We solve the Euler equations to compute the interaction of a Mach 1.22 shock wave with a helium bubble contaminated by 28% air by mass. A ninth-order upwind scheme is used to calculate the left and the right states of the primitive variables as required by the AUSMD algorithm. The low numerical dissipation of the AUSMD algorithm makes it an ideal choice for computing long-time behavior of the bubble after the shock passes over it. The algorithm combines well with the high spectral accuracy of the ninth-order upwind scheme. The basic trends in the evolving bubble match with earlier experimental and numerical observations. Effect of numerical schemes and grid sizes is also observed for this study. The Euler solver captures a large number of small-scale rolled-up vortices originally generated by the baroclinic torque term in the vorticity transport equation and later enhanced by the Kelvin–Helmholtz instability. Numerical schlieren, mass fraction, and vorticity contour plots are used to visualize the turbulent mixing zone that is a key feature of the translating and deforming bubble.

我们求解欧拉方程，计算出1.22马赫冲击波与质量百分比为28％的空气污染的氦泡之间的相互作用。根据AUSMD算法的要求，使用九阶迎风方案来计算原始变量的左状态和右状态。AUSMD算法的低数值耗散使其成为计算冲击经过后气泡的长期行为的理想选择。该算法很好地结合了九阶迎风方案的高光谱精度。不断发展的气泡的基本趋势与早期的实验和数值观察相吻合。这项研究还观察到数值方案和网格大小的影响。欧拉求解器捕获了大量最初由涡度输运方程中的斜压转矩项生成的小规模的卷起涡流，后来又由开尔文-亥姆霍兹不稳定性增强了。数值schlieren，质量分数和涡度等高线图用于可视化湍流混合区，这是平移和变形气泡的关键特征。