State Key Laboratory of Coal Combustion, Huazhong University of Science and Technology, Wuhan 430074, China.
School of Mathematics and Statistics, Huazhong University of Science and Technology, Wuhan 430074, China.
Phys Rev E. 2018 Feb;97(2-1):023306. doi: 10.1103/PhysRevE.97.023306.
An efficient third-order discrete unified gas kinetic scheme (DUGKS) is presented in this paper for simulating continuum and rarefied flows. By employing a two-stage time-stepping scheme and the high-order DUGKS flux reconstruction strategy, third order of accuracy in both time and space can be achieved in the present method. It is also analytically proven that the second-order DUGKS is a special case of the present method. Compared with the high-order lattice Boltzmann equation-based methods, the present method is capable to deal with the rarefied flows by adopting the Newton-Cotes quadrature to approximate the integrals of moments. Instead of being constrained by the second order (or lower order) of accuracy in the time-splitting scheme as in the conventional high-order Runge-Kutta-based kinetic methods, the present method solves the original Boltzmann equation, which overcomes the limitation in time accuracy. Typical benchmark tests are carried out for comprehensive evaluation of the present method. It is observed in the tests that the present method is advantageous over the original DUGKS in accuracy and capturing delicate flow structures. Moreover, the efficiency of the present third-order method is also shown in simulating rarefied flows.
本文提出了一种高效的三阶离散统一气体动力学格式（DUGKS），用于模拟连续体和稀薄流。通过采用两阶段时间步长方案和高阶 DUGKS 通量重构策略，本方法在时间和空间上都可以达到三阶精度。还分析证明了二阶 DUGKS 是本方法的一个特例。与基于高阶格子玻尔兹曼方程的方法相比，本方法能够通过采用牛顿-科特斯积分来近似矩的积分来处理稀薄流。与传统的基于高阶龙格-库塔的动力学方法中时间分裂方案的二阶（或更低阶）精度限制不同，本方法求解原始的玻尔兹曼方程，克服了时间精度的限制。进行了典型的基准测试以全面评估本方法。在测试中观察到，本方法在精度和捕捉精细流动结构方面优于原始 DUGKS。此外，本三阶方法在模拟稀薄流方面的效率也得到了展示。
