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Accuracy of the lattice Boltzmann method based on analytical solutions
1LITEC, Consejo Superior de Investigacion Cientificas, Maria de Luna 8, Zaragoza 50015, Spain. gah@sunserv.kfki.hu
Summary
A new method provides steady analytical solutions for the lattice Boltzmann method (LBM). This approach reveals how lattice orientation impacts LBM accuracy and offers insights into compressibility errors.
Area of Science:
- Computational fluid dynamics
- Numerical analysis
Background:
- The lattice Boltzmann method (LBM) is a powerful numerical technique for simulating fluid flows.
- Obtaining steady analytical solutions in LBM is challenging but crucial for understanding its behavior.
Purpose of the Study:
- To propose a simple method for deriving steady analytical solutions for the LBM.
- To investigate the influence of lattice orientation on LBM accuracy.
- To establish a relationship between compressibility error and velocity fields.
Main Methods:
- Development of a novel analytical approach to solve LBM equations.
- Systematic analysis of LBM accuracy concerning lattice-flow field alignment.
- Derivation of a direct correlation between compressibility error and velocity.
Main Results:
- A straightforward method yielding steady analytical solutions for LBM was successfully developed.
- The study demonstrates a quantifiable dependence of LBM accuracy on lattice and flow field orientation.
- A simple relationship connecting compressibility error and velocity field is established.
Conclusions:
- The proposed method offers a valuable tool for generating general analytical solutions in LBM.
- Understanding lattice orientation effects is key to improving LBM accuracy.
- The derived relation aids in analyzing and mitigating compressibility errors in LBM simulations.