Regularizing a vortex sheet near a separation point

Current methods for computing vortex sheet separation use a regularization parameter which is discontinuous from the body to the vortex sheet. We propose two methods for reducing the errors associated with the discontinuity and improving convergence with respect to the regularization parameter. The “velocity smoothing” method is the simpler of the two, and removes the discontinuity in regularization from one of the two equations where it occurs. The “tapered smoothing” method removes the discontinuity from both equations. In a model problem, both methods are found to converge much more rapidly (with exponents 3/2 and 2 versus 1/2 for the standard method) as the regularization parameter tends to zero. Unsteady algorithms are proposed for evolving the free sheet using the two methods, and are tested in a benchmark problem. Accuracy is significantly improved for similar computational expense.