Reduced-Order Semi-Implicit Schemes for Fluid-Structure Interaction Problems
POD–Galerkin reduced-order models (ROMs) for fluid-structure interaction problems (incompressible fluid and thin structure) are proposed in this paper. Both the high-fidelity and reduced-order methods are based on a Chorin-Temam operator-splitting approach. Two different reduced-order methods are proposed, which differ on velocity continuity condition, imposed weakly or strongly, respectively. The resulting ROMs are tested and compared on a representative haemodynamics test case characterized by wave propagation, in order to assess the capabilities of the proposed strategies.
We acknowledge the support by European Union Funding for Research and Innovation—Horizon 2020 Program—in the framework of European Research Council Executive Agency: H2020 ERC CoG 2015 AROMA-CFD project 681447 “Advanced Reduced Order Methods with Applications in Computational Fluid Dynamics” and the PRIN project “Mathematical and numerical modelling of the cardiovascular system, and their clinical applications”. We also acknowledge the INDAM-GNCS project “Tecniche di riduzione della complessità computazionale per le scienze applicate” and INDAM-GNCS young researchers project “Numerical methods for model order reduction of PDEs”.
- 7.Ballarin, F., Sartori, A., Rozza, G.: RBniCS – reduced order modelling in fenics. http://mathlab.sissa.it/rbnics (2016)
- 8.Barrault, M., Maday, Y., Nguyen, N.C., Patera, A.T.: An ‘empirical interpolation’ method: application to efficient reduced-basis discretization of partial differential equations. C.R. Math. 339(9), 667–672 (2004)Google Scholar
- 9.Colciago, C.M.: Reduced order fluid-structure interaction models for haemodynamics applications. Ph.D. Thesis, École Polytechnique Fédérale de Lausanne, N. 6285 (2014)Google Scholar
- 12.Fernández, M.A., Landajuela, M., Mullaert, J., Vidrascu, M.: Robin-Neumann schemes for incompressible fluid-structure interaction. Domain Decomposition Methods in Science and Engineering, vol. XXII. pp. 65–76. Springer, Cham (2016)Google Scholar
- 21.Quarteroni, A., Formaggia, L.: Mathematical modelling and numerical simulation of the cardiovascular system. In: Computational Models for the Human Body. Handbook of Numerical Analysis, vol. 12, pp. 3–127. Elsevier, Amsterdam (2004)Google Scholar