Understanding of various coupling schemes used for Fluid-Structure Interaction (FSI) is quite challening, considering especially that FSI problems often require high-fidelity simulations. However, efforts have been made to simplify the problem and gain some insights into the behaviour of different FSI coupling schemes [1-4]. One such a simplified model is the well-known spring-mass-damper system which is recast as an FSI problem. Despite its simplicity, this problems serves as a useful model to understand the characteristics of FSI coupling schemes.
This repository provides a set of Jupyter notebooks with embedded Python scripts to understand various properties and solution behaviour of different coupling schemes used for FSI. Python scripts provide functions to calculate
- spectral radius of the amplification matrix which tells us a great deal about stability and numerical damping characteristics, and
- numerical solutions of the FSI problem with different coupling schemes.
Currently, monolithic scheme and staggered schemes based on
- Dirichlet-Neumann coupling,
- force and displacement predictors, and
- Backward Euler time integration scheme
are covered. But the concepts can be extended to other types of schemes.
[1] C A Felippa, K C Park and C Farhat, Partitioned analysis of coupled mechanical systems, Computer Methods in Applied Mechanics and Engineering, 190:3247-3270, 2001. DOI
[2] W G Dettmer and D Perić, A new staggered scheme for fluid-structure interaction, International Journal for Numerical Methdos in Engineering, 93:1-22, 2013. DOI
[3] C Kadapa, A second-order accurate non-intrusive staggered scheme for the interaction of ultra-lightweight rigid bodies with fluid flow, Ocean Engineering, 217:107940, 2020. DOI
[4] W G Dettmer, A Lovrić, C Kadapa, D Perić, New iterative and staggered solution schemes for incompressible fluid-structure interaction based on Dirichlet-Neumann coupling, International Journal for Numerical Methdos in Engineering, 122:5204-5235, 2021. DOI