Level set & distance functions

Renato.

When solving free surface flows with level set methods we have to specify an interface as initial condition to transport through some way. I understood that the first interface would be the 0 level set of a signed distance function where the values < 0 indicate one fluid and values > 0 the other.

The signed distance function can be generated solving the following equation:

phi,t + sign(phi)*(1-||grad(phi)||)

where: phi: is the signed distance function; grad: gradient operator; sign: signal function; phi,t: time derivative of phi

Now, my question is: Which boundary (or initial) condition should I prescribe in order to get the first signed distance function according to the initial interface desired to transport?

I was thinking about prescribing a zero distance on nodes (I'm using FEM) of the interface as boundary conditions. Should I prescribe values positive and negative, as initial conditions, according to where is the fluid "A" and "B"? It was not clear for me in the papers I read (a bunch of Sussman's and Sethian's papers). They only tell about reinitialization procedures during the time integration procedure when a signed distance functions is already supposed to exist.

In VOF and pseudo-concentration methods we only need to set which fluid has "concentration" 1 and 0 as initial conditions to the transport solver (besides de flow conditions) and the problem is defined.

Does anybody could help me?

Thanks

Renato.