二维广义压力梯度方程的简单波

Simple Waves of Two-Dimensional Generalized Pressure Gradient Equations

摘要: 利用直接的方法讨论在自相似平面下气体动力学中二维广义压力梯度方程的特征分解理论，可以得到压强p与特征值Λ±的特征分解。进一步，若流动来自常状态，还可得到速度(u,v)的特征分解。由此可以得到与常状态流动相邻的流动是简单波，且说明简单波的流动区域是被一族直线所覆盖，沿着每条直线p,u,v均为常数。该结论推广Courant和Friedrichs的《超音速流和冲击波》一书中关于可约方程的著名结果。

Abstract: In this paper, the characteristic decompositions of the two-dimensional generalized pressure gradient equations in the self-similar plane are discussed by direct approach. The decompositions can allow a proof for simple wave. The decompositions of the pressure p and characteristics ± Λ are obtained. Furthermore, the velocity (u,v) can be also obtained if the flow comes from a constant state which is not previously discussed. This way, by the characteristic decomposition, we find that any wave adjacent to a constant state is a simple wave whose flow region is covered by an one-parametric family of independent lines, along each of which the pressure p and the velocity (u,v) are constant. This conclusion is devoted to extending the well-known result on reducible equations in Courant and Friedrichs’ book “Supersonic Flow and Shock Waves”.