[Paper Review] Lattice Boltzmann method for fluid-structure interaction in compressible flow

Abhimanyu Bhadauria, Benedikt Dorschner+1 more|arXiv (Cornell University)|Jul 3, 2021

Lattice Boltzmann Simulation Studies68 references18 citations

TL;DR

This paper presents a two-way fluid-structure interaction (FSI) scheme for compressible flows using a two-population lattice Boltzmann method (LBM) with an arbitrary Lagrangian-Eulerian (ALE) formulation on body-fitted meshes. By employing polynomial blending functions to localize mesh deformation, the method enables efficient, high-resolution simulation of multiple rigid bodies with independent motion, accurately capturing vortex-induced vibrations and transonic flutter in complex flows.

ABSTRACT

We present a two-way coupled fluid-structure interaction scheme for rigid bodies using a two-population lattice Boltzmann formulation for compressible flows. Arbitrary Lagrangian-Eulerian formulation of the discrete Boltzmann equation on body-fitted meshes is used in a combination with polynomial blending functions. The blending function approach localizes mesh deformation and allows treating multiple moving bodies with a minimal computational overhead. We validate the model with several test cases of vortex induced vibrations of single and tandem cylinders and show that it can accurately describe dynamic behavior of these systems. Finally, in the fully compressible regime, we demonstrate that the proposed model accurately captures complex phenomena such as transonic flutter over an airfoil.

Motivation & Objective

• To develop a robust, two-way coupled fluid-structure interaction model for compressible flows using lattice Boltzmann methods.
• To overcome the limitations of standard LBM in compressible flow regimes by using a two-population formulation with correction terms.
• To enable accurate simulation of moving rigid bodies on body-fitted, non-uniform meshes with minimal computational overhead.
• To extend existing LBM-FSI frameworks to handle multiple moving bodies and un-prescribed motion via mesh blending.
• To validate the model on benchmark problems including vortex-induced vibrations and transonic aeroelastic flutter.

Proposed method

• Uses a two-population lattice Boltzmann formulation to recover compressible Navier-Stokes equations with corrected stress tensors.
• Applies an arbitrary Lagrangian-Eulerian (ALE) formulation to allow mesh nodes to move with boundaries while maintaining stability.
• Employs polynomial blending functions to smoothly localize mesh deformation to the vicinity of moving bodies, reducing computational cost.
• Integrates a spring-mass system to model rigid body dynamics with two-way fluid-structure coupling.
• Uses semi-Lagrangian advection in the discrete Boltzmann equation to handle variable Courant numbers on non-uniform meshes.
• Implements force computation via momentum exchange and boundary conditions consistent with the LBM framework.

Experimental results

Research questions

• RQ1 Can a two-population LBM with ALE formulation accurately simulate compressible flows with moving rigid bodies?
• RQ2 How does the blending function approach compare to differential mesh deformation in terms of accuracy and computational cost for multiple moving bodies?
• RQ3 Can the model capture complex compressible flow phenomena such as transonic flutter and vortex-induced vibrations?
• RQ4 What is the performance and stability of the scheme in high-speed, compressible regimes with large mesh deformations?
• RQ5 How does the two-way coupling between fluid and structure affect dynamic behavior in FSI systems?

Key findings

• The model accurately captures vortex-induced vibrations (VIV) of single and tandem cylinders, reproducing known lock-in behavior and oscillation amplitudes.
• The scheme successfully simulates transonic flutter over an airfoil, including shock-induced instabilities and dynamic divergence.
• The blending function approach reduces computational overhead for multiple moving bodies by localizing mesh deformation to the vicinity of each body.
• The two-population LBM with correction terms maintains accuracy and stability across a wide range of Mach numbers, including supersonic regimes.
• The ALE formulation allows for large mesh distortions without re-meshing, enabling long-time simulations of complex FSI dynamics.
• The method achieves high resolution near moving boundaries while maintaining efficiency, outperforming purely Eulerian or Lagrangian approaches in complex geometries.