An accuracy analysis of the cascaded lattice Boltzmann method for the 1D advection-diffusion equation

Robert Straka1,2, Keerti Vardhan Sharma3

1AGH University of Science and Technology, Department of Heat Engineering and Environment Protection, Faculty of Metals Engineering and Industrial Computer Science, al. Mickiewicza 30, 30-059, Krakow, Poland.

2Czech Technical University in Prague, Department of Mathematics, Faculty of Nuclear Sciences and Physical Engineering, Trojanova 13, 120 00, Praha 2, Czech Republic.

3University of Wyoming, Paris Center of Innovation for Flow Through Porous Media, High Bay Research Facility, 651 N 19th street, Laramie, WY 82072, United States of America.



We analyze higher order error terms in a modified partial differential equation of a cascaded lattice Boltzmann method (CLBM) for one conservation law – the advection-diffusion equation. To inspect the behavior of the error terms we derived an equivalent finite difference equation (EFDE), this approach is different from other techniques like the Chapman-Engskog expansion, equivalent partial differential equations or the Maxwell iteration used in the literature. The resulting EFDE is obtained from the recurrence formulas of the lattice Boltzmann equations for the CLBM and is subsequently analyzed by standard analytical techniques. We have found relations of the LBM parameters which could cancel some of the higher order terms, making the method more accurate. The detailed derivation of the EFDE and higher order terms’ pre-factors is the main result of this paper. The resulting explicit form of the error terms are derived and presented.

Cite as:

Straka, R., & Sharma, K. V. (2020). An accuracy analysis of the cascaded lattice Boltzmann method for the 1D advection-diffusion equation. Computer Methods in Materials Science, 20(4), 173–184.

Article (PDF):

Key words:

Cascaded thermal lattice Boltzmann method, High order analysis, Advection-diffusion equation, Equivalent finite difference equation


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