Fluid structure interaction with curved space lattice Boltzmann

TL;DR

This paper introduces a new fluid-structure interaction simulation method combining a curved space lattice Boltzmann solver with a finite element shell model, enabling accurate, mesh-free coupling in complex geometries.

Contribution

The novel approach allows independent curved space LBM simulations without interpolation or re-meshing, coupled with FEM shells for enhanced FSI modeling.

Findings

Achieved resolution convergence in standard tests under metric deformation.

Verified mass, volume conservation, and momentum transfer accuracy.

Successfully simulated fluid flow interacting with deformable shells and flags.

Abstract

We present a novel method for fluid structure interaction (FSI) simulations where an original 2nd-order curved space lattice Boltzmann fluid solver (LBM) is coupled to a finite element method (FEM) for thin shells. The LBM can work independently on a standard lattice in curved coordinates without the need for interpolation, re-meshing or an immersed boundary. The LBM distribution functions are transformed dynamically under coordinate change. In addition, force and momentum can be calculated on the nodes exactly in any geometry. Furthermore, the FEM shell is a complete numerical tool with implementations such as growth, self-contact and strong external forces. We show resolution convergent error for standard tests under metric deformation. Mass and volume conservation, momentum transfer, boundary-slip and pressure maintenance are verified through specific examples. Additionally, a brief deformation stability analysis is carried out. Next, we study the interaction of a square fluid flow channel to a deformable shell. Finally, we simulate a flag at moderate Reynolds number, air flow channel. The scheme is limited to small deformations of O(10%) relative to domain size, by improving its stability the method can be naturally extended to multiple applications without further implementations.