摘要
本文对作者以前凭试凑、灵感、运气与经验得出的一系列非定常可压流动显式解析解，寻找线索，总结出其可能的推导途径，并以非定常可压等熵一维流为例，具体给出了四种新的求解方法。这些方法会对今后寻找工程热物理领域的非线性主控方程的解析解有所帮助。本文同时还给出了两个新的解析解。
Several algebraically explicit analytical solutions of nonlinear unsteady compressible flow equation set have been found by the author since the nineties with the method of trial and error, as well as inspiration and fortune. In this paper, some possible derivation approaches to find out such solutions are summarized. As an example, 4 derivation skills to solve the nonlinear unsteady compressible isentropic 1-D flow equation are given, which include: extending the symbolic method proposed by Heavside one century ago from ordinary differential equation to partial differential equation, developing a new method of separating variables with addition, solving the partial differential equations with constant source term by neglecting source term firstly and then satisfying it with lowest order partial differential derivative, lowering the non-linearity by choosing some relations which can be satisfied later. These skills will be helpful for solving other nonlinear equations. Two new explicit analytical solutions for unsteady 1-D compressible flow are given also.
出处
《工程热物理学报》
EI
CAS
CSCD
北大核心
2001年第2期159-162,共4页
Journal of Engineering Thermophysics
基金
国家自然科学基金资助项目!(No.59846006
59925615)
国家重点基础研究发展规划资助项目!(No.G19990
