Discrete velocity model and implicit scheme for the BGK equation of rarefied gas dynamics
Discrete velocity model and implicit scheme for the BGK equation of rarefied gas dynamics
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DOI：
10.1142/s0218202500000562
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发表时间：
2000-11-01
影响因子：
3.5
通讯作者：
Mieussens, L
中科院分区：
文献类型：
--
作者：
Mieussens, L
本文提出了一种用气体动力学中的BGK方程描述过渡流的数值计算方法。利用最小熵原理定义离散平衡函数，建立了该方程的离散速度模型。与连续模型一样，该模型保证了解的正性、矩的守恒和熵的耗散。然后用显式有限体积格式将离散速度模型在空间和时间上离散，证明了该格式满足上述性质。然后推导出一种线性化隐式格式，以有效地计算稳态；然后用几个测试用例验证该方法。
We present a numerical method for computing transitional flows as described by the BGK equation of gas kinetic theory. Using the minimum entropy principle to define a discrete equilibrium function, a discrete velocity model of this equation is proposed. This model, like the continuous one, ensures positivity of solutions, conservation of moments, and dissipation of entropy. The discrete velocity model is then discretized in space and time by an explicit finite volume scheme which is proved to satisfy the previous properties. A linearized implicit scheme is then derived to efficiently compute steady-states; this method is then verified with several test cases.