A new numerical simulation method of high Reynolds number flow around a cylinder

Abstract

A new finite-difference is presented to solve the unsteady two-dimensional Navier-Stokes equations in the vorticity stream function form and tested for the flow around a cylinder at Reynolds number Re of 103-104. The simulation uses a body-fitting Cartesian coordinate system in the physical plane which is transformed by conformal mapping to a grid with uniform mesh sizes in the computational domain. A new mixed difference scheme coupling the 3rd-order upwind scheme with the 4th-order central scheme is used for the discretization of the vorticity transport equation, while a 2nd-order central scheme is used for the discretization of the stream function equation. Some numerical results for flow past a circular cylinder at Re=1000 to 9500 and an elliptic cylinder with different angle of attack are given. This numerical method gives results comparable to those of previously published methods but does do using much less memory and computer time. The ease of setting boundary condition is another advantage of the present method. The influence of the initial condition and the grid system, time step is also discussed.