All example movies of multi-body deformable fluid–structure interaction were simulated with the 2D lattice
Boltzmann based reference map technique (LBRMT).

Sedimentation and Floatation of 514 Solids

Example of 2D lattice Boltzmann based reference map technique
Presented at SIAM Annual Meeting 2021
https://meetings.siam.org/sess/dsp_talk.cfm?p=116046

All 514 solids (shear modulus G=4) are under gravity. The upper half is set to be heavier than the fluid, the
lower half lighter: naturally, the solids would want to switch their positions. The LBRMT can capture the fine
details of deformable solids, as well as model the different physics of sedimentation and floatation without any
modification to the code.

The simulation (resolution=1024×512) was run with OpenMP 16 threads over 120,000 steps. The average
computation time for one update is 0.9255 second/step. Colors show vorticity.

Anchored Flexible Rotors

Example of 2D lattice Boltzmann based reference map technique
Presented at SIAM Annual Meeting 2021
https://meetings.siam.org/sess/dsp_talk.cfm?p=116046

Four flexible rotors (shear modulus G=24) are anchored at their center. A rotational spring force is applied to
each rotor, leading to twisting and bending of the solid.

The simulation (resolution=512×512) was run with OpenMP 16 threads for 100,000 steps (period=2). The
average computation time for one update is 0.2002 second/step. Colors show vorticity.

Soft Particle Sedimentation and Buoyancy

Example of 2D lattice Boltzmann based reference map technique
Presented at APS March Meeting 2021
https://meetings.aps.org/Meeting/MAR21/Session/X24.2

[Still under construction. More details will be added. Stay tuned!]

Master’s thesis: A lattice Boltzmann implementation of the reference map technique

Harvard University, Cambridge
May, 2020
Advised by Professor Chris Rycroft

Abstract: This thesis presents a hybrid fully-Eulerian numerical method for fluid–structure interaction (FSI)
simulation. The new method (LB-RMT) combines the reference map technique (RMT) and the lattice Boltzmann
(LB) method to simulate the interaction between the solid and the fluid, and incorporates an extrapolation zone
to update the solid-fluid interface. It simplifies the inter-phase coupling by taking advantage of the two Eulerian
-based methods: the RMT permits both the solid and the fluid to be represented on a single fixed mesh, and the
LB method uses a mesoscopic probabilistic view of particle motion to simplify macroscopic hydrodynamics
update. The LB-RMT also provides a novel approach to mesoscopically simulating solid deformation. Examples
consisting of a quasi-incompressible Navier–Stokes fluid with compressible neo-Hookean solids show this
method is flexible and robust in handling standard fluid–structure interactions and deformable solids with sharp
corners bending and twisting in fluid. A convergence study demonstrates the LB-RMT is of second-order accuracy,
improved from the previous first-order RMT. The method can be extended to handle dissolving solids and multi
-species cases like fluid–solid–gas simulation in two and three dimensions.