A free surface interpolation approach for rapid simulation of short waves in meshless numerical wave tank based on the radial basis function

Abstract

The meshless Numerical Wave Tank (NWT) has been developed based on the collocation method and the radial basis function. For simulating short waves, a free surface interpolation approach is proposed in this study in order to mitigate numerical dissipation and accelerate the simulation. A number of fundamental free surface nodes are employed in the procedure of solving algebraic equations with a full coefficient matrix, while many more free surface nodes are utilized in the time-stepping and smoothing procedure by applying the interpolation technique between each adjacent fundamental nodes. The NWT with the free surface interpolation approach is applied to simulate regular waves and irregular waves, and is then validated by both analytical solutions and experimental results. The numerical results are significantly improved by using the approach to increase the number of free surface boundary nodes, whilst the time consumption increases proportionally. For shorter waves, more interpolation nodes need be used. The good agreement between the present numerical results and the analytical and experimental results indicates that the free surface interpolation approach succeeds in rapidly and accurately simulating the propagation of short waves and irregular waves, covering a wide range of wave frequencies.