Abstract
This paper describes a characteristics-mix finite element method for the computation of incompressible Navi-er-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.
Highlights
This paper is devoted to the numerical approximation of incompressible viscous flows with variable density
We use a time-splitting, solving the first equation for a given velocity by using a characteristic stabilized finite element approach which is efficient when dealing with a pure convection equation, and we compute the divergence free solution of the last two equations by exploiting the advantages of FE methods, see [22]-[24]
We proposed a characteristics-mix finite element method to the case of incompressible viscous flows with variable density
Summary
This paper is devoted to the numerical approximation of incompressible viscous flows with variable density. The method uses a time splitting, solving separately the transport equation for the density and the momentum for the velocity, the incompressible constraint being treated through a projection method, see [8] This is the methodology followed in [3] [9]-[11]. We use a time-splitting, solving the first equation for a given velocity by using a characteristic stabilized finite element approach which is efficient when dealing with a pure convection equation, and we compute the divergence free solution of the last two equations by exploiting the advantages of FE methods, see [22]-[24].
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