Open Access

ARTICLE

Modified SFDI for Fully NonlinearWave Simulation

Guochun Xu¹, S Yan², Q.W. Ma^1,2,3

1 College of Shipbuilding Engineering, Harbin Engineering University, Harbin, China.
2 School of Mathematics, Computer Sciences and Engineering, City University London, EC1V 0HB.
3 Corresponding author. E-mail: q.ma@city.ac.uk

Computer Modeling in Engineering & Sciences 2015, 106(1), 1-35. https://doi.org/10.3970/cmes.2015.106.001

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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Keywords

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