Lattice Boltzmann model for two-dimensional unsteady Burgers' equation
Abstract
In this paper, a special lattice Boltzmann model is proposed to simulate two-dimensional unsteady Burgers' equation. The maximum principle and the stability are proved. The model has been verified by several test examples. Excellent agreement is obtained between numerical predictions and exact solutions. The cases of steep oblique shock waves are solved and compared with the two-point compact scheme results. The study indicates that lattice Boltzmann model is highly stable and efficient even for the problems with severe gradients.
- Publication:
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Journal of Computational and Applied Mathematics
- Pub Date:
- September 2007
- Bibcode:
- 2007JCoAM.206..432D
- Keywords:
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- Lattice Boltzmann method;
- Two-dimensional Burgers' equation;
- 4-bit model;
- Multi-scale analysis;
- Maximum principle