[Paper Review] Fluid-structure interaction simulations with a LES filtering approach in solids4Foam

Michele Girfoglio, Annalisa Quaini+1 more|arXiv (Cornell University)|Feb 16, 2021

Fluid Dynamics and Turbulent Flows5 citations

TL;DR

This paper evaluates the solids4Foam FSI toolbox in foam-extend by implementing a Leray-regularized large eddy simulation (LES) approach via the Evolve-Filter-Relax (EFR) algorithm for fluid-structure interaction at Reynolds numbers 100 and 400. The study demonstrates that solids4Foam is flexible and accurate for complex flows, though a restart bug limits long-term simulations, and the EFR method effectively stabilizes the simulation with reduced numerical dissipation compared to standard Navier-Stokes solvers.

ABSTRACT

The goal of this paper is to test solids4Foam, the fluid-structure interaction (FSI) toolbox developed for foam-extend (a branch of OpenFOAM), and assess its flexibility in handling more complex flows. For this purpose, we consider the interaction of an incompressible fluid described by a Leray model with a hyperelastic structure modeled as a Saint Venant-Kirchhoff material. We focus on a strongly coupled, partitioned fluid-structure interaction (FSI) solver in a finite volume environment, combined with an arbitrary Lagrangian-Eulerian approach to deal with the motion of the fluid domain. For the implementation of the Leray model, which features a nonlinear differential low-pass filter, we adopt a three-step algorithm called Evolve-Filter-Relax. We validate our approach against numerical data available in the literature for the 3D cross flow past a cantilever beam at Reynolds number 100 and 400.

Motivation & Objective

• To test the accuracy and robustness of the open-source solids4Foam FSI toolbox in foam-extend for complex fluid-structure interaction problems.
• To assess the flexibility of solids4Foam in integrating advanced fluid models, particularly the Leray-regularized LES approach.
• To validate the FSI solver against benchmark data for 3D cross-flow past a cantilever beam at Re=100 and Re=400.
• To investigate the performance of the Evolve-Filter-Relax (EFR) algorithm in stabilizing large eddy simulations within a partitioned, strongly coupled FSI framework.
• To identify and report critical software limitations, particularly the restart function error affecting interface accuracy.

Proposed method

• Implementation of the Leray model via the Evolve-Filter-Relax (EFR) algorithm, a three-step method that applies a nonlinear differential low-pass filter to the velocity field.
• Use of a strongly coupled, partitioned Dirichlet-Neumann (DN) FSI algorithm with the IQN-ILS method for interface convergence.
• Adoption of an arbitrary Lagrangian-Eulerian (ALE) formulation to handle fluid domain motion due to structural deformation.
• Modeling of the hyperelastic structure using a Saint Venant-Kirchhoff material law for compressible elasticity.
• Discretization via finite volume methods for both fluid and solid domains, with mesh refinement studies to assess convergence.
• Use of an indicator function based on velocity gradients to guide localized filtering in the EFR algorithm, ensuring regularization where needed.

Experimental results

Research questions

• RQ1 Can the solids4Foam FSI toolbox accurately simulate fluid-structure interaction at moderately high Reynolds numbers (Re=100 and 400)?
• RQ2 How does the EFR-LES approach compare to standard Navier-Stokes solvers in terms of accuracy and numerical dissipation for FSI problems?
• RQ3 To what extent does the EFR algorithm improve stability and reduce spurious oscillations in the fluid-structure interface?
• RQ4 What are the limitations of the current solids4Foam implementation, particularly regarding the restart functionality?
• RQ5 Can the EFR algorithm be seamlessly integrated into a partitioned FSI framework without major code modifications?

Key findings

• The EFR-LES approach in solids4Foam achieved better accuracy than standard Navier-Stokes solvers on coarser meshes, with lower total error (0.313 vs. 0.328 at Re=100) and improved convergence.
• At Re=100, the EFR algorithm on a 300k-mesh produced a drag coefficient of 1.236, closely matching the reference value of 1.24, with errors in displacement of -0.041 and -0.060 in x and y directions.
• At Re=400, the EFR method yielded a drag coefficient of 0.963, close to the benchmark value of 0.958, with a total error of 0.622, outperforming the NSE method on the same mesh.
• The indicator function in the EFR algorithm correctly localized regions requiring regularization, with high values near and behind the beam and in boundary layers.
• A critical software limitation was identified: the restart function introduces significant errors at the fluid-structure interface, degrading simulation quality and restricting use to short-duration runs.
• Despite the restart issue, the EFR implementation demonstrated modularity and ease of integration into solids4Foam, confirming the toolbox’s flexibility for extending to complex fluid models.