A Characteristics-Mix Stabilized Finite Element Method for Variable Density Incompressible Navier-Stokes Equations

This paper describes a characteristics-mix finite element method for the computation of incompressible Navier-Stokes equations with variable density. We have introduced a mixed scheme which combines a characteristics finite element scheme for treating the mass conservation equation and a finite element method to deal with the momentum equation and the divergence free constraint. The proposed method has a lot of attractive computational properties: parameter-free, very flexible, and averting the difficulties caused by the original equations. The stability of the method is proved. Finally, several numerical experiments are given to show that this method is efficient for variable density incompressible flows problem.