Meshless generalized finite difference method for water wave interactions with multiple-bottom-seated-cylinder-array structures

Abstract

This paper presents the meshless generalized finite difference method (GFDM) in conjunction with the truncated treatments of infinite domain for simulating water wave interactions with multiple-bottom-seated-cylinder-array structures. In the proposed scheme, the truncated treatments are introduced to deal with the infinite domain. Based on the moving least squares theory and second-order Taylor series expansion, the GFDM approximation formulation is constructed for water wave-structure interactions. It introduces the stencil selection algorithms to choose the stencil support of a certain node from the whole discretization nodes. In comparison with traditional finite difference methods, the proposed GFDM is free of mesh and available for irregular discretization nodes. Numerical investigations are presented to demonstrate the effectiveness of the proposed GFDM with two truncated treatments, absorbing boundary conditions (ABC) and perfectly matched layer (PML), for simulating water wave interactions with single- and four-cylinder-array structures. Then it successfully revisits the near trapped mode phenomenon of specific four-cylinder-array structures and the peak normalized horizontal forces around the cylinders with specific incident water wave. Finally numerical demonstration shows that the structures with porous outer wall can eliminate the near trapped mode phenomenon and reduce the peak normalized horizontal force of multiple-cylinder-array structures.