2023 , Volume 28, № 4, p.73-93

Purpose. When designing large partially immersed fixed structures located in tsunami-hazardous coastal waters, it is necessary to consider the possible impact of long surface waves such as tsunamis on them. Multivariate calculations make the application of algorithms for three-dimensional models (Navier–Stokes or Euler) computationally expensive. The most important characteristics of the interaction of waves with a semi-immersed body can often be obtained using shallow water (SW) models, which is confirmed by recent studies in the framework of one-dimensional (1D) SW models. However, numerical algorithms and calculation results in a two-dimensional (2D) formulation have not yet been published, even in the case of the dispersionless SW model. The development of such an algorithm has become the purpose of this study. Methodology. The algorithm for calculating the interaction of surface waves with fixed semisimmersed structures in the framework of the 2D dispersionless shallow water model is described in detail. For the numerical solution of the problem, the flow area is divided into two parts. The system of the shallow water equations for a flow with a free boundary is solved in the outer domain using the predictor-corrector scheme. In the inner region, the system of incompressible fluid equations for flow in the space between the bottom of a semi-immersed body and the bottom of the basin is solved using a modified McCormack scheme. A method of gluing these solutions at the boundary of the body is proposed. Results and conclusions. The first results of testing the developed algorithm are presented. The accuracy of the algorithm is estimated on the 2D problems of the impact of a bore and a solitary wave on a semi-immersed body in the form of a rectangular prism. The convergence of numerical solutions is confirmed when the grid is refined. We reveal the qualitative difference between the characteristics of wave-structure interaction obtained within the framework of the 2D and 1D models