Improving conservative level-set methods for multiphase simulations


Project Description

This projects starts with a newly developed conservative level-setmethodfor 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 notrequirereconstruction of the interface and that produces an approximation of the signeddistancefunction (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 functionsrequiresnon-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 obtainqualitativelygood 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.​​
Program - Applied Mathematics and Computer Science
Division - Computer, Electrical and Mathematical Sciences and Engineering
Field of Study - ​Applied mathematics and computational science

About the

David I. Ketcheson

Associate Professor, Applied Mathematics and Computational Science

David I. Ketcheson

​Professor Ketcheson's research interests are in the areas of numerical
analysis and hyperbolic PDEs. His work includes development of efficient
time integration methods, wave propagation algorithms, and modeling of
wave phenomena in heterogeneous media.

Desired Project Deliverables

​Implementation and testing of the proposed algorithm​