| Summary: | 碩士 === 國立臺灣海洋大學 === 輪機工程學系 === 104 === Based on the GL(n,R), an equal norm multiple scale Trefftz method (MSTM) associated with Lie-group scheme in Euclidean space is developed to describe nonlinear sloshing behaviors. When the non-linear sloshing phenomena are encountered in Trefftz method, some difficulties, like the boundary conditions with noisy perturbation, ill-conditioned system by using higher-order T-complete functions, controlled volume correction, and characteristic length selection, need to be overcome simultaneously. To tackle these complicated problems, the MSTM combined with the vector regularization method (VRM) is first adopted to eliminate the higher-order numerical oscillation phenomena and noisy dissipation in boundary value problem. Then, the weighting factors of initial- and boundary value problems are introduced into the linear system to prevent the elevation from vanishing without iterative computational controlled volume. More importantly, we combined the explicit scheme based on the GL(n,R) with implicit scheme to reduce iteration number and increase computational efficiency. A comparison of the results of the present study with those in the literature shows that the proposed approach is better than previously reported methods and presents a simple and stable way to cope with the nonlinear sloshing problems.
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