THE MODIFIED COLLOCATION TREFFTZ METHOD AND LAPLACIAN DECOMPOSITION FOR SOLVING TWO-DIMENSIONAL STOKES PROBLEMS

Authors

Chia-Ming Fan, Department of Harbor and River Engineering & Computation and Simulation Center, National Taiwan Ocean University, Keelung 20224, Taiwan, R.O.C.Follow
Hong-Huei Li, Department of Harbor and River Engineering & Computation and Simulation Center, National Taiwan Ocean University, Keelung 20224, Taiwan, R.O.C.
Chung-Lun Kuo, Department of Systems Engineering and Naval Architecture, National Taiwan Ocean University, Keelung 20224, Taiwan, R.O.C.

Abstract

In this paper, the two-dimensional Stokes problem is analyzed by the modified collocation Trefftz method (MCTM) and the Laplacian decomposition. The coupled Stokes equations are converted to three Laplace equations by utilizing the Laplacian decomposition and then the boundary-type meshless MCTM is adopted to solve the resultant Laplace equations. The MCTM, free from mesh and numerical quadrature, is derived from the conventional Trefftz method by considering the characteristic length of the domain, which stabilize the numerical scheme and obtain highly accurate results. Besides, the solutions are expressed as the linear combination of T-complete functions and the velocity as well as pressure are coupled by collocating the boundary conditions. Several numerical examples are provided to demonstrate the efficacy and accuracy of the proposed meshless scheme. In addition, the numerical results demonstrates that the proposed meshless scheme can solve the Stokes problems accurately in simplyand doubly-connected domains.

Recommended Citation

Fan, Chia-Ming; Li, Hong-Huei; and Kuo, Chung-Lun (2011) "THE MODIFIED COLLOCATION TREFFTZ METHOD AND LAPLACIAN DECOMPOSITION FOR SOLVING TWO-DIMENSIONAL STOKES PROBLEMS," Journal of Marine Science and Technology: Vol. 19: Iss. 5, Article 8.
DOI: 10.51400/2709-6998.2166
Available at: https://jmstt.ntou.edu.tw/journal/vol19/iss5/8