CLASSICAL AREAS OF PHENOMENOLOGY |
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Entropy and weak solutions in the lattice Bhatnagar–Gross–Krook model |
Ran Zheng(冉政)† and Xu Yu-Peng(许宇鹏) |
Shanghai Institute of Applied Mathematics and Mechanics, Shanghai University, Shanghai 200072, China |
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Abstract We derive the entropy functions whose local equilibria are suitable to recover the Euler-like equations in the framework of the lattice Boltzmann method. Numerical examples are also given, which are consistent with the above theoretical arguments. In all cases, we observe a negative entropy range existing near the shock, while numerical oscillations are captured.
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Received: 24 March 2011
Revised: 18 May 2011
Accepted manuscript online:
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PACS:
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47.11.Qr
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(Lattice gas)
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47.10.ad
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(Navier-Stokes equations)
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51.10.+y
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(Kinetic and transport theory of gases)
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51.30.+i
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(Thermodynamic properties, equations of state)
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Fund: Project supported by the National Natural Science Foundation of China (Grant Nos. 90816013 and 10572083). |
Cite this article:
Ran Zheng(冉政) and Xu Yu-Peng(许宇鹏) Entropy and weak solutions in the lattice Bhatnagar–Gross–Krook model 2011 Chin. Phys. B 20 114702
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