Stable and contact‐free time stepping for dense rigid particle suspensions. (30th October 2019)

• Record Type: Journal Article
• Authors: Bystricky, Lukas; Shanbhag, Sachin; Quaife, Bryan
• Is Part Of: International journal for numerical methods in fluids. Volume 92:Number 2(2020)
• Page Start: 94
• Page End: 113
• Publication Date: 2019-10-30
• Subjects: boundary integral method -- collision handling -- rheology -- rigid body suspensions -- Stokes flow; Fluid dynamics -- Mathematics -- Periodicals; 532
• DOI: 10.1002/fld.4774
• Languages: English
• ISSNs: 0271-2091

Abstract

Summary: We consider suspensions of rigid bodies in a two‐dimensional viscous fluid. Even with high‐fidelity numerical methods, unphysical contact between particles occurs because of spatial and temporal discretization errors. We extend a time stepping method that avoids overlap by imposing a minimum separation distance between all pairs of bodies. In its original form, the method discretizes interactions between different particles explicitly. Therefore, to avoid stiffness, a large minimum separation distance is used. In this paper, we introduce a new implicit time stepping method that is able to simulate dense suspensions with large time step sizes and a small minimum separation distance. The method is tested on various unbounded and bounded flows, and rheological properties of the resulting suspensions are computed. Abstract : We develop a time stepping method to simulate rigid body suspensions in a viscous fluid. By combining a contact algorithm with implicit interactions, suspensions with nearly‐touching bodies are simulated. We analyze the convergence of the method and use the simulations to investigate rheological properties of the flow.