Meshless generalized finite difference method with a domain-decomposition method for solving Helmholtz equation and its application to caisson resonance problems

Abstract

This paper aims at presenting a meshless Generalized Finite Difference Method (GFDM) for solving the Helmholtz equation. In particular, in order to tackle the problem where a fluid domain is divided into different parts by a thin-wall structure, a Domain-Decomposition Method (DDM) is introduced to prevent interactions between node pairs coming from different parts of the flow domain. Two rigorous benchmarks are performed to validate the convergence and accuracy of the present GFDM-DDM model. Furthermore, caisson resonance problems are also investigated and discussed based on the novel numerical tool. It is shown that the present GFDM-DDM model can provide satisfactory predictions for resonance modes in caisson resonance problems, and hence can be treated as a powerful numerical tool in ocean engineering design due to its accurate and efficient characteristics.