Field‐to‐field coupled fluid structure interaction: A reduced order model study

Abstract

The standard Fluid-Structure Interaction (fsi) coupling, that uses as unknowns velocity and pressure for the fluid and displacements for the solid, is compared against two novel types of coupling, the first one a three-field coupling (velocity-pressure-stress/displacement-pressure-stress) introduced by the authors in a recent work, and a two-field coupling (velocity-pressure/displacement-pressure) introduced in this paper, in this way completing our set of Field to Field (f2f) equations, all stabilized by means of the Variational Multi-Scale (vms) method using dynamic and orthogonal subscales. The solid two-field fsi coupling formulation is benchmarked statically and dynamically. Proper Orthogonal Decomposition (pod) is applied to all three fsi formulations to obtain reduced basis and asses their performance in a reduced space. Numerical tests are shown comparing all three formulations. By correctly resolving the Cauchy stress tensor, the three-field fsi coupling proves to provide more accurate results in both Full Order Model (fom) and Reduced Order Model (rom) spaces than its counterparts for a similar number of degrees of freedom, making it a reliable formulation. f2f pairing appears to be beneficial, providing more accurate results in all cases shown; mixed pairing with a three-field formulation in the solid appears to produce very precise results as well. K E Y W O R D S field-to-field coupling, fluid structure interaction, mixed methods, proper orthogonal decomposition, reduced order models, variational multiscale method