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2006•Modern Physics Letters BRequires access

ERROR ANALYSIS OF LATTICE BOLTZMANN BGK MODEL BASED ON EXTRAPOLATION TECHNIQUE

Shanling Han, Zhongqin Lin, Ping Zhu, Xinmin Lai

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Abstract

The lattice Boltzmann method, which can simulate the macroscopic behavior of fluid flow, is a relatively new approach. The error analysis of the lattice Boltzmann BGK model is proposed based on extrapolation technique. According to the Filippova procedure, the error estimation formula is derived. The theory analysis shows that the error of lattice Boltzmann method is proportional to the lattice size and the relaxation parameter. The non-equilibrium part of the distribution function leads to the main error. Finally, the proposed error analysis method is validated by numerical simulation of the lid-driven flows in a square cavity. The numerical results agree well with the theory analysis results.

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What this paper is about

The lattice Boltzmann method, which can simulate the macroscopic behavior of fluid flow, is a relatively new approach. The error analysis of the lattice Boltzmann BGK model is proposed based on extrapolation technique. According to the Filippova procedure, the error estimation formula is derived. The theory analysis shows that the error of lattice Boltzmann method is proportional to the lattice size and the relaxation parameter. The non-equilibrium part of the distribution function leads to the main error. Finally, the proposed error analysis method is validated by numerical simulation of the lid-driven flows in a square cavity. The numerical results agree well with the theory analysis results.

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Available abstract

The lattice Boltzmann method, which can simulate the macroscopic behavior of fluid flow, is a relatively new approach. The error analysis of the lattice Boltzmann BGK model is proposed based on extrapolation technique. According to the Filippova procedure, the error estimation formula is derived. The theory analysis shows that the error of lattice Boltzmann method is proportional to the lattice size and the relaxation parameter. The non-equilibrium part of the distribution function leads to the main error. Finally, the proposed error analysis method is validated by numerical simulation of the lid-driven flows in a square cavity. The numerical results agree well with the theory analysis results.

Key concepts: Lattice Boltzmann methods, Extrapolation, Statistical physics, Bhatnagar–Gross–Krook operator, HPP model, Lattice gas automaton, Distribution function, Boltzmann equation

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