Numerical simulation of square cavity flow by second-order up-wind finite volume method

A discretization scheme based on unstructured grids and the Finite Volume Method (FVM) with secondary-order accuracy was investigated in this paper. In order to achieve secondary-order accuracy, Taylor's formula was used on the interface for the convection term. NND (Non-oscillatory, containing No free parameters and Dissipative scheme) was employed to cope with the gradient term in Taylor's formula to avoid the instability of the center difference scheme. The Delaunay triangle grids were employed and the square cavity flow was systematically simulated. The nodes and the elements number were 12960 and 25600 respectively. The Semi-Implicit Method for the Pressure-Linked Equations Consistent (SIMPLEC) method was used on pressure correction. The steady flow numerical simulation results with Reynolds number up to 5000 were given in good agreement with the benchmark solution. The less grid number was used in this paper. The present method has good convergence and stability and furthermore, the relaxation factor has little effect on the results.