  Existing artificial compression based reinitialization scheme for
conservative level set method has a few drawbacks, like distortion of
fluid-fluid interface, unphysical patch formation away from the interface and
lack of mass conservation. In this paper, a novel reinitialization approach has
been presented which circumvents these limitations by reformulating the
reinitialization equation. With the reformulated procedure, the present
approach is able to reinitialize the level set function without causing any
unwanted movement of the interface contour. The unphysical patch formation away
from the interface is also resolved here by avoiding the use of ill-conditioned
contour normal vectors. As a result of this measure, there is a significant
improvement in the mass conservation property. In addition, the simplified form
of the new reinitialization equation enables one to choose a much larger time
step during the reinitialization iteration. Moreover, the new formulation also
helps in reducing the amount of numerical computations per time step, leading
to an overall reduction in the computational efforts. In order to evaluate the
performance of the present formulation, a set of test problems involving
reinitialization of stationary level set functions is carried out first. Then,
the efficacy of the proposed reinitialization scheme is demonstrated using a
set of standard two-dimensional scalar advection based test problems and
incompressible two-phase flow problems. Finally, the ability to deal with
complex mesh types is demonstrated by solving a test problem on an unstructured
mesh consisting of finite volume cells having triangular and quadrilateral
shapes.
