可压缩Kelvin-Helmholtz不稳定性低耗散锐界面方法直接模拟

采用低耗散WENO(weighted essential non-oscillatory)格式及锐界面方法模拟可压缩Kelvin-Helmholtz不稳定性问题.由于物质界面被描述成一种接触间断, 该方法可精确求解切向速度间断.基于优化模板对原始光滑指标进行正规化后, 得到一种低耗散WENO格式.修正后的方法显著降低了普通流动区域的过衰减问题, 保持了良好的激波捕捉性能, 并可获得与混合格式相当的求解精度.不同于以往求解单一流体或易混界面时, 通过初始设定有限宽度的剪切层或快速数值耗散以抑制高波数模态, 该方法允许高波数扰动的发展.计算结果表明, 高波数扰动展现出与以往理想Kelvin-Helmholtz不稳定性问题数值模拟或线化理论结果不同的特征, 但与有限厚度的剪切层结果相符. 

Direct Simulation of the Compressible Kelvin-Helmholtz Instability with a Low-Dissipation Sharp-Interface Method

A sharp-interface method combined with a low-dissipation weighted essential non-oscillatory (WENO) scheme was introduced to simulate the compressible Kelvin-Helmholtz instability. As the material interface was described as a contact discontinuity, this method resolved the exact tangential velocity discontinuity. By normalizing the original smoothness indicators with that of the optimal stencil, a modified WENO method with low dissipation was developed. While still keeping good shock-capturing properties, the modified method decreases the over damping in moderate flow field considerably, and is able to achieve comparable accuracy as that of hybrid methods. Different from previous simulations with single fluid or miscible interface methods, which suppress the high-wave-number modes by initially prescribed finite-width shear layer or fast numerical dissipation, this method allows the development of high-wave-number perturbation. However, the simulations still suggest that the high-wave-number perturbation show different behavior from previous simulations and linear theory on ideal Kelvin-Helmholtz instability but resemble those on shear layer with finite thickness.