HIGHER-ORDER SOLUTIONS OF SQUARE DRIVEN CAVITY FLOW USING A VARIABLE-ORDER MULTIGRID METHOD

A new higher-order method is devised for the numerical simulation of square driven cavity flows. The spatial derivatives of the Navier-Stokes equations are discretized by means of the modified differential quadrature (MDQ) method. The resulting system of ordinary differential equations (ODEs) in time is then integrated by the classical fourth-order Runge-Kutta-Gill (RKG) scheme. The elliptic (Poisson) equation is solved by means of a new variable-order multi-grid method. The numerical simulations of the square driven cavity flows are carried out with spatial order of accuracy up to 10th order. The results suggest that the higher-order solutions are more reliable than the well-known results obtained by Ghia et al.