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A hybrid reduced-order model for segregated fluid-structure interaction solvers in an ALE approach at high Reynolds number

Valentin Nkana Ngan, Giovanni Stabile, Andrea Mola, Gianluigi Rozza

Abstract

This study introduces a first step for constructing a hybrid reduced-order models (ROMs) for segregated fluid-structure interaction in an Arbitrary Lagrangian-Eulerian (ALE) approach at a high Reynolds number using the Finite Volume Method (FVM). The ROM is driven by proper orthogonal decomposition (POD) with hybrid techniques that combines the classical Galerkin projection and two data-driven methods (radial basis networks , and neural networks/ long short term memory). Results demonstrate the ROM ability to accurately capture the physics of fluid-structure interaction phenomena. This approach is validated through a case study focusing on flow-induced vibration (FIV) of a pitch-plunge airfoil at a high Reynolds number 10000000.

A hybrid reduced-order model for segregated fluid-structure interaction solvers in an ALE approach at high Reynolds number

Abstract

This study introduces a first step for constructing a hybrid reduced-order models (ROMs) for segregated fluid-structure interaction in an Arbitrary Lagrangian-Eulerian (ALE) approach at a high Reynolds number using the Finite Volume Method (FVM). The ROM is driven by proper orthogonal decomposition (POD) with hybrid techniques that combines the classical Galerkin projection and two data-driven methods (radial basis networks , and neural networks/ long short term memory). Results demonstrate the ROM ability to accurately capture the physics of fluid-structure interaction phenomena. This approach is validated through a case study focusing on flow-induced vibration (FIV) of a pitch-plunge airfoil at a high Reynolds number 10000000.
Paper Structure (27 sections, 49 equations, 16 figures, 4 tables, 2 algorithms)

This paper contains 27 sections, 49 equations, 16 figures, 4 tables, 2 algorithms.

Table of Contents

  1. Motivation and state-of-the-art
  2. Governing equations of the fluid-structure interaction problem and turbulence modeling
  3. Structural dynamics equations
  4. Fluid dynamics equations and turbulence modeling
  5. Coupling conditions at the interface
  6. Mesh motion strategy
  7. Numerical Methodology
  8. Numerical discretization of the full-order model
  9. The pressure gradient term
  10. The convective term
  11. The diffusion term
  12. The PIMPLE algorithm
  13. The reduced problem
  14. The proper orthogonal decomposition
  15. POD-Galerkin projection for velocity and pressure equations
  16. ...and 12 more sections

Figures (16)

  • Figure 1: (a) Schematic of the fluid-structure system considered: a foil allowed to undergo 2 degrees of freedom fully passive plunging and pitching motion with spring constraints Wang2020, (b) a picture of the zoomed mesh with 12 556 cells (control volumes) and 26 316 node points near an airfoil of chord length 1.0m, (c) picture showing the position of the foil in the computational domain
  • Figure 2: The decay of the POD modes eigenvalues for velocity, pressure, pointDisplacement, and Eddy viscosity fields. Color code: blue -- velocity, green --pressure, red -- pointDisplacement, magenta -- eddy viscosity
  • Figure 3: Comparison of the velocity and pressure fields. First row velocities comparison and second row pressure comparison. Column (a) FOM fields, column (b) reduced solution with POD-NNs and column (c) reduced solution with POD-LSTM. The snapshots are captured in the second period i.e. $t=T=0.1\ $s
  • Figure 4: Comparison of the eddy viscosity and grid node displacement fields. First row eddy viscosity comparison and second row grid node displacement comparison. Column (a) FOM fields, column (b) reduced solution with POD-NNs and column (c) reduced solution with POD-LSTM. The snapshots are captured in the second period i.e. $t=T=0.1\ $s
  • Figure 5: Sensitivity study of the error (log-scale) in the $L^2$-norm versus the time evolution of the velocity field. The red line shows the results obtained inside and outside the time window
  • ...and 11 more figures