Numerical Solution of Two-dimensional Channel Flow of Viscous Incompressible Fluid past an Elliptic Cylinder

Abstract

We studied a two-dimensional flow of viscous incompressible fluid past a thin elliptic cylinder in a rectilinear channel. The major axis of the cylinder has the same length as the channel width, and the center of the cylinder is placed on the midplane of the channel. Reynolds number R and the angle of attack θ of the cylinder range, respectively, between 50 and 1000 and between 0° and 40°. The new upwind difference scheme by Kawamura Kuwahara (1984) is applied to the stream function-vorticity formalism of the Navier-Stokes equations. The boundary-fitted curvilinear coordinate systems by Thompson et al (1976) are used to transform the physical plane onto a simple calculation plane. The line-Jacobi method of iteration is applied to the solution of the Poisson type equation of the stream function. The Euler explicit method of solution is applied to the solution of the vorticity equation.