11 research outputs found
Hydrodynamics of Suspensions of Passive and Active Rigid Particles: A Rigid Multiblob Approach
We develop a rigid multiblob method for numerically solving the mobility
problem for suspensions of passive and active rigid particles of complex shape
in Stokes flow in unconfined, partially confined, and fully confined
geometries. As in a number of existing methods, we discretize rigid bodies
using a collection of minimally-resolved spherical blobs constrained to move as
a rigid body, to arrive at a potentially large linear system of equations for
the unknown Lagrange multipliers and rigid-body motions. Here we develop a
block-diagonal preconditioner for this linear system and show that a standard
Krylov solver converges in a modest number of iterations that is essentially
independent of the number of particles. For unbounded suspensions and
suspensions sedimented against a single no-slip boundary, we rely on existing
analytical expressions for the Rotne-Prager tensor combined with a fast
multipole method or a direct summation on a Graphical Processing Unit to obtain
an simple yet efficient and scalable implementation. For fully confined
domains, such as periodic suspensions or suspensions confined in slit and
square channels, we extend a recently-developed rigid-body immersed boundary
method to suspensions of freely-moving passive or active rigid particles at
zero Reynolds number. We demonstrate that the iterative solver for the coupled
fluid and rigid body equations converges in a bounded number of iterations
regardless of the system size. We optimize a number of parameters in the
iterative solvers and apply our method to a variety of benchmark problems to
carefully assess the accuracy of the rigid multiblob approach as a function of
the resolution. We also model the dynamics of colloidal particles studied in
recent experiments, such as passive boomerangs in a slit channel, as well as a
pair of non-Brownian active nanorods sedimented against a wall.Comment: Under revision in CAMCOS, Nov 201
GPU accelerated shake and rattle algorithms for systems with holonomic constraints
The dynamic of complex fluid can be described by including viscoelastic stress tensor
into the equation of Non-Newtonian fluid. Different models are used to evaluate the stress tensor at
various levels, with the multi-scale model being the most effective
GPU accelerated shake and rattle algorithms for systems with holonomic constraints
The dynamic of complex fluid can be described by including viscoelastic stress tensor
into the equation of Non-Newtonian fluid. Different models are used to evaluate the stress tensor at
various levels, with the multi-scale model being the most effective
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An immersed boundary method for rigid bodies
We develop an immersed boundary (IB) method for modeling flows around fixed or moving rigid bodies that is suitable for a broad range of Reynolds numbers, including steady Stokes flow. The spatio-temporal discretization of the fluid equations is based on a standard staggered-grid approach. Fluid-body interaction is handled using Peskin's IB method; however, unlike existing IB approaches to such problems, we do not rely on penalty or fractional-step formulations. Instead, we use an unsplit scheme that ensures the no-slip constraint is enforced exactly in terms of the Lagrangian velocity field evaluated at the IB markers. Fractionalstep approaches, by contrast, can impose such constraints only approximately, which can lead to penetration of the flow into the body, and are inconsistent for steady Stokes flow. Imposing no-slip constraints exactly requires the solution of a large linear system that includes the fluid velocity and pressure as well as Lagrange multiplier forces that impose the motion of the body. The principal contribution of this paper is that it develops an efficient preconditioner for this exactly constrained IB formulation which is based on an analytical approximation to the Schur complement. This approach is enabled by the near translational and rotational invariance of Peskin's IB method. We demonstrate that only a few cycles of a geometric multigrid method for the fluid equations are required in each application of the preconditioner, and we demonstrate robust convergence of the overall Krylov solver despite the approximations made in the preconditioner. We empirically observe that to control the condition number of the coupled linear system while also keeping the rigid structure impermeable to fluid, we need to place the immersed boundary markers at a distance of about two grid spacings, which is significantly larger from what has been recommended in the literature for elastic bodies. We demonstrate the advantage of our monolithic solver over split solvers by computing the steady state flow through a two-dimensional nozzle at several Reynolds numbers. We apply the method to a number of benchmark problems at zero and finite Reynolds numbers, and we demonstrate first-order convergence of the method to several analytical solutions and benchmark computations
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Hydrodynamics of suspensions of passive and active rigid particles: A rigid multiblob approach
We develop a rigid multiblob method for numerically solving the mobility problem for suspensions of passive and active rigid particles of complex shape in Stokes flow in unconfined, partially confined, and fully confined geometries. As in a number of existing methods, we discretize rigid bodies using a collection of minimally resolved spherical blobs constrained to move as a rigid body, to arrive at a potentially large linear system of equations for the unknown Lagrange multipliers and rigid-body motions. Here we develop a block-diagonal preconditioner for this linear system and show that a standard Krylov solver converges in a modest number of iterations that is essentially independent of the number of particles. Key to the efficiency of the method is a technique for fast computation of the product of the blob-blob mobility matrix and a vector. For unbounded suspensions, we rely on existing analytical expressions for the Rotne-Prager-Yamakawa tensor combined with a fast multipole method (FMM) to obtain linear scaling in the number of particles. For suspensions sedimented against a single no-slip boundary, we use a direct summation on a graphical processing unit (GPU), which gives quadratic asymptotic scaling with the number of particles. For fully confined domains, such as periodic suspensions or suspensions confined in slit and square channels, we extend a recently developed rigid-body immersed boundary method by B. Kallemov, A. P. S. Bhalla, B. E. Griffith, and A. Donev (Commun. Appl. Math. Comput. Sci. 11 (2016), no. 1, 79-141) to suspensions of freely moving passive or active rigid particles at zero Reynolds number. We demonstrate that the iterative solver for the coupled fluid and rigid-body equations converges in a bounded number of iterations regardless of the system size. In our approach, each iteration only requires a few cycles of a geometric multigrid solver for the Poisson equation, and an application of the block-diagonal preconditioner, leading to linear scaling with the number of particles. We optimize a number of parameters in the iterative solvers and apply our method to a variety of benchmark problems to carefully assess the accuracy of the rigid multiblob approach as a function of the resolution. We also model the dynamics of colloidal particles studied in recent experiments, such as passive boomerangs in a slit channel, as well as a pair of non-Brownian active nanorods sedimented against a wall