基于超声速边界层转捩的WENO格式对比分析

基于高精度weighted essentially non-oscillation(WENO)格式对马赫数为4.5,雷诺数为10000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Runge-Kutta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. 

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

Large eddy simulations of the transition process in a supersonic flat-plate boundary layer at free-stream Mach number of 4.5 and Reynolds number of 10000 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 a pair 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 fifth-order 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 a problem with high frequency fluctuation or capture fine eddy, it's advisable to use the scheme higher than seventh-order.