A high-order blended compact difference (BCD) scheme for two-dimensional steady incompressible viscous flows

In this study, we propose a novel sixth-order blended compact difference (BCD) schemes for solving the 2D vorticity-stream function formulation of the incompressible Navier-Stokes (N-S) equations. The proposed BCD schemes are designed by blending explicit and implicit compact difference schemes, simplifying the algorithm design and coding for solving the 2D N-S equations. Furthermore, we developed a new fifth-order accuracy boundary scheme for the vorticity of various incompressible viscous flows. To validate the effectiveness of the BCD schemes, we conducted numerical experiments involving the 2D N-S equations with exact solutions and Dirichlet boundary conditions, the classical lid-driven square cavity, the backward-facing step flow, and natural convection problems. We compare the numerical results computed by the proposed BCD scheme with those existing results in the literature. It is shown that the numerical results using the BCD scheme on coarser grids are in good agreement with available calculation results on finer grids across all cases in the literature.