This projects starts with a
newly developed conservative level-set method
for multiphase flows. This method combines ideas from the level-set and
the volume of fluid schemes into a monolithic model. The model contains a consistent term
that regularizes the Jacobian of the non-linear equation and that penalizes deviations
from the signed distance function.
The result is a conservative level-set model that does
not require reconstruction of the interface and that produces an approximation of
the signed distance function (to the fluids
interface).
In the current project we aim to improve the method in
the following three fronts:
- The current form of the method does not require
extra stabilization of the advective term since it depends upon the
penalization term. This however, implies that one can't reduce the influence of
the penalization or instabilities might start to appear. We want to introduce
extra and independent stabilization to the advective term.
The model is a conservation law for a
regularized Heaviside function. The reason for this is that integration of
discontinuous functions requires non-standard
methodologies within the context of finite elements.
We plan to use state of the art integration
techniques that would allow us to use exact Heaviside functions improving the
conservation properties and overall quality of
the solution.
- The model contains a user defined parameter. To
obtain qualitatively good results one might need to select this parameter
depending on the problem. This dependency can be mitigated via optimal control
theory that would allow the algorithm to automatically
select an optimal parameter for any given problem.
We plan to test each modification to the method via a set
of well established benchmarks in the
area of multiphase flows.