高阶WENO格式数值粘性对模拟R-T不稳定性的影响

The influence of the numerical viscosity of high-order weighted essentially non-oscillatory (WENO) schemes on simulation of Rayleigh-Taylor instability

利用3、5、7和9阶精度WENO格式求解二维无量纲Euler和Navier-Stokes方程对可压缩流体中的Rayleigh-Tay-lor不稳定性进行了数值模拟.通过研究该不稳定性后期激发出的Kelvin-Helmholtz不稳定性的强弱,详细分析了数值粘性和物理粘性对数值解的影响.计算结果表明,无粘情况下,格式精度和网格数量决定了数值流场的细微结构,高精度密网格得到的数值解通常是非物理的;有粘情况下,当格式固有的数值粘性远小于物理粘性时,所得到的数值解一般是可信的.

The third, fifth, seventh, and ninth order WENO schemes were used to solve the two-dimensional non- dimensionalized Euler and Navier-Stokes equations to simulate Rayleigh-Taylor instability for compressible fluid. By studying the intensity of Kelvin-Helmholtz instability induced by Rayleigh-Taylor instability, the influence of numer- ical and physical viscosities on the numerical solution was analyzed. The numerical results show that the order of schemes and the refinement of meshes determine the small-scale structure of the numerical flow field while the physical viscosity is ignored and the numerical solutions based on high-order schemes with fine grids usually are non-physical. Under the condition of considering the physical viscosity, the results of numerical simulation are generically faithful while the numerical viscosity inherent in the scheme is significantly smaller than the physical viscosity.