| Stokes equations are such equations which are used to describe Newton flow with viscosity. Method of regularized sources, i.e. MRS, one of non-singular method of fundamental solution, i.e. MFS, is developed aiming to solving Stokes equations. In order to avoid artificial boundary, which is introduced in classical MFS for locating source points, regularized parameter is taken in this paper for the coincidence of source points and collocation points. The fundamental solution of axisymmetric regularized sources is calculated by integrating regularized sources over spherical coordinate system, and thus the expressions of pressure and velocity to Stokes flow are developed. The resulted pressure and velocity, which are calculated by the linear combination of inner nodal values, can be regarded as the analytical solutions due to the singularity of Direc Delta function in the infinite space.As one of typical Stokes flow problems, Driven cavity flow is considered to test accuracy and robustness of numerical methods, though no analytical solution is pro-posed yet. In this paper, we take three-dimensional driven cavity for testing proposed method of regularized sources. At the same time, hollow tube case is also considered to test computation performance of MRS further. In order to exam numerical results efficiently, finite difference method in fine mesh grid is also taken for comparison. As a result, we can see that the proposed MRS can solve Stokes flow problems effectively, and the results convergent with the greater number of collocation points. As expected, however, MRS is highly dependent on regularized parameter. Currently, authors are trying to make the connection between regularized parameter and collocation points with the purpose of achieving automatic selection of optimum regularized parameter. Acceptable numerical results of MRS are listed at the end of this paper. The related connection of regularized parameter and discrete step is also attached. |
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