超燃冲压发动机燃烧室一维稳态跨声速流动方程在临界声速点存在奇异初值问题,现有的基于L’Hospital法则的求解方法在原理上存在较大的初值误差,影响一维稳态跨声速计算的精度。为此,本文提出了一种基于变量代换的改进算法,通过定义新的流动变量W=-Ma2+2Ma,构造出了非奇异的一维稳态跨声速流动方程。消除了微分方程的奇异性,有效的解决了一维稳态跨声速流动计算过程中存在的奇异初值问题。 The one-dimensional steady-state transonic flow equation in a scramjet engine combustor has a singular initial value problem at the critical acoustic velocity point. The existing method based on L’Hospital has a large initial value error in principle and affects one-dimensional steady Accuracy of transonic sound velocity calculation. To this end, this paper presents an improved algorithm based on variable substitution. By defining a new flow variable W = -Ma2 + 2Ma, a non-singular one-dimensional steady-state transonic flow equation is constructed. It eliminates the singularity of differential equations and effectively solves the singular initial value problem existing in the computation of one-dimensional steady transonic flow.