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Lattice Boltzmann model for two-dimensional unsteady Burgers’ equation. (English) Zbl 1115.76064
Summary: A special lattice Boltzmann model is proposed to simulate two-dimensional unsteady Burgers’ equation. The maximum principle and 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 two-point compact scheme results. The study indicates that lattice Boltzmann model is highly stable and efficient, even for the problems with severe gradients.

MSC:
76M28 Particle methods and lattice-gas methods
76D99 Incompressible viscous fluids
76L05 Shock waves and blast waves in fluid mechanics
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