# Convection-diffusion lattice Boltzmann scheme for irregular lattices

## Abstract

In this paper, a lattice Boltzmann (LB) scheme for convection diffusion on irregular lattices is presented, which is free of any interpolation or coarse graining step. The scheme is derived using the axioma that the velocity moments of the equilibrium distribution equal those of the Maxwell-Boltzmann distribution. The axioma holds for both Bravais and irregular lattices, implying a single framework for LB schemes for all lattice types. By solving benchmark problems the authors have shown that the scheme is indeed consistent with convection diffusion. Furthermore, they have compared the performance of the LB schemes with that of finite difference and finite element schemes. The comparison shows that the LB scheme has a similar performance as the one-step second-order Lax-Wendroff scheme: it has little numerical diffusion, but has a slight dispersion error. By changing the relaxation parameter {omega} the dispersion error can be balanced by a small increase of the numerical diffusion.

- Authors:

- Publication Date:

- Research Org.:
- Agrotechnological Research Inst., Wageningen (NL)

- OSTI Identifier:
- 20067702

- Resource Type:
- Journal Article

- Journal Name:
- Journal of Computational Physics

- Additional Journal Information:
- Journal Volume: 160; Journal Issue: 2; Other Information: PBD: 20 May 2000; Journal ID: ISSN 0021-9991

- Country of Publication:
- United States

- Language:
- English

- Subject:
- 42 ENGINEERING; 99 GENERAL AND MISCELLANEOUS//MATHEMATICS, COMPUTING, AND INFORMATION SCIENCE; BOLTZMANN EQUATION; MESH GENERATION; CONVECTION; DIFFUSION; CALCULATION METHODS

### Citation Formats

```
Sman, R.G.M. van der, and Ernst, M.H.
```*Convection-diffusion lattice Boltzmann scheme for irregular lattices*. United States: N. p., 2000.
Web. doi:10.1006/jcph.2000.6491.

```
Sman, R.G.M. van der, & Ernst, M.H.
```*Convection-diffusion lattice Boltzmann scheme for irregular lattices*. United States. doi:10.1006/jcph.2000.6491.

```
Sman, R.G.M. van der, and Ernst, M.H. Sat .
"Convection-diffusion lattice Boltzmann scheme for irregular lattices". United States. doi:10.1006/jcph.2000.6491.
```

```
@article{osti_20067702,
```

title = {Convection-diffusion lattice Boltzmann scheme for irregular lattices},

author = {Sman, R.G.M. van der and Ernst, M.H.},

abstractNote = {In this paper, a lattice Boltzmann (LB) scheme for convection diffusion on irregular lattices is presented, which is free of any interpolation or coarse graining step. The scheme is derived using the axioma that the velocity moments of the equilibrium distribution equal those of the Maxwell-Boltzmann distribution. The axioma holds for both Bravais and irregular lattices, implying a single framework for LB schemes for all lattice types. By solving benchmark problems the authors have shown that the scheme is indeed consistent with convection diffusion. Furthermore, they have compared the performance of the LB schemes with that of finite difference and finite element schemes. The comparison shows that the LB scheme has a similar performance as the one-step second-order Lax-Wendroff scheme: it has little numerical diffusion, but has a slight dispersion error. By changing the relaxation parameter {omega} the dispersion error can be balanced by a small increase of the numerical diffusion.},

doi = {10.1006/jcph.2000.6491},

journal = {Journal of Computational Physics},

issn = {0021-9991},

number = 2,

volume = 160,

place = {United States},

year = {2000},

month = {5}

}