A novel vortex scheme with instantaneous vorticity conserved boundary conditions

• A novel method to deal with the boundary vortices.
• The instantaneous circulation is conserved at each time-step.
• The fluctuating pressure coefficient can be obtained well.
• The accuracy of the surface pressure coefficient improves better.
• This scheme can be extended to the other vortex method and any bluff body.

In the existing stream function based vortex methods, the solution to deal with the boundary vortex blobs is mainly eliminating the blobs that penetrate the cylinder and compensating the lost vorticity in the next time step. However, the instantaneous vorticity cannot be guaranteed to be zero, which leads to inaccuracy fluid forces. In this paper, a novel vortex scheme based on instantaneous vorticity conserved boundary conditions (IVCBC) is proposed to deal with the boundary vortices over a circular cylinder. Instead of eliminating the blobs inside, it introduces identical number of new vortex blobs outside the cylinder to counteract the strengths of the ones inside to ensure the instantaneous vorticity zero, and keep the cylinder’s surface being streamline. Long time simulation of two-dimensional viscous incompressible flows is performed at Reynolds numbers 9.5×1039.5×103, 5.5×1045.5×104, 1×105 and 1.4×1051.4×105. The results reveal that the proposed method is converged, and it significantly improves the precision of predicting the fluid forces, especially the fluctuating fluid forces and the Reynolds stress. Furthermore, this method can be extended to models of multiple circular cylinders, and any shape bluff bodies.