Local grid refinement for nonlinear waves

ABSTRACT This article introduces a numerical technique by refining grids in the region near the free surface to optimize both calculation efficiency and solution accuracy for the inviscid, nonlinear-wave problems. To demonstrate the improvement by this technique, the authors first investigate a solitary wave traveling along a uniform-depth channel. The numerical work using the locally-refined grids can save up to 70. of CPU time, as compared with those using uniformly fine grids at the comparable accuracy. Second, a more complicated example of the fully nonlinear water wave generated by a moving submerged obstacle is illustrated. The obstacle impulsively starts in its steady supercritical motion, stops suddenly for a while, and then accelerates immediately again to a constant critical speed, sequentially in a shallow water channel. This body motion constructs an interesting free-surface phenomenon of a series of solitary-wave train catching up with a sole solitary wave, all occurring right ahead of the mo...

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