基于超声速边界层转捩的WENO格式对比分析

Comparison and analysis of WENO schemes base on supersonic boundary layer transition

基于高精度weighted essentially non-oscillation(WENO)格式对马赫数为4.5,雷诺数为10 000的超声速来流条件下平板边界层转捩过程进行了大涡模拟.无黏通量分别用5阶、7阶、9阶WENO格式进行离散,黏性通量离散采用4阶中心差分格式,时间推进采用具有总变差递减(TVD)性质的3阶精度RungeKutta方法.通过在入口边界叠加一对等幅最不稳定第一模态谐波扰动,分别采用3种WENO格式计算得到了平板层流边界层失稳转捩的演化过程.结果表明:5阶WENO格式的数值耗散明显高于7阶和9阶WENO格式,在捕捉湍流涡和流场脉动特性上存在明显不足.9阶WENO格式的耗散小,能够捕捉到流场更小尺度的涡和高频脉动.研究具有高频脉动特性的问题或者欲捕捉精细涡结构时,建议采用7阶以上的高精度格式.

Large eddy simulations of the transition process in a supersonic flat-plate boundary layer at free-stream Mach number of 4.5and Reynolds number of 10 000 were carried out using high precision weighted essentially non-oscillation（WENO）schemes.The inviscid flux was discretized by fifth-order,seventh-order,ninth-order WENO schemes separately and the viscous flux was discretized by fourth-order center difference scheme.The temporal discretization was made by means of third-order Runge-Kutta with total variation diminishing（TVD）.By imposing apair of the most unstable oblique first-mode disturbances on the inflow boundary,the transition progress of the flow from laminar,transition process to full turbulence was compared using three WENO schemes.Results indicate that the fifthorder WENO scheme is more dissipative than the seventh-order and ninth-order schemes,so it’s difficult to capture eddy and pulse in the flow field.The dissipation of ninth-order WENO scheme is small,enabling to capture smaller eddy and high frequency.To study aproblem with high frequency fluctuation or capture fine eddy,it’s advisable to use the scheme higher than seventh-order.