Meshless BEM for Three-dimensional Stokes Flows

This paper describes a combination of the dual reciprocity method (DRM) and the method of fundamental solution (MFS) as a meshless BEM (DRM-MFS) to solve three-dimensional Stokes flow problems by the velocity-vorticity formulation, where the DRM is based on the compactly supported, positive definite radial basis functions (CS-PD-RBF). In the velocity-vorticity formulation, both of the diffusion type vorticity equations and the Poisson type velocity equations are solved by DRMMFS. Here a typical internal cubic cavity flow and an external flow past a sphere are presented. The results are acceptable. Furthermore, this paper provides a preliminary work for applications to the three-dimensional Navier-Stokes equations. keyword: Velocity-vorticity formulation, Stokes flow, meshless, boundary element method, radial basis function, dual reciprocity method, method of fundamental solution

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