These codes were very recently uploaded (March 20th, 2024) from my system and have yet to be vetted for general distribution/use. I am currently working through commenting, cleaning and re-testing these solver which were put together approximately 1 year ago. Please allow me the next few weeks to clean up the codes so as to make them more instructive, easy to use, and bug-free.
If the reader is still compelled to experiment I encourgae them to do so, however, while this disclaimer is being displayed I suggest that one exercises reasonable caution when using the partitoned solvers provided.
For detailed configuartion, installation and operation instructions, in particular for the redbKIT based solvers, please follow the steps contained in the brief INSTALL.md file provided.
2D Rigid-Body FSI solver
This partitioned FSI scheme was developed at the University of British Columbia by the graduate students of my superviosor Dr. Rajeev Jaiman. It uses stabilized streamline-upwind Petrov-Galerkin (SUPG) Pm/Pm-1/Pm iso-parametric finite elements to satisfy the inf–sup condition of the fluid domain equations. The solid domain is simply modelled as an elastically mounted rigid cylinder that is free to translate along its two directional degrees of freedom. Temporal discretization is achieved via the generalized-α method for each set of domain equations.
Further reading on this approach can be found in
2D & 3D redbKIT-based solvers
This repository contains 2D and 3D high-fidelity computational fluid-structure interaction solvers built (mainly) in MATLAB. They are primarily focused on solving two-field problems in a partitioned fashion, where the incompressible Navier-Stokes equations - written in the Arbitrary Lagrangian Eulerian (ALE) form - are coupled with the nonlinear elastodynamics structural equations. For 2D FSI problems the user has the option to choose either a linear elastic constitutive material model for the structural mechanics solver (2D_Part_FSI_LE) or a nonlinear St. Venant Kirchhoff material model (2D_Part_FSI_SVK). For 3D FSI problems, the user can additionally choose a nearly-incompressible NeoHookean constitutive material model for the structural mechanics solver (3D_Part_FSI_NH).
These solvers all use a Galerkin least-squares finite element strategy for each set of domain specific equations. Here we exclusively use higher-order P2 finite elements for the structural equations and stable Taylor-Hood P2/P1 mixed finite elements for the fluid equations. A second-order backward difference scheme is adopted for the temporal discretization of the fluid domian whilst the generalized-α method is used for the structural domian.
In all cases (except for the 2D rigid-body solver) each code was derived from a corresponding redbKIT monolithic FSI solver. These solvers were decomposed into their baseline elements and were then strategically reassembled and further built upon such that we finally ended up with a partitioned numerical framework. These partitoned solvers (given above) served as a robust testbed for my subsequent investigation of "coupling instability in low mass-ratio partitioned FSI simulations". From this effort, algorithmic solutions to stabilize and accelerate the fixed point coupling procedure comensurate with the partitioned approach were recommended.
Features unique to the partitioned strategy that have been included in each of the solvers provided include:
-
Coupling Methods:
- Anderson Acceleration
- Generalized Broyden
- Broyden's Second Method
- Multi-Vector Least Square
- Dynamic Aitken Relaxation
- Constant Relaxation
- Pure Gauss-Seidel Iterations
-
Filtering Strategies:
- QR1 filtering
- QR2 (Classic Gram-Schmidt) filtering
- QR2 (Modified Gram-Schmidt) filtering
- QR2 (Householder Reflections) filtering
- POD filtering
-
Interface Mapping Techniques:
- Nearest Neighbour Interpolation
- Projection and Linear Interpolation
- Radial Basis Function Interpolation
-
Extrapolation Methods:
- Constant
- Linear
- Quadratic
- Cubic
-
- Interface tracking
- Adaptive Regularization Least Squares
- Selective Secant Inclusion
- Truncated SVD filtering
For absolute clarity, the redbKIT toolkit by itself is an AMAZING resource for (young) academics seeking an education in the finite element method and reduced-order modelling. As such, I strongly recommend the reader fork that repository and work through redbKIT's numerous well crafted example problems. *I personally give this resource the lion's share of credit in helping me complete my graduate studies.*
These solvers, however, are of a monolthic construction and thus require the linearization of one set of domain equations with respect to the other for the system of equations to be solvable. If the interested reader is more interested in the details of partitioned coupling, however, or would like to develop one of the respective domain solvers independently of the other domain they may find the tools found in this repository very useful.
Lastly, for those readers seeking a more digestible version of the rebKIT-based monolthic FSI solvers or the individual (rebKIT-based) domain-specific solvers I have additionally compiled what I believe to be useful resources in the following repositories:
redbKIT is a MATLAB library for finite element simulation and reduced-order modeling of Partial Differential Equations developed at EPFL - Chair of Modeling and Scientific Computing).
In particular, it includes straightforward implementations of many of the algorithms presented in the companion book:
For further details please visit redbKIT website.
redbKIT is distributed under BSD 2-clause license
Copyright (c) 2015-2017, Ecole Polytechnique Fédérale de Lausanne (EPFL) All rights reserved.
Redistribution and use in source and binary forms, with or without modification, are permitted provided that the following conditions are met:
- Redistributions of source code must retain the above copyright notice, this list of conditions and the following disclaimer.
THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS "AS IS" AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL THE COPYRIGHT HOLDER OR CONTRIBUTORS BE LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE.
redbKIT was developed and maintained by Federico Negri. Paola Gervasio (Università degli Studi di Brescia) is gratefully acknowledged for granting the use of parts of the finite element code MLife.
If you have any questions regarding the contents of this repository or the use of these solvers, please feel to email me at josetg@vt.edu.