Proper orthogonal decomposition and model order reduction for multiphysics problems such as biofilm, porous media, fluid-structure interaction

The overall goal of this project is the development, numerical analysis and high performance scientific computing of proper orthogonal decomposition (POD) [1,2] applied to some multiphysics problems in which flow and solids interact. Examples are biofilm models [5], porous media applications [6], or full fluid-structure interaction [3,4]. Since pre-existing in-house and open-source github codes (based on deal.II, C++) to fluid-structure interaction exist [4], we may start with those and later adapt the framework to the other previously mentioned models. The POD shall be analyzed for different bases in order to study the approximation properties. Depending on the outcome, afterward the focus may be on computational aspects of error-controlled routines or some rigorous numerical analysis. In the last part, current practical problems in which the above models arise will be addressed.

Doctoral Researcher: Hendrik Fischer

Scientific Advisors: Thomas Wick, Amélie Fau

1. A. Caiazzo, T. Iliescu, V. John, and S. Schyschlowa; A numerical investigation of velocity–pressure reduced order models for incompressible flows. Journal of Computational Physics, 259:598–616, 2014
2. D. Wells. Stabilization of POD-ROMs. PhD dissertation, Virginia Tech, 2015
3. T. Richter; Fluid-Structure Interaction, Springer, 2017
4. T. Wick; Solving Monolithic Fluid-Structure Interaction Problems in Arbitrary Lagrangian Eulerian Coordinates with the deal.II Library, Archive of Numerical Software (ANS), Vol. 1 (2013), pp. 1-19
5. D Feng, I Neuweiler, R Nogueira, U Nackenhorst; Modeling of Symbiotic Bacterial Biofilm Growth with an Example of the Streptococcus–Veillonella sp. System, Bulletin of Mathematical Biology 83 (5), 1-36, 2021
6. M Bause, FA Radu, U Köcher, Space–time finite element approximation of the Biot poroelasticity system with iterative coupling, Computer Methods in Applied Mechanics and Engineering, Vol. 320, pp. 745-768