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

Chao-Feng Shih1, Yung-Wei Chen1,3,*, 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: 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

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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APA Style
Shih, C., Chen, Y., Chang, J., Soon, S. (2021). The equal-norm multiple-scale trefftz method for solving the nonlinear sloshing problem with baffles. Computer Modeling in Engineering & Sciences, 127(3), 993-1012. https://doi.org/10.32604/cmes.2021.012702
Vancouver Style
Shih C, Chen Y, Chang J, Soon S. The equal-norm multiple-scale trefftz method for solving the nonlinear sloshing problem with baffles. Comput Model Eng Sci. 2021;127(3):993-1012 https://doi.org/10.32604/cmes.2021.012702
IEEE Style
C. Shih, Y. Chen, J. Chang, and S. Soon "The Equal-Norm Multiple-Scale Trefftz Method for Solving the Nonlinear Sloshing Problem with Baffles," Comput. Model. Eng. Sci., vol. 127, no. 3, pp. 993-1012. 2021. https://doi.org/10.32604/cmes.2021.012702



cc This work is licensed under a Creative Commons Attribution 4.0 International License , which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
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