Numerical Solution of Stokes Flow in a Circular Cavity Using Mesh-free Local RBF-DQ

This work reports the results of a numerical investigation of Stokes flow problem in a circular cavity as an irregular geometry using mesh-free local radial basis function-based differential quadrature (RBF-DQ) method. This method is the combination of differential quadrature approximation of derivatives and function approximation of Radial Basis Function. As a result, the method can be used to directly approximate the derivatives of dependent variables on a scattered set of knots. In this study knots were distributed irregularly in the solution domain using the Halton sequences. The method is applied on a two-dimensional geometry. The obtained results from the numerical simulations are compared with those gained by previous works. Outcomes prove that the current technique is in very good agreement with previous investigations and this fact that RBF-DQ method is an accurate and flexible method in solution of partial differential equations (PDEs).