Level Set Method and Ghost Fluid Method
 

I am studying the Level set method(LSM) and Ghost Fluid Method(GFM)recently and want to make a solver in OF,

but I have some question now ,

If the zero level set corss a cell,the cell is occupied partly by air and partly
by water, My question is how to define the velocity in this cell ,because I shoule
extroplate the real value to the ghost cell and the evolution of the levle set function need the velocity in each cell。