The desingularization smoothing parameter is introduced in calculating the induced velocity on trailing vortex surface.

For the defect that it is hard to determine the smoothing parameter in time-varying conditions, the adaptive optimizing strategy based on contributing ratio is proposed.

As the non-degeneracy condition holds and the smoothing parameter tends to zero, an S-stationary point of the MPCC problem is equivalent to a KKT point of the smoothing nonlinear programming.