高分辨率格式在非定常无粘可压缩流动中的应用研究(英文)

Numerical experiments using one high-resolution scheme for unsteady inviscid compressible flows

本文发展了一种计算非定常无粘可压缩流动的高分辨率格式。通量计算采用AUSMPW+Rie-mann求解器,其中使用了基于单调性的压力加权函数f,并与Roe Riemann求解器进行比较。为提高精度,使用五阶WENO格式进行左右状态插值,且时间推进采用三阶TVD Runge-Kutta方法。用该方法对移动接触间断问题、Sod激波管问题、二维激波反射问题和双马赫反射问题进行了数值计算,数值结果表明基于五阶WENO插值的AUSMPW+格式有很高的激波及接触间断分辨能力,并比基于五阶WENO插值的Roe格式有更高的计算效率。

One high-resolution scheme is developed to compute unsteady, inviscid, compressible flows. In this paper, we are concerned about AUSMPW＋ Riemann solver with the weighting function f based on pressure by considering monotonicity and compare it with Roe Riemann solver. For better accuracy, fifth-order WENO schemes are adopted to interpolate higher order left and right states across a cell interface. Third-order TVD Runge-Kutta method is used to advance the solution in time. The performance of the schemes has been assessed in four typical unsteady inviscid compressible flow problems： moving contact discontinuity problem, Sod＇s problem, regular shock reflection, and double Mach reflection of a strong shock. AUSMPW＋ scheme with fifth-order WENO schemes interpolation proves to have the great capabilities to capture shock and contact discontinuities with high resolution and be more efficient than Roe scheme.