Investigation of numerical algorithms applied to study the wave propagation and breaking

It is a challenge to capture the large deformation of the free surface. The present study develops numerical algorithms based on the meshless method for investigating wave propagation and breaking. A new gradient model is constructed to solve numerical perturbations. A new method for detecting free surface particles is proposed to improve the precision. The linked list search method is used to improve the searching speed, and the conjugate gradient (CG) approach is utilized to solve the Poisson equation, which enhances the calculation efficiency. A high-precision numerical wave flume is established, and the generated waves agree well with the analytical solution. The velocity field and the wave propagation process are displayed to confirm the wave attenuation. The runup and breaking of the solitary waves propagating to the shore are studied. Comparisons with the analytical solutions and experimental results indicate that this numerical algorithm can simulate wave propagation and break very well. Three pressure points were installed on the coast to track the impact close to the wave breaking. After the wave breaks, the wave frequency will be concentrated at a low frequency and produce more energy according to the wavelet transform analysis that is finally performed.