An Integral Equation Method for the Simulation of Doubly-Periodic Suspensions of Rigid Bodies in a Shearing Viscous Flow

Jun Wang Yau Mathematical Sciences Center, Tsinghua University Ehssan Nazockdast he University of North Carolina at Chapel Hill, Chapel Hill Alex Barnett Flatiron Institute, Simons Foundation

Numerical Analysis and Scientific Computing mathscidoc:2205.25004

Journal of Computational Physics, 2021.1
With rheology applications in mind, we present a fast solver for the time-dependent effective viscosity of an infinite lattice containing one or more neutrally buoyant smooth rigid particles per unit cell, in a two-dimensional Stokes fluid with given shear rate. At each time, the mobility problem is reformulated as a 2nd-kind boundary integral equation, then discretized to spectral accuracy by the Nyström method and solved iteratively, giving typically 10 digits of accuracy. Its solution controls the evolution of particle locations and angles in a first-order system of ordinary differential equations. The formulation is placed on a rigorous footing by defining a generalized periodic Green’s function for the skew lattice. Numerically, the periodized integral operator is split into a near image sum— applied in linear time via the fast multipole method—plus a correction field solved cheaply via proxy Stokeslets. We use barycentric quadratures to evaluate particle interactions and velocity fields accurately, even at distances much closer than the node spacing. Using first- order time-stepping we simulate, for example, 25 ellipses per unit cell to 3-digit accuracy on a desktop in 1 hour per shear time. Our examples show equilibration at long times, force chains, and two types of blow-ups (jamming) whose power laws match lubrication theory asymptotics.
Stokes flow, Boundary integral equation, Periodic Rheology, Generalized Greens function, Quadrature
[ Download ] [ 2022-05-17 12:32:58 uploaded by jwang_thu ] [ 495 downloads ] [ 0 comments ]
@inproceedings{jun2021an,
  title={An Integral Equation Method for the Simulation of Doubly-Periodic Suspensions of Rigid Bodies in a Shearing Viscous Flow},
  author={Jun Wang, Ehssan Nazockdast, and Alex Barnett},
  url={http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20220517123258099079189},
  booktitle={Journal of Computational Physics},
  year={2021},
}
Jun Wang, Ehssan Nazockdast, and Alex Barnett. An Integral Equation Method for the Simulation of Doubly-Periodic Suspensions of Rigid Bodies in a Shearing Viscous Flow. 2021. In Journal of Computational Physics. http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20220517123258099079189.
Please log in for comment!
 
 
Contact us: office-iccm@tsinghua.edu.cn | Copyright Reserved