一种流体力学统一变分原理及其在孤立子域或孤立点上的应用

A Consistent Variational Principle of Hydromechanics and Its Application in Isolated Subfield or Isolated Point

根据流体力学基本方程组,本文应用最优化加权残数法建立了一种流体力学统一变分原理。其优点如下:泛函和变分原理的建立极为容易;可将基本方程组导出的各种流体力学问题转化为统一的最优化问题;所得解是某种意义下的最佳解。本文根据孤立城最优化权残法将统一变分原理应用到任一孤立子域上,从而求出水动力方程仅适用于该孤立点的解(点解)。对孤立子城或孤立点独立求解时均不需要考虑与其它子域或其它点的相容条件,但要考虑全部边界条件并补充若干对徽分方程求导所得的导残数方程。

According to the basic equation of hydromechanics, by adopting the most optimum weighted residual method,a consistent variational principle of hydromechanics is established. Its advantages are as follows:functional and viriational principle can be easily established . the different hydromechanical problems developed by basic equation groups can be changed into optimum one, and the solutions are the best in s sense. In light of optimum weighted residual method of the isolated field,the consistent variational principle can be used to either isolated subfield . thus the solutions developed from hydrodynamic equations are only suitable for the isolated subfield. In the same way, we can get the solution from hydrodynamic equation which only fits the isolated point. As the solutions for isolated subfield or points are being developed separately, it does not need to consider the compatibility between the two. But the total boundary conditions with the suplementary derivative residual e-quations developed from differential equations should be taken into account.