Description
- Abstract:
- In this thesis we develop a loosely coupled splitting method for coupled problems called the Robin-Robin splitting method. As the name suggests, this method is based on Robin-type interface coupling conditions, used in place of the traditional Dirichlet and Neumann conditions at the interface. We first apply these conditions to two model systems: (1) where two parabolic equations are coupled across an interface, and (2) where parabolic and hyperbolic equations are coupled across an interface. We analyze these systems together using a novel unified framework and show that the error decreases nearly optimally as $\mathcal{O}(\Delta t \sqrt{\log{1+ \frac{1}{\Delta t}}})$. The success of the analysis relies on the construction of a particular continuous function, $\phi$, that acts as a lifting operator from the interface to the interior. We then apply this Robin-Robin method to the fluid-structure interaction problem in both a time-semi-discrete framework and a fully discrete framework. Using a variation of the parabolic/hyperbolic lifting operator $\phi$, we demonstrate that the method is unconditionally stable and that the error also decreases nearly optimally as $\mathcal{O}(\Delta t \sqrt{\log{1+ \frac{1}{\Delta t}}})$, although this behavior can be significantly delayed depending on the values of the physical parameters. As the Robin-Robin method is unconditionally stable in time, it does not suffer from the added-mass instability known to pose an issue for other loosely coupled splitting methods applied to the fluid-structure interaction problem. Notably, this is the first provably stable, nearly optimal loosely coupled splitting method for the fluid-structure interaction problem.
- Notes:
- Thesis (Ph. D.)--Brown University, 2022
Citation
Durst, Rebecca Frances,
"Recent Advances in Splitting Methods Based on Robin-Robin Coupling Conditions"
(2022).
Applied Mathematics Theses and Dissertations.
Brown Digital Repository. Brown University Library.
https://repository.library.brown.edu/studio/item/bdr:v34deskr/
Relations
Collection:
-
Applied Mathematics Theses and Dissertations
Theses and Dissertations for the Applied Mathematics department....