document: In the current CLSVOF method, the normal vector is calculated directly by discretising the LS gradient using a finite difference scheme. By appropriately choosing one of three finite difference schemes (central, forward, or backward differencing), it has been demonstrated that thin liquid ligaments can be well resolved see Xiao (2012). Although a high order discretisation scheme (e.g. 5th order WENO) has been found necessary for LS evolution in pure LS methods to reduce mass error, low order LS discretisation schemes (2nd order is used here) can produce accurate results when the LS equation is solved and constrained as indicated above in a CLSVOF method (see Xiao, 2012), since the VOF method maintains 2nd order accuracy. This is a further reason to adopt the CLSVOF method, which has been used for all the following simulations of liquid jet primary breakup.