Accurate numerical schemes based on the lattice Boltzmann methods for multi-dimensional diffusion equations

Shinsuke Suga ()
Additional contact information
Shinsuke Suga: Center for Social and Environmental Systems Research, National Institute for Environmental Studies, 16-2, Onogawa, Tsukuba, Ibaraki, 305-8506, Japan

International Journal of Modern Physics C (IJMPC), 2014, vol. 25, issue 04, 1-25

Abstract: We propose accurate explicit numerical schemes based on the lattice Boltzmann (LB) method for multi-dimensional diffusion equations. In LB schemes, the velocity models D2Q9 and D2Q13 are used for two-dimensional equations and D3Q19 and D3Q25 for three-dimensional equations. We introduce free parameters that characterize the weight of the equilibrium distribution functions to reduce numerical errors. Consistency analysis through the fourth-order Chapman–Ensgok expansion of the distribution functions gives an approximate diffusion equation with error terms up to fourth-order. The relaxation parameter and weight parameters are determined so that second-order error terms are eliminated in the approximate equation. Stability analysis shows that we can find a relaxation parameter so that each of the presented schemes is stable for given diffusion coefficients and discretizing parameters. Numerical experiments for the isotropic and anisotropic benchmark problems show that the presented schemes derived from the velocity models D2Q13 and D3Q25 are useful for numerical simulations of practical problems governed by two- and three-dimensional diffusion equations, respectively. In particular, schemes in which the value of the relaxation parameter is set to be 1 demonstrate a fourth-order accuracy under the stability condition.

Keywords: Lattice Boltzmann method; multi-dimensional diffusion equation; fourth-order Chapman–Ensgok expansion; accuracy; stability; 11.25.Hf; 123.1K (search for similar items in EconPapers)
Date: 2014
References: View complete reference list from CitEc
Citations:

Downloads: (external link)
http://www.worldscientific.com/doi/abs/10.1142/S0129183113501040
Access to full text is restricted to subscribers

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:wsi:ijmpcx:v:25:y:2014:i:04:n:s0129183113501040

Ordering information: This journal article can be ordered from

DOI: 10.1142/S0129183113501040

Access Statistics for this article

International Journal of Modern Physics C (IJMPC) is currently edited by H. J. Herrmann

More articles in International Journal of Modern Physics C (IJMPC) from World Scientific Publishing Co. Pte. Ltd.
Bibliographic data for series maintained by Tai Tone Lim ().