| Summary: | 碩士 === 國立臺灣海洋大學 === 海洋環境資訊學系 === 101 === A space-time least-squares finite-element method based on the adaptive bi-tree meshes for shallow-water equations is developed. Adaptation of the bi-tree mesh is controlled by the square of residual of approximations. Model is applied to sinusoidal wave propagation in (1) a constant depth channel, (2) a constant slope channel, and (3) a step channel, respectively, to study wave-bathymetry interactions and wave deformations. Computed results with bi-tree meshes are compared with those obtained with uniform meshes. It is found that with similar accuracy, 30% meshes can be saved using bi-tree meshes comparing with using uniform meshes in the constant slope channel case. In the constant slope channel case, shoaling and nonlinearity become significant when slope of the channel increases; In general, using bi-tree meshes can save 20% meshes. Two amplitudes (a = 0.1 m and 0.5 m) of the sinusoidal wave was considered in the step channel case. For small amplitude (a = 0.1 m), shoaling and nonlinearity are insignificant; using bi-tree meshes can save 35% meshes. However, for large amplitude (a = 0.5 m), shoaling and nonlinearity are pronounced, and wave deforms substantially; similar amount of meshes is needed for both bi-tree meshes and uniform meshes.
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