An implicit meshless rbf-based differential quadrature method applied to the lid-driven cavity problem

In the present study, a numerical investigation of steady-state Stokes flow problem on a lid-driven square cavity is carried out using mesh-free local radial basis function-based differential quadrature (RBF-DQ) method. This method is a combination of differential quadrature approximation of derivatives and function approximation of RBF. The weighting coefficients of (RBF-DQ) method are determined by using Radial Basis Functions (RBF) as test functions instead of using high-order polynomials. Discretized derivatives of velocity and pressure at a point is defined by a weighted linear sum of functional values at its neighboring points. In this work, this method is applied to the two-dimensional Stokes flow in a fully coupled form using a staggered arrangement of primitive variables. Results obtained from the RBF-DQ method are compared with the existing result in the literature on lid-driven cavity problem. In order to get better understanding for the RBF-DQ method, outcomes are discussed in details.