TY - JOUR
T1 - Contact-aware simulations of particulate Stokesian suspensions
AU - Lu, Libin
AU - Rahimian, Abtin
AU - Zorin, Denis
N1 - Funding Information:
We extend our thanks to George Biros, David Harmon, Ehssan Nazockdast, Bryan Quaife, Michael Shelley, and Etienne Vouga for stimulating conversations about various aspects of this work. This work was supported by the US National Science Foundation ( NSF) through grants DMS-1320621 and DMS-1436591.
Publisher Copyright:
© 2017 Elsevier Inc.
PY - 2017/10/15
Y1 - 2017/10/15
N2 - We present an efficient, accurate, and robust method for simulation of dense suspensions of deformable and rigid particles immersed in Stokesian fluid in two dimensions. We use a well-established boundary integral formulation for the problem as the foundation of our approach. This type of formulation, with a high-order spatial discretization and an implicit and adaptive time discretization, have been shown to be able to handle complex interactions between particles with high accuracy. Yet, for dense suspensions, very small time-steps or expensive implicit solves as well as a large number of discretization points are required to avoid non-physical contact and intersections between particles, leading to infinite forces and numerical instability. Our method maintains the accuracy of previous methods at a significantly lower cost for dense suspensions. The key idea is to ensure interference-free configuration by introducing explicit contact constraints into the system. While such constraints are unnecessary in the formulation, in the discrete form of the problem, they make it possible to eliminate catastrophic loss of accuracy by preventing contact explicitly. Introducing contact constraints results in a significant increase in stable time-step size for explicit time-stepping, and a reduction in the number of points adequate for stability.
AB - We present an efficient, accurate, and robust method for simulation of dense suspensions of deformable and rigid particles immersed in Stokesian fluid in two dimensions. We use a well-established boundary integral formulation for the problem as the foundation of our approach. This type of formulation, with a high-order spatial discretization and an implicit and adaptive time discretization, have been shown to be able to handle complex interactions between particles with high accuracy. Yet, for dense suspensions, very small time-steps or expensive implicit solves as well as a large number of discretization points are required to avoid non-physical contact and intersections between particles, leading to infinite forces and numerical instability. Our method maintains the accuracy of previous methods at a significantly lower cost for dense suspensions. The key idea is to ensure interference-free configuration by introducing explicit contact constraints into the system. While such constraints are unnecessary in the formulation, in the discrete form of the problem, they make it possible to eliminate catastrophic loss of accuracy by preventing contact explicitly. Introducing contact constraints results in a significant increase in stable time-step size for explicit time-stepping, and a reduction in the number of points adequate for stability.
KW - Boundary integral
KW - Complex fluids
KW - Constraint-based collision handling
KW - High volume fraction flow
KW - Particulate Stokes flow
KW - SDC time stepping
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U2 - 10.1016/j.jcp.2017.06.039
DO - 10.1016/j.jcp.2017.06.039
M3 - Article
AN - SCOPUS:85022227390
SN - 0021-9991
VL - 347
SP - 160
EP - 182
JO - Journal of Computational Physics
JF - Journal of Computational Physics
ER -