Abstract: To keep interface fixed.we derive formula of smoothing parameter in level set re-initialization equation and form a implicit re-initialization method.It was proved that as the developed method is used to reinitialize the level set function for ensuring sign of level set function on nodes near interlace the time step need only to satisfy the original CFL condition.Finally,the improved method is combined with the original method to make an accurate and fast implicit re-initialization method. Numerical examples illustrate effectiveness of the methods.

Key words: level set, re-initialization, smoothing parameter, CFL condition