H定理直接联系着动力学方法的稳定性，一直是各种简化求解Boltzmann方程方法的重要研究方向之一。本文证明了离散速度方向模型在平衡态和非平衡态下以及全部流动领域内都存在日定理，表明离散速度方向模型具有内在的稳定性。为了提高离散速度方向模型的数值稳定性，本文找到了一组该模型满足H定理的充分条件，该条件具有清晰的物理意义和简单的数学形式，可以方便地应用在数值计算中。
The H theorem is an important subject for the kinetic methods to reduce the Boltzmann equation because it is closely related to the stability. In this paper, we proved that an H theorem exists for the discrete velocity direction model both at equilibrium state and at non-equilibrium state in the whole flow regime, which shows the intrinsic stability to the discrete velocity direction model. To enhance the numerical stability of the discrete velocity direction model, we gained a set of sufficient conditions, which are clear in physics and simple in mathematics. In addition, this set of conditions can be easily applied into the numerical calculations.
参考文献
| [1] | Yong WA;Luo LS .Nonexistence of H theorem for some lattice Boltzmann models[J].Journal of Statistical Physics,2005(1/2):91-103. |
| [2] | Zhang ZY;Xu JZ;Qi ZG;Xi G .A discrete velocity direction model for the Boltzmann equation and applications to micro gas flows[J].Journal of Computational Physics,2008(10):5256-5271. |
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