Algebraic method of generating moving grid with local refinement applied to nonlinear-wave problems

The article discussed the algebraic moving-grid generation method with stream-function flow model to study the nonlinear-wave problems involving largely-displaced boundary. By solving the Laplace equation transformed in a transient boundary-fitted grid system we were able to assess the local grid-refinement technique on two problems: one for a solitary wave propagating along a long channel of uniform water depth, and the other for the free-surface flow disturbed by a vertical plate accelerated horizontally in a resting water channel. We first validated the model by comparing the calculated results in various uniform grids with the small-time perturbation solution and other investigations, and then quantified the computational efficiency and solution accuracy of the result using the grid-refinement technique in numerical model. In our study, it showed that the numerical work using the locally-refined grids saves up to 50-60% of CPU time, as compared with those using uniformly fine grids at the comparable accuracy.