Numerical computation of three-dimensional incompressible viscous flows in the primitive variable form by local multiquadric differential quadrature method

In this paper, the local multiquadric differential quadrature (LMQDQ) method is applied on three-dimensional incompressible flow problems. The LMQDQ method is among the newly proposed mesh-free methods. Unlike the traditional differential quadrature (DQ) method, the weighting coefficients of LMQDQ method are determined by using the radial basis functions (RBFs) as the trial functions instead of high-order polynomials. The main concern of this paper is to discuss the effectiveness of using LMQDQ method to solve 3-D incompressible Navier–Stokes (N–S) equations in the primitive-variable form. Three-dimensional lid-driven cavity flow problem with Reynolds numbers of 100, 400 and 1000 was chosen as a test case to validate the LMQDQ method. The computed velocity profiles along the vertical and horizontal centerlines are given and compared with available data in the literature.