In the present work, local radial basis function (RBF) collocation method is used to solve the Stokes problem numerically. Benefits of the local meshless method is its flexibility of handling complex computational domain and interface. Local meshless method produces sparse coefficient matrix, though its structure is depending on the placement of nodes, and type of boundary conditions. The Stokes equations are collocated in a rectangular region with different interface conditions and direct solvers are used instead of iterative algorithm. Due to the unknown boundary conditions for the pressure term in the Stokes equations, value of the pressure is obtained by integrating the Stokes equations and eliminating the constant of integration. In the numerical implementation, circular, elliptic and Deltoid like interfaces are taken into consideration to test performance of the proposed approach for complex problems. Meshless solution of the Stokes equations for the first two problems are compared with the published results in the literature. The last problem is different form the first two problems in the sense that the continuity equation is also discontinuous and the velocity has nonzero value in both the inner and outer sub-domains.

在目前的工作中，使用局部径向基函数（RBF）配置方法来数值求解斯托克斯问题。局部无网格方法的好处是它可以灵活处理复杂的计算域和接口。尽管其结构取决于节点的位置和边界条件的类型，但局部无网格方法仍会生成稀疏系数矩阵。Stokes方程在界面条件不同的矩形区域中并置，并且使用直接求解器代替迭代算法。由于Stokes方程中压力项的边界条件未知，因此可以通过对Stokes方程进行积分并消除积分常数来获得压力值。在数值实现中，圆形 考虑了椭圆形和类似于Deltoid的接口，以测试所提出方法对复杂问题的性能。将前两个问题的斯托克斯方程的无网格解与文献中发表的结果进行了比较。最后一个问题与前两个问题有所不同，因为连续性方程式也是不连续的，并且速度在内部和外部子域中都具有非零值。