# Simulation of low-Reynolds-number flow via a time-independent lattice-Boltzmann method

## Abstract

We present a numerical method to solve the equations for low-Reynolds-number (Stokes) flow in porous media. The method is based on the lattice-Boltzmann approach, but utilizes a direct solution of time-independent equations, rather than the usual temporal evolution to steady state. Its computational efficiency is 1[endash]2 orders of magnitude greater than the conventional lattice-Boltzmann method. The convergence of the permeability of random arrays of spheres has been analyzed as a function of mesh resolution at several different porosities. For sufficiently large spheres, we have found that the convergence is quadratic in the mesh resolution. [copyright] [ital 1999] [ital The American Physical Society]

- Authors:

- (Chemical Engineering Department, University of Florida, Gainesville, Florida 32611-6005 (United States))

- Publication Date:

- OSTI Identifier:
- 6327169

- Alternate Identifier(s):
- OSTI ID: 6327169

- Resource Type:
- Journal Article

- Journal Name:
- Physical Review. E, Statistical Physics, Plasmas, Fluids, and Related Interdisciplinary Topics

- Additional Journal Information:
- Journal Volume: 60:3; Journal ID: ISSN 1063-651X

- Country of Publication:
- United States

- Language:
- English

- Subject:
- 71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS; BOLTZMANN EQUATION; CONVERGENCE; LATTICE PARAMETERS; NUMERICAL SOLUTION; PERMEABILITY; POROSITY; POROUS MATERIALS; VISCOUS FLOW; EQUATIONS; FLUID FLOW; INTEGRO-DIFFERENTIAL EQUATIONS; KINETIC EQUATIONS; MATERIALS 661300* -- Other Aspects of Physical Science-- (1992-)

### Citation Formats

```
Verberg, R., and Ladd, A.J.
```*Simulation of low-Reynolds-number flow via a time-independent lattice-Boltzmann method*. United States: N. p., 1999.
Web. doi:10.1103/PhysRevE.60.3366.

```
Verberg, R., & Ladd, A.J.
```*Simulation of low-Reynolds-number flow via a time-independent lattice-Boltzmann method*. United States. doi:10.1103/PhysRevE.60.3366.

```
Verberg, R., and Ladd, A.J. Wed .
"Simulation of low-Reynolds-number flow via a time-independent lattice-Boltzmann method". United States. doi:10.1103/PhysRevE.60.3366.
```

```
@article{osti_6327169,
```

title = {Simulation of low-Reynolds-number flow via a time-independent lattice-Boltzmann method},

author = {Verberg, R. and Ladd, A.J.},

abstractNote = {We present a numerical method to solve the equations for low-Reynolds-number (Stokes) flow in porous media. The method is based on the lattice-Boltzmann approach, but utilizes a direct solution of time-independent equations, rather than the usual temporal evolution to steady state. Its computational efficiency is 1[endash]2 orders of magnitude greater than the conventional lattice-Boltzmann method. The convergence of the permeability of random arrays of spheres has been analyzed as a function of mesh resolution at several different porosities. For sufficiently large spheres, we have found that the convergence is quadratic in the mesh resolution. [copyright] [ital 1999] [ital The American Physical Society]},

doi = {10.1103/PhysRevE.60.3366},

journal = {Physical Review. E, Statistical Physics, Plasmas, Fluids, and Related Interdisciplinary Topics},

issn = {1063-651X},

number = ,

volume = 60:3,

place = {United States},

year = {1999},

month = {9}

}

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