AN EFFICIENT SCHEME FOR UNSTEADY-FLOW PAST AN OBJECT WITH BOUNDARY CONFORMAL TO A CIRCLE

An efficient finite-difference method is presented for studying unsteady two-dimensional incompressible flow past an object with boundary conformal to a circle. At each time step the computations of vorticity transport and streamfunction are decoupled and based on a body-fitted, prowake, orthogonal grid. To handle the no-slip condition properly and efficiently, a new wall-vorticity conditioning algorithm is proposed and incorporated into the vorticity transport equation. When the object presents sharp edges, this algorithm performs particularly well in that it yields a significant increase in the time step increment that can be used in comparison to other known "decoupled" methods. In the method developed here the vorticity is advanced by an implicit scheme of Crank-Nicholson type, and the streamfunction equation is solved by a multigrid technique based on body-fitted coordinates. As an application, the experiment on flow past an inclined thin ellipse with angle of attack ranging from 5-degrees to 85-degrees, and at Reynolds number 200 and 400, is presented in detail. Depending on the angle of attack, the computed results present in the long run a quasi-steady or quasi-periodic feature, as demonstrated by the flow pattern and by the curves of drag, lift, and moment coefficients. Furthermore, the pivot point, with respect to which the thin ellipse exercises no torque, is also investigated and compared to the asymptotic result based on Kirchhoff theory. Such a result might be useful in modeling a pivoting prosthetic heart valve.