Multiphase flows are generated in several industrial domains. The numerical simulation of such flows need to have an exact tracking of the different phase interfaces. The level set method is one of the simplest methods used to study the moving front of the flow. But it is known that this method generates a non mass conservation, and do not respect the uniformity of the signed distance function. Several corrections are usually proposed to solve these problems when using the Level set method. In this paper, a novel two steps correction method is proposed in order to guarantee the flow mass conservation and the exact shape of the flow front. The first step concerns the correction of the mass loss. It consists to add in the transport equation, a penalty or constraint term, built to force the velocity field to satisfy the mass balance or to preserve the conservative property. This term is multiplied to an adjustable penalty factor (β). The second step consists to impose that the isocontours of the level set function (φ) always respect the same distance. With this way, the costly reinitialization procedure is eliminated. The performance of the method is demonstrated and validated using several cases involving two-phase flow. The numerical experiments show that the accuracy and performances of our method is drastically improved compared to other methods. The approach will then applied to track an air-liquid interface in a case of an air bubble moving in a constant volume of liquid. In this case, the classical level set method reveals to be not conservative. A solution is then proposed in order to introduce a correction. To do, Navier-Stokes, continuity and energy equations are coupled to describe the flow and its thermal behavior. A finite element method is used to solve the equations. The solution is also verified by solving the dam-break problem, and bubble rising in water. Good agreements with referenced solutions are demonstrated for all tow investigated problems.

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