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@@ -6,22 +6,23 @@ interaction problems: mathematical modeling and numerical approximation"** | |
| | <!-- --> | <!-- --> | | ||
| | -- | -- | | ||
| | **Author** | Luca Heltai <[email protected]> | | ||
| | **GitHub Repository:** | https://github.com/luca-heltai/fsi-suite | | ||
| | **GitHub Pages:** | https://luca-heltai.github.io/fsi-suite/ | | ||
| | **GitHub Repository:** | <https://github.com/luca-heltai/fsi-suite> | | ||
| | **GitHub Pages:** | <https://luca-heltai.github.io/fsi-suite/> | | ||
| | **Licence:** | see the file [LICENCE.md](./LICENCE.md) | | ||
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| ## Course Introduction | ||
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| Fluid-structure interaction (FSI) refers to the multiphysics coupling between | ||
| the laws that describe fluid dynamics and structural mechanics. | ||
| the laws that describe fluid dynamics and structural mechanics. | ||
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| This page collects the material that I have used for a course given at Kaust | ||
| (https://www.kaust.edu.sa/en) during the spring semester of 2022. | ||
| (<https://www.kaust.edu.sa/en>) during the spring semester of 2022. | ||
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| The course covers three main topics: i) basics of continuum mechanics, ii) | ||
| mathematical modeling of FSI problems, and iii) numerical implementations based | ||
| on the finite element method. Theoretical lectures are backed up by applied | ||
| laboratories based on the C++ language, using example codes developed with the | ||
| open source finite element library deal.II (www.dealii.org). I cover basic | ||
| open source finite element library deal.II (<www.dealii.org>). I cover basic | ||
| principles of continuum mechanics, discuss Lagrangian, Eulerian, and Arbitrary | ||
| Lagrangian-Eulerian formulations, and cover different coupling strategies, both | ||
| from the theoretical point of view, and with the aid of computational | ||
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@@ -32,8 +33,8 @@ finite element approximations for the solution of continuum mechanics problems, | |
| including non-linear mechanics, computational fluid dynamics, and | ||
| fluid-structure-interaction problems. | ||
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| A glimpse of the PDEs that are discussed in the course is given by the following | ||
| graph | ||
| A glimpse of the PDEs that are discussed in the course is given by the following | ||
| graph | ||
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| @dotfile serial.dot width=100% | ||
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| The laboratory part should enable a PhD student working on numerical analysis | ||
| of PDEs to implement state-of-the-art adaptive finite element codes for FSI | ||
| problems, that run in parallel, using modern C++ libraries. The implementation | ||
| are based on the `deal.II` library (www.dealii.org). | ||
| are based on the `deal.II` library (<www.dealii.org>). | ||
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| Main topics covered by these lectures: | ||
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@@ -57,27 +58,27 @@ Main topics covered by these lectures: | |
| Continuous Integration Status | ||
| ----------------------------- | ||
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| Up to date online documentation for the codes used in the laboratories is here: | ||
| Up to date online documentation for the codes used in the laboratories is here: | ||
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| https://luca-heltai.github.io/fsi-suite/ | ||
| <https://luca-heltai.github.io/fsi-suite/> | ||
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| | System | Status | | ||
| | ------ | ------- | | ||
| | ------ | ------- | | ||
| | **Continous Integration** | [](https://github.com/luca-heltai/fsi-suite/actions/workflows/tests.yml) | | ||
| | **Docker** | [](https://github.com/luca-heltai/fsi-suite/actions/workflows/docker.yml) | | ||
| | **Doxygen** | [](https://github.com/luca-heltai/fsi-suite/actions/workflows/doxygen.yml) | | ||
| | **Indent** | [](https://github.com/luca-heltai/fsi-suite/actions/workflows/indentation.yml) | | ||
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| ## Useful links | ||
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| One of my courses on theory and practice of finite elements: | ||
| - https://www.math.sissa.it/course/phd-course/theory-and-practice-finite-element-methods | ||
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| - <https://www.math.sissa.it/course/phd-course/theory-and-practice-finite-element-methods> | ||
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| Exceptional video lectures by Prof. Wolfgang Bangerth, that cover all the | ||
| things you will ever need for finite element programming. | ||
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| - https://www.math.colostate.edu/~bangerth/videos.html | ||
| - <https://www.math.colostate.edu/~bangerth/videos.html> | ||
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| ## Quick start | ||
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| Will run program-name with program-options, possibly via mpirun, passing -np N to mpirun. | ||
| Here is a list of programs you can run: | ||
| linear_elasticity.g mpi_stokes.g | ||
| distributed_lagrange mesh_handler poisson | ||
| distributed_lagrange.g mesh_handler.g poisson.g | ||
| dof_plotter mpi_linear_elasticity reduced_lagrange | ||
| dof_plotter.g mpi_linear_elasticity.g reduced_lagrange.g | ||
| fsi_test mpi_poisson stokes | ||
| fsi_test.g mpi_poisson.g stokes.g | ||
| linear_elasticity mpi_stokes | ||
| linear_elasticity.g mpi_stokes.g | ||
| distributed_lagrange mesh_handler poisson | ||
| distributed_lagrange.g mesh_handler.g poisson.g | ||
| dof_plotter mpi_linear_elasticity reduced_lagrange | ||
| dof_plotter.g mpi_linear_elasticity.g reduced_lagrange.g | ||
| fsi_test mpi_poisson stokes | ||
| fsi_test.g mpi_poisson.g stokes.g | ||
| linear_elasticity mpi_stokes | ||
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| Programs ending with .g are compiled with debug symbols. To see help on how to run | ||
| any of the programs, add a -h flag at the end. | ||
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| The above command will download the latest docker image from the `main` branch | ||
| of this repository (which is built and uploaded to | ||
| https://hub.docker.com/r/heltai/fsi-suite at every commit to master), mount the | ||
| <https://hub.docker.com/r/heltai/fsi-suite> at every commit to master), mount the | ||
| current directory, in a directory with the same path inside the container, and | ||
| the program you selected. For example, | ||
| the program you selected. For example, | ||
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| ./fsi-suite.sh -np 4 mpi_poisson.g | ||
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| conditions, forcing terms, finite element spaces, etc. by editing the | ||
| configuration file which is created the first time you run the program, and then | ||
| passing it as an argument to the program itself, i.e., in the example above, the | ||
| parameter file that would be generated is `used_mpi_poisson.g_2d.prm`, which you | ||
| parameter file that would be generated is `used_mpi_poisson.g.prm`, which you | ||
| can edit and then pass as input to the program itself: | ||
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| ./fsi-suite.sh -np 4 mpi_poisson.g used_mpi_poisson.g_2d.prm | ||
| ./fsi-suite.sh -np 4 mpi_poisson.g used_mpi_poisson.g.prm | ||
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| If you want to read some documentation of what each parameter does and how it | ||
| works, you can call the program passing a non-existing parameter file: | ||
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| The created parameter file will also contain documentation for each parameter. | ||
| Running again the same command will now use the parameter file that was just | ||
| created: | ||
| created: | ||
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| ./fsi-suite.sh -np 4 mpi_poisson.g my_test.prm | ||
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| | setup_system | 1 | 0.0124s | 18% | | ||
| | solve | 1 | 0.00547s | 7.8% | | ||
| +---------------------------------+-----------+------------+------------+ | ||
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| ## Course program | ||
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| A tentative detailed program is shown below | ||
| A tentative detailed program is shown below | ||
| (this will be updated during the course to reflect the actual course content) | ||
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| 1. Course introduction. | ||
| 1. Course introduction. | ||
| - Motivating examples | ||
| - Basic principles and background knowledge. | ||
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| 2. Recap on Finite Element Methods | ||
| - Introduction to deal.II. | ||
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| 3. Basic principles of continuum mechanics | ||
| - conservation equations | ||
| 3. Basic principles of continuum mechanics | ||
| - conservation equations | ||
| - constitutive equations | ||
| - kinematics | ||
| - transport theorems | ||
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| 3. Lagrangian formulation of continuum mechanics (solids). | ||
| - Static and compressible linear elasticity | ||
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| 4. Recap on mixed problems | ||
| 4. Recap on mixed problems | ||
| - Static incompressible linear elasticity | ||
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| 5. Eulerian formulation of continuum mechanics | ||
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| 6. Recap on time discretization schemes | ||
| - Time dependent Stokes problem | ||
| - Time dependent linear elasticity (wave equations) | ||
| 7. Treating non-linearities | ||
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| 7. Treating non-linearities | ||
| - IMEX | ||
| - predictor corrector | ||
| - fixed point | ||
| - Newton | ||
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| 8. Navier-Stokes equations | ||
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| 9. Segregated coupling | ||
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