高阶气体动理学格式在湍流数值模拟中的应用

本文回顾了高阶气体动理学格式在湍流数值模拟中的应用。与传统的Riemann求解器相比,气体动理学格式可以提供时空耦合的演化过程,这对发展高精度格式十分重要。因此,基于两步四阶时间离散和高精度WENO重构,发展了具有四阶时间精度的气体动理学格式。该格式有更高的数值精度和稳定性,并且具有更好的处理复杂流动问题的能力。目前,两步四阶格式已经成功地应用到低雷诺数湍流直接数值模拟和高雷诺数工程湍流RANS模拟中,包括低速槽道湍流、超声速均匀各向同性衰减湍流、二维亚声速翼型湍流和三维跨声速翼身湍流等。数值结果表明该格式对湍流直接数值模拟和湍流RANS模拟具有高数值精度和高数值稳定性。下一步将利用高阶气体动理学格式研究更具有挑战性的可压缩湍流问题,例如超声速湍流边界层和激波边界相互作用等。

High-order gas-kinetic scheme for numerical simulation of turbulence

We review the application of high-order gas-kinetic scheme(HGKS)in the numerical simulations of turbulence.HGKS was developed based on the two-stage fourth-order temporal discretization and high-order weighted essentially non-oscillation(WENO)reconstruction.Compared with the classical Riemann solvers,the high-order temporal evolution process,which is extremely helpful in the design of robust,accurate,and efficient higher-order schemes,can be used to construct a spatial-temporal coupled gas-kinetic flux solver.Currently,HGKS has been successfully applied in the direct numerical simulations and Reynolds averaged Navier-Stokes(RANS)simulations of turbulence,including low-speed turbulent channel flows,the decaying supersonic isotropic turbulence,the subsonic NACA0012 airfoil turbulence,and the transonic ARA M100 wing-body turbulence.The numerical results show that HGKS has the high accuracy and outstanding robustness for turbulence simulations.In summary,the HGKS provides a powerful computational tool for studying turbulent flows,especially for compressible turbulence.In the future,more challenging studies will be conducted,including the supersonic turbulent boundary layers and the shock-boundary layer interaction.