Piston-driven numerical wave tank based on WENO solver of well-balanced shallow water equations

A numerical wave tank equipped with apiston type wave-maker ispresentedfor long-duration28simulations of longwavesin shallow water. Both wavemakerand tankaremodelledusingthe nonlinear shallow water equations,with motions of the numerical piston paddle accomplished via a linear mapping technique. Three approaches are used to increase computational efficiency and accuracy. First, the model satisfies the exact conservation property (C-property), a stepping stone towards properly balancing each term in the governing equation. Second,a high-order WENO methodis used to reduce accumulation of truncation error. Third ,a cut-off algorithm is implemented to handle contaminated digits arising fromround-off error. If not treated, such errors could prevent a numerical scheme from satisfying the exact C-property in long-duration simulations. Extensive numerical tests are performed to examine the well-balanced property, high order accuracy,and shock-capturing ability of the present scheme. Correct implementation of the wave paddle generator is verified by comparing numerical predictions against analytical solutions of sinusoidal, solitary, and cnoidal waves. In all cases, the model gives satisfactory results for small-amplitude, low frequency waves. Error analysisis used to investigate model limitations and derive a user criterion fo rlongwave generation by the model