Abstract
In this paper, we continue our efforts toward numerical simulation of high $Re$ ($1000 \leq Re \leq 9500$) unsteady incompressible flows with the finite difference method on the curvilinear half-staggered mesh. The finite difference scheme and the projection method for the numerical solution of the incompressible Navier--Stokes equations in primitive variables was proposed and verified in [L. C. Huang, J. Comput. Math, to appear]. Here we derive the discrete Poisson equation on the curvilinear half-staggered mesh and discuss its properties. For unsteady complex flow simulation, rapid solution of this equation is crucial; the multilevel one-way dissection methods offer effective solutions. Numerical simulation of high $Re$ flows around circular and aerofoil-shaped cylinders show our method to be efficient and robust.
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