National Key Laboratory of Science and Technology on Aerodynamic Design and Research, Northwestern Polytechnical University, Xi'an, Shaanxi 710072, China.
Phys Rev E. 2017 May;95(5-1):053307. doi: 10.1103/PhysRevE.95.053307. Epub 2017 May 26.
In our study, the dual time-stepping strategy of the gas-kinetic scheme is constructed and used for the simulation of unsteady flows. In comparison to the previous implicit gas-kinetic scheme, both the inviscid and viscous flux Jacobian are considered in our work, and the linear system of the pseudo-steady-state is solved by applying generalized minimal residual algorithm. The accuracy is validated by several numerical cases, the incompressible flow around blunt bodies (stationary circular cylinder and square cylinder), and the transonic buffet on the NACA0012 airfoil under hybrid mesh. The numerical cases also demonstrate that the present method is applicable to approach the fluid flows from laminar to turbulent and from incompressible to compressible. Finally, the case of acoustic pressure pulse is carried out to evaluate the effects of enlarged time step, and the side effect of enlarged time step is explained. Compared with the explicit gas-kinetic scheme, the proposed scheme can greatly accelerate the computation and reduce the computational costs for unsteady flow simulations.
在我们的研究中，构建并使用气体动理学方案的双时间步策略来模拟非定常流。与之前的隐式气体动理学方案相比，我们的工作中同时考虑了无粘和粘性通量雅可比矩阵，并应用广义最小残差算法来求解伪稳态线性系统。通过几个数值算例验证了精度，包括钝体周围的不可压缩流（静止的圆形和方形圆柱体）以及混合网格上 NACA0012 翼型的跨声速抖振。这些数值算例还表明，本方法适用于从层流向湍流、从不可压缩流到可压缩流的流动逼近。最后，进行了声压脉冲的算例来评估增大时间步长的效果，并解释了增大时间步长的副作用。与显式气体动理学方案相比，所提出的方案可以大大加速非定常流模拟的计算并降低计算成本。
