Aline Lefebvre-Lepot (École Polytechnique, Paris)

Numerical simulation of rigid particles in Stokes flow: lubrication correction for general shapes of particles

We address the problem of numerical simulation of suspensions of rigid particles in a Stokes flow. We focus on the inclusion of the singular short range interaction effects (lubrication effects) in the simulations when the particles come close one to another. The problem is solved without introducing new hypothesis nor model. As in [1], the key idea is to decompose the velocity and pressure flows in a sum of a singular and a regular part. Here, the singular part is computed using an explicit asymptotic expansion of the solution when the distance goes to zero, similar to the one proposed in [2]. It can be computed for any locally convex particles (that is, the particles have to be convex close to the contact point) with regular shapes. Using [2] as an intermediate result, we prove that the remaining part is regular in the sense that it is bounded independently of the distance. As a consequence, only a small number of degrees of freedom are necessary to obtain accurate results. The method is tested in dimension 2. We show that, as expected, the convergence is independent of the distance.

References:
[1] A. Lefebvre-Lepot, B. Merlet, and T. N. Nguyen. An accurate method to include lubrication forces in numerical simulations of dense stokesian suspensions. Journal of Fluid Mechanics 769:369-386, 2015.
[2] M. Hillairet and T. Kelai. Justification of lubrication approximation: an application to fluid/solid interactions. Asymptotic Analysis 95(3-4):187-241, 2015.

See slides.