Stable Numerical Method Applying a Total Variation Diminishing Scheme for Incompressible Flow

To solve incompressible Navier-Stokes equations, a stable finite difference method applying a total variation diminishing (TVD) upwind scheme originally designed for compressible flow is proposed. The validity and the receptivity of this method employing such a TVD scheme for application to incompressible flow analysis are investigated by the evaluation of the accuracy, stability, and convergence rate. Using the generalized implicit simplified marker and cell (SMAC solution method combined with the TVD scheme, three-dimensional developing entry flows through a square curved duct are calculated and compared with available experimental data and some computational results obtained by quadratic upstream interpolations for the convective kinematics (QUICK) schemes, as well as by third-order upwind schemes