Localized Trefftz method for wave generation and propagation in a two-dimensional numerical wave tank

Abstract

This study proposes a meshless numerical method for nonlinear free surface wave propagation, known as the localized Trefftz method (LTM). The method employs the fundamental solution of the Laplace equation as Tcomplete functions and integrates the explicit Euler method, semi-Lagrangian method, ramp functions, and sponge layers to construct a numerical wave flume, enabling accurate and efficient simulation of wave generation and propagation. Based on potential flow theory, wave propagation is formulated as a time-dependent boundary value problem governed by the Laplace equation for velocity potential and two nonlinear free surface boundary conditions. To absorb wave energy and prevent reflection, a sponge layer is implemented at the end of the flume. Initially, LTM is applied to simulate the generation of finite-amplitude, high-steepness waves at the wave generation end. Subsequently, it is used to model the propagation of regular waves over underwater obstacles, incorporating an exponential decay function in the sponge layer to further mitigate wave reflection at the flume's end. As LTM does not require global mesh generation, it is computationally efficient and particularly suitable for moving boundary problems. The accuracy and stability of the proposed method are validated through comparative analyses of four numerical examples against existing numerical results.