Numerical simulation of non-breaking solitary wave run-up using exponential basis functions

A meshless method based on exponential basis functions (EBFs) is developed to simulate the propagation of solitary waves and run-up on the slope. The presented method is a boundary-type meshless method applying the exponential basis functions with complex exponents. The solution of governing equations is considered as a series of these basis functions. Boundary conditions are satisfied through a point-wise collocation approach. Based on the presented EBF meshless method, a new formula is introduced for the maximum run-up height on different slopes, valuable for engineering applications. The results obtained through the numerical method in the prediction of solitary wave propagation and estimation of run-up are verified through the comparison with experimental data. The comparison with 159 experimental data indicates that this new formula is more accurate than the preceding formulas in predicting the maximum run-up of non-breaking solitary waves. Minimum calculation time and convenient performances are the other advantages of this method.