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arXiv · 1906.11036

Discrete unified gas kinetic scheme for nonlinear convection-diffusion equations

Jinlong Shang·Zhenhua Chai·Huili Wang·Baochang Shi
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Abstract

In this paper, we develop a discrete unified gas kinetic scheme (DUGKS) for general nonlinear convection-diffusion equation (NCDE), and show that the NCDE can be recovered correctly from the present model through the Chapman-Enskog analysis. We then test the present DUGKS through some classic convection-diffusion equations, and find that the numerical results are in good agreement with analytical solutions and the DUGKS model has a second-order convergence rate. Finally, as a finite-volume method, DUGKS can also adopt the non-uniform mesh. Besides, we performed some comparisons among the DUGKS, finite-volume lattice Boltzmann model (FV-LBM), single-relaxation-time lattice Boltzmann model (SLBM) and multiple-relaxation-time lattice Boltzmann model (MRT-LBM). The results show that the DUGKS model is more accurate than FV-LBM, more stable than SLBM, and almost has the same accuracy as the MRT-LBM. Besides, the using of non-uniform mesh may make DUGKS model more flexible.

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Jinlong Shang, Zhenhua Chai, Huili Wang, Baochang Shi. 2019-06-16. Discrete unified gas kinetic scheme for nonlinear convection-diffusion equations. https://doi.org/10.1103/physreve.101.023306

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