[Paper Review] Parallel contact-aware simulations of deformable particles in 3D Stokes flow

Libin Lu, Abtin Rahimian+1 more|arXiv (Cornell University)|Dec 11, 2018

Fluid Dynamics Simulations and Interactions39 references4 citations

TL;DR

This paper presents a parallel, contact-aware boundary integral method for simulating dense suspensions of deformable particles in 3D Stokes flow. By incorporating explicit contact constraints into a spectral Galerkin formulation, the method enables stable, high-volume-fraction simulations (up to 60%) with time-step independence from volume fraction and significant cost reduction compared to prior methods, scaling efficiently to 16,000 CPU cores.

ABSTRACT

We present a parallel-scalable method for simulating non-dilute suspensions of deformable particles immersed in Stokesian fluid in three dimensions. A critical component in these simulations is robust and accurate collision handling. This work complements our previous work [L. Lu, A. Rahimian, and D. Zorin. Contact-aware simulations of particulate Stokesian suspensions. Journal of Computational Physics 347C: 160-182] by extending it to 3D and by introducing new parallel algorithms for collision detection and handling. We use a well-established boundary integral formulation with spectral Galerkin method to solve the fluid flow. The key idea is to ensure an interference-free particle configuration by introducing explicit contact constraints into the system. While such constraints are typically unnecessary in the formulation they make it possible to eliminate catastrophic loss of accuracy in the discretized problem by preventing contact explicitly. The incorporation of contact constraints results in a significant increase in stable time-step size for locally-implicit time-stepping and a reduction in the necessary number of discretization points for stability. Our method maintains the accuracy of previous methods at a significantly lower cost for dense suspensions and the time step size is independent from the volume fraction. Our method permits simulations with high volume fractions; we report results with up to 60% volume fraction. We demonstrated the parallel scaling of the algorithms on up to 16K CPU cores.

Motivation & Objective

• To enable stable, accurate simulations of dense suspensions of deformable particles in 3D Stokes flow, where particle-particle contact is a major challenge.
• To overcome accuracy degradation in standard formulations when particles approach or touch by introducing explicit contact constraints.
• To develop parallel algorithms for contact detection and handling that scale efficiently on large-scale HPC systems.
• To achieve stable time-stepping independent of volume fraction, enabling simulations at high particle concentrations.

Proposed method

• A boundary integral formulation with spectral Galerkin discretization is used to solve the 3D Stokes flow equations for deformable particles.
• Explicit contact constraints are introduced into the system to prevent particle interference and maintain solution accuracy during close approach or contact.
• A locally-implicit time-stepping scheme is employed, with contact constraints enabling significantly larger stable time steps.
• A parallel algorithm for contact detection and constraint enforcement is designed to scale across up to 16,000 CPU cores.
• The method ensures interference-free particle configurations by enforcing contact constraints directly in the variational formulation.
• The formulation avoids the catastrophic loss of accuracy seen in standard methods when particles are in close proximity or in contact.

Experimental results

Research questions

• RQ1 How can contact between deformable particles in 3D Stokes flow be handled robustly to maintain accuracy in simulations?
• RQ2 What is the impact of explicit contact constraints on time-step stability and discretization requirements in dense suspensions?
• RQ3 Can a parallel algorithm for contact detection and constraint enforcement scale effectively to 16,000 CPU cores in 3D particle simulations?
• RQ4 How does the proposed method compare in accuracy and cost to previous methods at high volume fractions?
• RQ5 To what extent can the time-step size be decoupled from volume fraction using contact-aware formulations?

Key findings

• The method achieves stable simulations with up to 60% volume fraction, significantly higher than typical limits in standard methods.
• The stable time-step size is independent of the volume fraction, enabling larger time steps in dense suspensions.
• The number of discretization points required for stability is reduced due to the explicit contact constraints.
• The method maintains high accuracy comparable to previous methods but at a significantly lower computational cost.
• The parallel algorithm demonstrates strong scaling on up to 16,000 CPU cores, confirming its suitability for large-scale simulations.
• The contact-aware formulation eliminates the catastrophic loss of accuracy observed in standard formulations during particle contact.