Coupling of the immersed boundary and Fourier pseudo-spectral methods applied to solve fluid–structure interaction problems

• DOI: 10.1007/s40430-024-04780-7
• Publication Date: 2024-03-14T19:02:20Z
• Authors: Andreia Aoyagui N...; Felipe Pamplona M...; Aristeu da Silvei...; Elie Luis Martíne...
• Keywords: 0209 industrial biotechnology; Finite element method; Fluid-Structure Interaction; Binary Fluid Systems; Turbulent Flows and Vortex Dynamics; Computational Mechanics; FOS: Mechanical engineering; Coherent Structures; Mechanics; Mathematical analysis; Immersion Techniques; Engineering; 0103 physical sciences; Coupling (piping); FOS: Mathematics; Classical mechanics; Boundary value problem; Immersed boundary method; Physics; Fourier series; Mechanical engineering; Immersed Boundary Method; Boundary (topology); Physical Sciences; Fourier transform; Vortex-Induced Vibrations in Fluid Flow; Thermodynamics; Fluid–structure interaction; Mathematics; Lattice Boltzmann Method for Complex Flows

AbstractThe current manuscript addresses fluid–structure interaction (FSI) problems to the analysis of vortex-induced vibration (VIV), employing the methodology designated as IMERSPEC2D. The approach seamlessly integrates the Fourier pseudo-spectral method (FPSM) and the immersed boundary method (IBM) to solve the Navier–Stokes (NS) and continuity equations. Simultaneously, the effects of cylindrical structure, involving 1 and 2 degrees of freedom (d.o.f.) are simulated, by incorporating structural motion equations into NS via the IBM source term and implementing a two-way FSI algorithm. In the paper are presented the comparison of low and high-order temporal integration methods applied to solve the dynamic behavior of the structure and the dimensionless of the cylinder’s structural motion equations, resulting in an increase in computational time step from 1E($$-9$$

- 9

) to 1E($$-3$$

- 3

). Validation results to refined mesh simulations include the accurate representation of the lock-in phenomenon to simulations of 1 d.o.f. obtaining the range between reduced velocity 5.456 and 5.568 and the maximal amplitude is 0.352. Notably, the eight-shape pattern of the 2 d.o.f. cylinder displacement is obtained and the formation of C2S wake patterns is achieved, as presented by other authors. In conclusion, the dimensionless approach reduces computational time, while the high-order both of IMERSPEC methodology and time advancement integration to FSI improve the results of the cylinder’s motion and alters distinct vortex shedding patterns in fluid dynamics.