Local radial basis function collocation method for stokes equations with interface conditions

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.