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

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 simply- and doubly-connected domains.