“…The fourth step is a hyperbolic problem for the scalar level-set function ~b. This problem is solved by using a upwinding scheme where the advection term is discretized using a third-order scheme [18,19,23]. That is, u -V~b at x ° is estimated using the known values of ~b at the five points X -2, X -l , X 0, X 1 , and X 2, which lie on the line that is parallel to u and passes through x °, u. V4>(x °) = lu(x°)l ~ rj4~(xJ) where ~i = IX i __ X0]/h.…”