An integral equation formulation for rigid bodies in Stokes flow in three dimensions

Corona, Eduardo; Greengard, Leslie; Rachh, Manas; Veerapaneni, Shravan

doi:10.1016/j.jcp.2016.12.018

Cited by 40 publications

(44 citation statements)

References 42 publications

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“…Sedimentation requires overcoming a few challenges. First, the bodies must be mobile, as has been accomplished in previous work for dense concentrations of deformable and rigid bodies [2,17,18,57,59,62]. Second, contacts and overlap between bodies must be prevented.…”

Section: Discussionmentioning

confidence: 99%

A boundary-integral framework to simulate viscous erosion of a porous medium

Quaife¹,

Moore²

2018

Journal of Computational Physics

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We develop numerical methods to simulate the fluid-mechanical erosion of many bodies in two-dimensional Stokes flow. The broad aim is to simulate the erosion of a porous medium (e.g. groundwater flow) with grainscale resolution. Our fluid solver is based on a second-kind boundary integral formulation of the Stokes equations that is discretized with a spectrally-accurate Nyström method and solved with fast-multipoleaccelerated GMRES. The fluid solver provides the surface shear stress which is used to advance solid boundaries. We regularize interface evolution via curvature penalization using the θ-L formulation, which affords numerically stable treatment of stiff terms and therefore permits large time steps. The overall accuracy of our method is spectral in space and second-order in time. The method is computationally efficient, with the fluid solver requiring O(N ) operations per GMRES iteration, a mesh-independent number of GMRES iterations, and a one-time O(N 2 ) computation to compute the shear stress. We benchmark single-body results against analytical predictions for the limiting morphology and vanishing rate. Multibody simulations reveal the spontaneous formation of channels between bodies of close initial proximity. The channelization is associated with a dramatic reduction in the resistance of the porous medium, much more than would be expected from the reduction in grain size alone.

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Section: Discussionmentioning

confidence: 99%

A boundary-integral framework to simulate viscous erosion of a porous medium

Quaife¹,

Moore²

2018

Journal of Computational Physics

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“…Besides the moving overlapping grid approach employed here, a variety of classical numerical techniques for moving complex geometries have been extended to this regime, including arbitrary Lagrangian-Eulerian (ALE) methods [16][17][18], level-set methods [19,20], fictitious domain methods [21], embedded boundary methods [22] and immersed boundary methods [11,[23][24][25][26][27][28][29][30][31][32][33][34]. Recently, new approaches to handle moving geometries have also been developed for this regime, such as methods based on boundary-integral equations [35] and implicit mesh discontinuous Galerkin methods [36,37].…”

Section: Introductionmentioning

confidence: 99%

A stable partitioned FSI algorithm for rigid bodies and incompressible flow in three dimensions

Banks

Henshaw

Schwendeman

et al. 2018

Journal of Computational Physics

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This paper describes a novel partitioned algorithm for fluid-structure interaction (FSI) problems that couples the motion of rigid bodies and incompressible flow. This is the first partitioned algorithm that remains stable and second-order accurate, without sub-time-step iterations, for very light, and even zero-mass, bodies in three dimensions. This new added-mass partitioned (AMP) algorithm extends the previous developments in [1,2] by generalizing the added-damping tensors to account for arbitrary three-dimensional rotations, and by employing a general quadrature for the surface integral over a rigid body to derive the discrete AMP interface condition for the fluid pressure. Stability analyses for two three-dimensional model problems show that the algorithm remains stable for bodies of any mass when applied to the relevant model problems. The resulting AMP algorithm is implemented in parallel using a moving composite grid framework to treat one or more rigid bodies in complex three-dimensional configurations. The new three-dimensional algorithm is verified and validated though several benchmark problems, including the motion of a sphere in a viscous incompressible fluid and the interaction of a bi-leaflet mechanical heart valve and a pulsating fluid. Numerical simulations confirm the predictions of the stability analysis even for complex problems, and show that the AMP algorithm remains stable, without sub-iterations, for light and even zero-mass three-dimensional rigid bodies of general shape. These benchmark problems are further used to examine the parallel performance of the algorithm and to investigate the conditioning of the linear system for the pressure including the newly derived AMP interface conditions.

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“…A recent publication considers three-dimensional simulations of rigid bodies [17], but uses a different contact algorithm than the STIV we used. It is unclear that this contact algorithm will be able to resolve dense suspensions where there are many contacts.…”

Section: Discussionmentioning

confidence: 99%

Stable and contact‐free time stepping for dense rigid particle suspensions

Bystricky

Shanbhag

Quaife

2019

Numerical Methods in Fluids

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We consider suspensions of rigid bodies in a two-dimensional viscous fluid. Even with highfidelity numerical methods, unphysical contact between particles occurs because of spatial and temporal discretization errors. We apply the method of Lu et al. [Journal of Computational Physics, 347:160-182, 2017] where overlap is avoided by imposing a minimum separation distance. 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 extend the method of Lu et al. by treating all interactions implicitly. This new time stepping method 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.

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An integral equation formulation for rigid bodies in Stokes flow in three dimensions

Cited by 40 publications

References 42 publications

A boundary-integral framework to simulate viscous erosion of a porous medium

A boundary-integral framework to simulate viscous erosion of a porous medium

A stable partitioned FSI algorithm for rigid bodies and incompressible flow in three dimensions

Stable and contact‐free time stepping for dense rigid particle suspensions

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