Many atomization processes are characterized by large density ratios coupled with large shear. Numerical simulations are known for becoming unstable in these physical conditions. We developed a new mass and momentum consistent algorithm for CLSVOF method. Based on Rudman's work, the originality of our approach is to avoid using a sub-grid by splitting flux calculation between neighboring cells. The method is validated by comparing simulations with theoretical results and experimental air assisted atomization of a coaxial jet.