A Forcing Fictitious Domain Method to Simulate Fluid-particle Interaction of Particles with Super-quadric Shape

In this work, we develop a new framework to directly simulate super-quadric (SQ) particles in
fluid flows based on a forcing fictitious domain method. Specifically, a super-quadric particle
function is used to represent the particle shape of different types in a flexible manner. The
immersion of particles in the fluid is handled by imposing rigid solid body motion in the
particle domain, as well as adding a local forcing term to the Navier-Stokes equations by
calculating the integral of both the pressure gradient and the particle velocity over the whole
particle domain. Particle shapes are varied by changing the five super-quadric parameters of
the SQ equation. We validate our approach by performing simulations of flow around a fixed
particle and sedimentation of a particle in a channel in 2D and 3D. The validation results
indicate that the current simulation results show a good agreement with experimental data.
Moreover, our method is used to study the flow around fixed non-spherical particles with
different orientations and particle Reynolds numbers. The particle Reynolds numbers vary
from 0.1 to 3000. The super-quadric particles exemplarily considered in the current study are
an ellipsoidal particle and fibre-like particles. We present the results for drag and lift
coefficients at different particle orientations and different particle Reynolds numbers. The
obtained results lay the foundation to apply the framework to flown through multi-particle
systems in the near future.