An Efficient, Interface-Preserving Level Set Re-distancing Algorithm and Its Application to Interfacial Incompressible Fluid Flow

Mark Sussman (1) , Emad Fatemi

1 FSU - Florida State University [Tallahassee]

This paper is dedicated to the memory of Dr. Emad Fatemi who was a very kind person and a truly original scientist. Abstract. In Sussman, Smereka, & Osher (1994), A n umerical scheme was presented for computing incom-pressible air-water ows 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 \con-straint" along with higher order diierence schemes in order to make the iteration method more accurate and eecient. 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 ows with noticeably better resolved results at reduced cost. We v alidate our results with experiment and theory. We s h o w 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.

Mots clés: Distance function; Incompressible; Level Sets AMS subject classiications 65M06; 76D05; 76T05

Domaines: Mécanique des structures [physics.class-ph]

Mark Sussman, Emad Fatemi. An Efficient, Interface-Preserving Level Set Re-distancing Algorithm and Its Application to Interfacial Incompressible Fluid Flow. SIAM Journal on Scientific Computing, 1999, 20 (4), pp.1165 - 1191. ⟨10.1137/S1064827596298245⟩. ⟨hal-01694576⟩