多介质动力学模型的解析解

Analytical solutions of multimedia dynamic models

为了系统地探讨解析解的求解方法,按照多介质动力学模型中相的数量,对常见的模型形式进行建模,使用常微分方程的解析解求解理论,以消元法为例,研究并给出了典型三相及四相系统解析解的求解过程。对于五相及五相以上系统,一般不能得出解析解。在排放速率函数不可导,以及相体积、相平流流速和温度不恒定的情况下,很难求出模型的解析解。使用MATLAB可得出两相系统的解析解,暂不能得出三相及四相系统的解析解。以上研究结果为多介质动力学模型解析解的使用提供了方法依据。

To discuss the analytical solutions of multimedia dynamic models(MDMs) systematically, models were built for possible types of MDMs according to the phase number, and then ordinary differential equation solving theories were employed to give solving processes of analytical solution of three-phase and four-phase system MDMs. It is generally impossible to obtain the analytical solution for MDMs containing five and more phases. When the emission rate functions were non-differentiable, or phase volumes, phase advection rates and temperature were not constant, the analytical solutions could be hardly obtained. Currently, MATLAB could not calculate the analytical solutions for complex models. The results provide methodological bases for the analytical solutions of MDMs.