Simulating Fluid–Structure Interactions

Fluid-structure interactions (FSI) are ubiquitous in nature, laboratory, and industrial setting. For example, animal locomotion, fluid flowing through porous media, or cheese being stirred and pumped through a cheese making machine. However, FSI problems are challenging to solve analytically or simulate numerically, due to their nonlinear, multi-physics nature.

In particular, it is difficult to reconcile the dilemma of choosing a discretization framework. Solid simulations are typically computed in a Lagrangian framework. whereas fluid dynamics are more conveniently done from the Eulerian perspective.  Methods such as Arbitrary Lagrangian-Eulerian and Immersed Boundary methods are proposed to address this challenge, but they require extra computations to bridge the discretization from different perspectives.

My group mate Nick Derr and I have been working with our advisor, Chris, on developing a fully Eulerian method, the reference map technique (Rycroft et al. 2020) along with a 3D implementation of it. We recently submitted our manuscript and published our code on GitHub.

predeformed
Snapshots from a simulation movie, where an incompressible neo-Hookian solid is stretch in the x direction at T=0, then let relax to equilibrium.

The reference map technique is rooted in large deformation solid mechanics, so the method is particularly suitable for simulating immersed soft, very deformable solids. The idea of the reference map is simple and elegant, and the essence of it is to find a way to calculate the deformation in the material in the current physical space, rather than the undeformed reference space. Being on a fixed regular grid comes with computational time advantages, giving the method a performance edge in many-body interaction problems.

The 3D code is developed with distributed memory parallelism, specialized data structures and methods to ensure efficiency. For instance, a new least squares-regression based extrapolation algorithm is developed to address challenges of field extrapolation in 3D.

Below I show some example simulations to show what the reference map technique can do.

  1. Settling and floating of objects in fluid
150 ellipsoids, half lighter and half heavier than the fluid, settling in a box.
Various spheres sedimenting on a permeable incline in fluid.

2. Mixing by rotating paddles

Two spinners rotating in opposite directions, stirring a box of fluid.

3. A beam twisting

An immersed beam being twisted at both ends.

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