Open Access

ARTICLE

The Equal-Norm Multiple-Scale Trefftz Method for Solving the Nonlinear Sloshing Problem with Baffles

by Chao-Feng Shih¹, Yung-Wei Chen^1,3,*, Jiang-Ren Chang², Shih-Ping Soon¹

1 Department of Marine Engineering, National Taiwan Ocean University, Keelung, 202-24, Taiwan
2 Department of Systems Engineering and Naval Architecture, National Taiwan Ocean University, Keelung, 202-24, Taiwan
3 Center of Excellence for Ocean Engineering, National Taiwan Ocean University, Keelung, 202-24, Taiwan

* Corresponding Author: Yung-Wei Chen. Email:

(This article belongs to the Special Issue: Modeling Real World Problems with Mathematics)

Computer Modeling in Engineering & Sciences 2021, 127(3), 993-1012. https://doi.org/10.32604/cmes.2021.012702

Received 10 July 2020; Accepted 09 February 2021; Issue published 24 May 2021

Abstract

In this paper, the equal-norm multiple-scale Trefftz method combined with the implicit Lie-group scheme is applied to solve the two-dimensional nonlinear sloshing problem with baffles. When considering solving sloshing problems with baffles by using boundary integral methods, degenerate geometry and problems of numerical instability are inevitable. To avoid numerical instability, the multiple-scale characteristic lengths are introduced into T-complete basis functions to efficiently govern the high-order oscillation disturbance. Again, the numerical noise propagation at each time step is eliminated by the vector regularization method and the group-preserving scheme. A weighting factor of the group-preserving scheme is introduced into a linear system and then used in the initial and boundary value problems (IBVPs) at each time step. More importantly, the parameters of the algorithm, namely, the T-complete function, dissipation factor, and time step, can obtain a linear relationship. The boundary noise interference and energy conservation are successfully overcome, and the accuracy of the boundary value problem is also improved. Finally, benchmark cases are used to verify the correctness of the numerical algorithm. The numerical results show that this algorithm is efficient and stable for nonlinear two-dimensional sloshing problems with baffles.

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