Eulerian simulation of complex suspensions and biolocomotion in three dimensions

Abstract

We present a numerical method specifically designed for simulating three-dimensional fluid–structure interaction (FSI) problems based on the reference map technique (RMT). The RMT is a fully Eulerian FSI numerical method that allows fluids and large-deformation elastic solids to be represented on a single fixed computational grid. This eliminates the need for meshing complex geometries typical in other FSI approaches and greatly simplifies the coupling between fluid and solids. We develop a three-dimensional implementation of the RMT, parallelized using the distributed memory paradigm, to simulate incompressible FSI with neo-Hookean solids. As part of our method, we develop a field extrapolation scheme that works efficiently in parallel. Through representative examples, we demonstrate the method’s suitability in investigating many-body and active systems, as well as its accuracy and convergence. The examples include settling of a mixture of heavy and buoyant soft ellipsoids, lid-driven cavity flow containing a soft sphere, and swimmers actuated via active stress.

A projection method for porous media flow

“…Many porous media problems of interest feature boundaries, and the method is amenable to specialization towards that end through the use of level sets or the reference map itself as in (Lin et al, 2022). While the equations it simulates are often derived in the context of soil and rock Figure 3: Parallel efficiencies of the computational method on 1-16 CPU cores for a variety of grid sizes in two (left) and three (right) dimensions.…”

“…Elastic stresses are produced by deformation of a solid body occupying the domain Ω relative to an unstressed reference configuration Ω 0 . We will calculate elastic stresses using the reference map technique (RMT) (Kamrin et al, 2012;Rycroft et al, 2020;Lin et al, 2022). A position in the reference frame ξ ∈ Ω 0 corresponds to a particular material point of the deforming body, while a position in the deformed frame x ∈ Ω corresponds to a particular location in physical space.…”

“…where the advective derivatives are calculated using the ENO2 method. Given the calculation of the deformation gradient as described, we let the solid stress be given by a neo-Hookean model (Lin et al, 2022),…”

Self-buckling and self-writhing of semi-flexible microorganisms

“…Other approaches to this stiff numerical problem with different treatments of the hydrodynamics have recently been developed. [69][70][71][72][73][74][75][76][77][78] The parameters (Z, D, t f ) = (2, 10 À3 , 10 À2 ), timestep size Dt = 10 À3 , and spatial gridspacing Ds = 1/64 are fixed for the duration unless otherwise stated.…”

Rapid flapping and fibre-reinforced membrane wings are key to high-performance bat flight

“…finite ) deformation. Computational studies are indispensable for these complex systems that are intractable analytically [24]. By investigating the flapping Strouhal number and membrane reinforcement independently, we determine their direct influence on the flow field and wing deformations and ultimately explain the influence of these unique features on bat flight performance.…”