A Remark on Computing Distance Functions

We propose a new method for the reconstruction of the signed distance function in the context of level set methods. The new method is a modification of the algorithm which makes use of the PDE equation for the distance function introduced by M. Sussman, P. Smereka, and S. Osher (1994, J. Comput. Phys.119, 146). It is based mainly on the use of a truly upwind discretization near the interface. Comparison with the previous algorithm shows a definite improvement. When used with a first-order upwind scheme, the method provides first-order accuracy for the signed distance function in the whole computational domain, and second-order accuracy in the location of the interface. A second-order version of the method is also presented.