NUMERICAL SIMULATION OF SOLITARY WAVE RUN-UP ON THE BEACH BY A MESHLESS METHOD BASED ON EXPONENTIAL BASIS FUNCTIONS

Solitary waves are often applied for simulating tsunami phenomenon. In this article, a meshless method based on exponential basis functions (EBFs) is developed to simulate the propagation of solitary waves and run-up on the slope. This method is a boundary-type meshless method using exponential basis functions with complex exponents. The solution to governing equations is considered as a series of these basis functions and boundary conditions satisfied via a point-wise collocation approach. In this research, the simplified Navier-Stokes equations in the Lagrangian form for an incompressible inviscid fluid are employed. Governing equations and boundary conditions are established on pressure as a potential equation. A stable Lagrangian time marching algorithm is developed for tracking free surface on the beach. So, the solution process can be preceded by boundary nodes tracking, and the most important characteristics of a fluid, such as the displacement, velocity, and acceleration, are the results of pressure Laplace equation. Geometry updating is only performed by changing the location of boundary nodes, and there is no need to mesh generation or any integration in solution process. According to the Lagrangian formulation, the numerical solution is performed at a time marching approach using an implicit two-step algorithm. In this algorithm, pressure equation is solved twice a step, and position of boundary nodes is corrected at the end of each time step. Minimum calculation time, convenient performance, and high accuracy in the solution process are the advantages of this method. The results of the present numerical method in the prediction of solitary wave propagation and estimation of run-up are verified through the comparison with experimental data. Different wave amplitude cases are simulated, and the resulted run-up is compared with experiments. The results show that presented meshless method and developed time marching algorithm are capable of simulating the run-up under non-breaking condition quiet accurately.