A vorticity-based method for incompressible unsteady viscous flows

Abstract

A novel approach is presented, based on the integral form of the vorticity formulation, in which the vorticity transport equation is solved by using the cell-centred finite-volume method, while the velocities needed at the centre of each control volume are calculated by a modified Biot–Savart formula in conjunction with a fast summation algorithm. The vorticity and mass conservation in the flow are guaranteed during the calculation by virtue of the finite volume approach and the method of implementing the boundary conditions at the body surface. As an example, both the early stage development and long term evolution of the flow around an impulsively started circular cylinder are computed using the method. The present results are compared with other numerical and experimental results for the same flow problem and show good agreement.