Model order reduction for bifurcating phenomena in Fluid-Structure Interaction problems

Abstract

This work explores the development and the analysis of an efficient reduced order model for the study of a bifurcating phenomenon, known as the Coandȃ effect, in a multi-physics setting involving fluid and solid media. Taking into consideration a Fluid-Structure Interaction problem, we aim at generalizing previous works towards a more reliable description of the physics involved. In particular, we provide several insights on how the introduction of an elastic structure influences the bifurcating behaviour. We have addressed the computational burden by developing a reduced order branch-wise algorithm based on a monolithic Proper Orthogonal Decomposition. We compared different constitutive relations for the solid, and we observed that a nonlinear hyperelastic law delays the bifurcation w.r.t. the standard model, while the same effect is even magnified when considering linear elastic solid.

Driving bifurcating parametrized nonlinear PDEs by optimal control strategies: application to Navier–Stokes equations with model order reduction

“…Indeed we have the existence and uniqueness of the solution only above a certain critical value for the viscosity, that for this test case corresponds to 𝜇 * ≈ 0.96. Such value has been found in different works and numerical contexts for this benchmark [31,43,44]. It can be obtained either "a posteriori" by looking at the behaviour of the flow while varying the viscosity, or "a priori" by investigating the change of sign of the leading eigenvalue w.r.t.…”

“…For Dirichlet test case we chose 𝑁 = 12 basis functions, while for the other test cases the basis number is 𝑁 = 20. Such value is chosen in analogy with reduction results obtained in the uncontrolled scenario, see e.g., [31,43,44]. The former choice is due to the presence of two multiplier variables, which increase the global ROM dimension (from 13𝑁 to 15𝑁 ), and jeopardize the robustness of the reduced nonlinear solver.…”

“…Thus, when we reach the aforementioned critical value, one recirculation zone expands whereas the other shrinks, giving rise to an asymmetric jet. This phenomenon is called the Coanda effect and has been extensively studied in literature within different contexts [24,31,43,44,46,47,57].…”