粘性物质中正激波稳定性分析

用线性稳定性理论,分析粘性物质中的正激波稳定性问题.粘性物质中任意强度的一维激波,其稳定性问题可归结为处理复数范围内的特征值问题,该特征值问题由两个一阶常微分方程及一个二阶常微分方程构成.这些常微分方程的系数依赖于流动的基本流场的物理量及其梯度.所获得的特征值问题由一个四阶精度的有限差分离散求解.分析考虑物质粘性的金属铝中的正激波稳定性,可以看出,正激波运动是稳定的,并且激波速度对波前和波后的小扰动量的衰减有相反的作用,而物质粘性有致稳的作用.

Stability of Normal Shock Waves in Viscous Materials

Stability of normal shock waves in viscous materials is analyzed with linear stability theory(LST).Equation of state of material adopts "stiff gas" expression.Stability problem of one-dimensional shock waves with arbitrary shock strength in viscous material is attribute to an eigenvalue problem with regard to complex number.The eigenvalue problem concerns two first-order ordinary differential equations and one second-order equation.Their coefficients depend on physics variables and gradients.The eigenvalue problem is discretized and solved in a four-order precision finite difference scheme.With analysis on stability of shock waves in aluminum under high pressure,it is shown that one dimensional shock wave is stable.It shows that the velocity of shock wave has opposite effects on attenuation of perturbation ahead and behind shock front.Viscosity of material makes the attenuation more rapidly.