- Title Information
- Title
- Recent Advances in Splitting Methods Based on Robin-Robin Coupling Conditions
- Type of Resource (primo)
- dissertations
- Name:
Personal
- Name Part
- Durst, Rebecca Frances
- Role
- Role Term:
Text
- creator
- Name:
Personal
- Name Part
- Guzman, Johnny
- Role
- Role Term:
Text
- Advisor
- Name:
Personal
- Name Part
- Shu, Chi-Wang
- Role
- Role Term:
Text
- Reader
- Name:
Personal
- Name Part
- Burman, Erik
- Role
- Role Term:
Text
- Reader
- Name:
Corporate
- Name Part
- Brown University. Department of Applied Mathematics
- Role
- Role Term:
Text
- sponsor
- Origin Information
- Copyright Date
- 2022
- Physical Description
- Extent
- xii, 195 p.
- digitalOrigin
- born digital
- Note:
thesis
- Thesis (Ph. D.)--Brown University, 2022
- Genre (aat)
- theses
- 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.
- Subject (fast)
(authorityURI="http://id.worldcat.org/fast", valueURI="http://id.worldcat.org/fast/01041273")
- Topic
- Numerical analysis
- Subject (fast)
(authorityURI="http://id.worldcat.org/fast", valueURI="http://id.worldcat.org/fast/00928033")
- Topic
- Fluid-structure interaction--Mathematical models
- Language
- Language Term (ISO639-2B)
- English
- Record Information
- Record Content Source (marcorg)
- RPB
- Record Creation Date
(encoding="iso8601")
- 20220706