Numerous physical phenomena in nature involve the motion of interfaces separating two or more regions. The level-set method was a PDE-based approach designed to capture the interface motion through the evolution of a signed distance function. This exploratory project aims to further extend the level-set method to unstructured adaptive Cartesian grids.
We plan to address the following research task: Development of a level-set solver supporting the adaptive Cartesian grids, and various data structures including both tree and list-based data structures. This solver will be coupled to an adaptive Cartesian grid adaptor for interface based grid adaptations to improve the interface resolution and decrease the numerical errors near the interface.
A set of software tools will be developed and made available that can be used to both train students with basic interface dynamics, and to conduct research in challenging engineering and scientific disciplines.
