High-volume fraction simulations of two-dimensional vesicle suspensions

TL;DR

This paper develops advanced numerical algorithms for simulating dense suspensions of two-dimensional vesicles in viscous fluids, addressing challenges like interface resolution, stiffness, and long-range interactions to improve robustness and accuracy.

Contribution

It extends existing boundary integral methods with semi-implicit interaction treatment, special near-singular integral integration, and spectral collision detection for high-volume vesicle simulations.

Findings

Enhanced simulation robustness for concentrated vesicle suspensions

Accurate modeling of intra- and inter-vesicle hydrodynamic interactions

Demonstrated effectiveness in both confined and unconfined flows

Abstract

We consider numerical algorithms for the simulation of the rheology of two-dimensional vesicles suspended in a viscous Stokesian fluid. The vesicle evolution dynamics is governed by hydrodynamic and elastic forces. The elastic forces are due to local inextensibility of the vesicle membrane and resistance to bending. Numerically resolving vesicle flows poses several challenges. For example, we need to resolve moving interfaces, address stiffness due to bending, enforce the inextensibility constraint, and efficiently compute the (non-negligible) long-range hydrodynamic interactions. Our method is based on the work of {\em Rahimian, Veerapaneni, and Biros, "Dynamic simulation of locally inextensible vesicles suspended in an arbitrary two-dimensional domain, a boundary integral method", Journal of Computational Physics, 229 (18), 2010}. It is a boundary integral formulation of the Stokes equations coupled to the interface mass continuity and force balance. We extend the algorithms presented in that paper to increase the robustness of the method and enable simulations with concentrated suspensions. In particular, we propose a scheme in which both intra-vesicle and inter-vesicle interactions are treated semi-implicitly. In addition we use special integration for near-singular integrals and we introduce a spectrally accurate collision detection scheme. We test the proposed methodologies on both unconfined and confined flows for vesicles whose internal fluid may have a viscosity contrast with the bulk medium. Our experiments demonstrate the importance of treating both intra-vesicle and inter-vesicle interactions accurately.