Comparison of three simulation methods for colloidal aggregates in Stokes flow: Finite elements, lattice Boltzmann and Stokesian dynamics

2013 ◽  
Vol 86 ◽  
pp. 199-209 ◽  
Author(s):  
Eva Schlauch ◽  
Martin Ernst ◽  
Ryohei Seto ◽  
Heiko Briesen ◽  
Martin Sommerfeld ◽  
...  
Keyword(s):  
Finite Elements ◽  
Stokes Flow ◽  
Lattice Boltzmann ◽  
Simulation Methods ◽  
Stokesian Dynamics ◽  
Colloidal Aggregates

FULL NEWTON LATTICE BOLTZMANN METHOD FOR TIME-STEADY FLOWS USING A DIRECT LINEAR SOLVER

2007 ◽  
Vol 18 (04) ◽  
pp. 652-660 ◽  
Author(s):  
DAVID R. NOBLE ◽  
DAVID J. HOLDYCH
Keyword(s):  
Lattice Boltzmann Method ◽  
Stokes Flow ◽  
Lattice Boltzmann ◽  
Linear Equations ◽  
Steady Flows ◽  
Linear System Of Equations ◽  
Flow Limit ◽  
Non Linear ◽  
Two Dimensional Flow ◽  
Boltzmann Method

A full Newton lattice Boltzmann method is developed for time-steady flows. The general method involves the construction of a residual form for the time-steady, nonlinear Boltzmann equation in terms of the probability distribution. Bounce-back boundary conditions are also incorporated into the residual form. Newton's method is employed to solve the resulting system of non-linear equations. At each Newton iteration, the sparse, banded, Jacobian matrix is formed from the dependencies of the non-linear residuals on the components of the particle distribution. The resulting linear system of equations is solved using a direct solver designed for sparse, banded matrices. For the Stokes flow limit, only one matrix solve is required. Two dimensional flow about a periodic array of disks is simulated as a proof of principle, and the numerical efficiency is carefully assessed. For the case of Stokes flow (Re = 0) with resolution 251×251, the proposed method performs more than 100 times faster than a standard, fully explicit implementation.

scholarly journals Suspensions of prolate spheroids in Stokes flow. Part 1. Dynamics of a finite number of particles in an unbounded fluid

1993 ◽  
Vol 251 ◽  
pp. 411-442 ◽  
Author(s):  
Ivan L. Claeys ◽  
John F. Brady
Keyword(s):  
Stokes Flow ◽  
Expansion Method ◽  
Simulation Method ◽  
Multipole Moment ◽  
Simple Shear Flow ◽  
Stokesian Dynamics ◽  
Reynolds Number Flow ◽  
Prolate Spheroids ◽  
Number Flow ◽  
Unbounded Fluid

A new simulation method is presented for low-Reynolds-number flow problems involving elongated particles in an unbounded fluid. The technique extends the principles of Stokesian dynamics, a multipole moment expansion method, to ellipsoidal particle shapes. The methodology is applied to prolate spheroids in particular, and shown to be efficient and accurate by comparison with other numerical methods for Stokes flow. The importance of hydrodynamic interactions is illustrated by examples on sedimenting spheroids and particles in a simple shear flow.

A Comparison Between Lattice-Boltzmann and Finite-Element Simulations of Fluid Flow in Static Mixer Reactors

1998 ◽  
Vol 09 (08) ◽  
pp. 1123-1128 ◽  
Author(s):  
D. Kandhai ◽  
D. J.-E. Vidal ◽  
A. G. Hoekstra ◽  
H. Hoefsloot ◽  
P. Iedema ◽  
...  
Keyword(s):  
Experimental Data ◽  
Finite Element ◽  
Fluid Flow ◽  
Lattice Boltzmann ◽  
Complex Geometry ◽  
Simulation Methods ◽  
Static Mixer ◽  
Chemical Reactors ◽  
Mixing Performance ◽  
Boltzmann Method

We present a comparison between the finite-element and the lattice-Boltzmann method for simulating fluid flow in a SMRX static mixer reactor. The SMRX static mixer is a piece of equipment with excellent mixing performance and it is used in highly efficient chemical reactors for viscous systems like polymers. The complex geometry of this mixer makes such 3D simulations nontrivial. An excellent agreement between the results of the two simulation methods and experimental data was found.

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