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Projection Based Semi-Implicit Partitioned Reduced Basis Method for Fluid-Structure Interaction Problems.

Monica Nonino1, Francesco Ballarin2, Gianluigi Rozza3

  • 1Department of Mathematics, University of Vienna, Oskar-Morgenstern Platz, 1090 Vienna, Austria.

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Summary
This summary is machine-generated.

This study introduces a Reduced Order Model for unsteady Fluid-Structure Interaction (FSI) using POD-Galerkin methods. The model efficiently simulates complex FSI problems with varying parameters.

Keywords:
Elastic solidFluid-structure interactionIncompressible fluidProper orthogonal decompositionReduced basis methodSegregated algorithm

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Area of Science:

  • Computational Fluid Dynamics (CFD)
  • Computational Solid Mechanics
  • Reduced Order Modeling (ROM)

Background:

  • Fluid-Structure Interaction (FSI) problems are crucial in many engineering applications.
  • Traditional numerical simulations of unsteady FSI are computationally expensive.
  • Reduced Order Models (ROMs) offer a computationally efficient alternative for complex simulations.

Purpose of the Study:

  • To present a POD-Galerkin based Reduced Order Model for unsteady Fluid-Structure Interaction problems.
  • To extend existing ROMs for FSI to handle unsteady, coupled problems.
  • To assess the model's capabilities in handling parametrized FSI scenarios.

Main Methods:

  • Development of a partitioned algorithm with semi-implicit coupling.
  • Application of Chorin-Temam projection scheme for incompressible Navier-Stokes.
  • Utilizing Robin coupling condition and Arbitrary Lagrangian Eulerian formulation.
  • Proper Orthogonal Decomposition (POD) for reduced basis generation.

Main Results:

  • Successfully extended segregated ROM for FSI to unsteady problems.
  • Coupled an incompressible Newtonian fluid with a linear elastic solid in 2D.
  • Validated the model through three test cases: non-parametrized, geometrically parametrized, and shear modulus parametrized problems.

Conclusions:

  • The presented POD-Galerkin ROM is effective for unsteady FSI problems.
  • The model demonstrates capability in handling both non-parametrized and parametrized FSI scenarios.
  • This approach offers a significant reduction in computational cost for complex FSI simulations.