An efficient, interface-preserving level set redistancing algorithm and its application to interfacial incompressible fluid flow

In Sussman, Smereka, and Osher [J. Comp. Phys., 94 (1994), pp. 146-159], a numerical scheme was presented for computing incompressible air-water flows using the level set method. Crucial to the above method was a new iteration method for maintaining the level set function as the signed distance from the zero level set. In this paper we implement a "constraint" along with higher order difference schemes in order to make the iteration method more accurate and efficient. Accuracy is measured in terms of the new computed signed distance function and the original level set function having the same zero level set. We apply our redistancing scheme to incompressible flows with noticeably better resolved results at reduced cost. We validate our results with experiment and theory. We show that our "distance level set scheme" with the added constraint competes well with available interface tracking schemes for basic advection of an interface. We perform basic accuracy checks and more stringent tests involving complicated interfacial structures. As with all level set schemes, our method is easy to implement.