma

doi:10.3970/cmes.2015.106.001
Source CMES: Computer Modeling in Engineering & Sciences, Vol. 106, No. 1, pp. 1-35, 2015
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Keywords Modified SFDI, gradient estimation, nonlinear water waves, QALEFEM.
Abstract

In the Meshless Local Petrove-Galerkin based on Rankine source solution (MLPG-R), a simplified finite difference interpolation (SFDI) scheme was developed for numerical interpolation and gradient calculation (CMES, Vol. 23(2), pp. 75-89). Numerical tests concluded that the SFDI is generally as accurate as the linear moving least square method (MLS) but requires less CPU time. In this paper, a modified SFDI is proposed for numerically modelling of nonlinear water waves, considering the typical feature of the spatial variation of the wave-related parameters. Systematic numerical investigations are carried out and the results indicate that the modification considerably improves the robustness of the SFDI on gradient estimation. Although the scheme is originally derived for meshless method, its feasibility and accuracy in the mesh-based methods are discussed here through the fully nonlinear wave simulation using the Quasi Arbitrary Lagrangian Eulerian Finite Element Method (QALE-FEM), which is based on fully nonlinear potential theory.

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