快速流场求解的参数多项式方法

研究了进行流场求解的超快速方法——参数多项式方法的原理。从分析参数多项式方法和加权残值法的联系出发 ,证明得到若取足够多的控制点数 ,无论是控制点数大于基函数个数 ,还是控制点数等于基函数个数 ,或者选取有限个控制点 ,在相应的条件下 ,都可以得出这样的结论 :参数多项式方法的求解结果实质上可等同于加权残值法的求解结果。通过研究 ,进一步认识了参数多项式法原理的完备性 ,为其工程应用提供了理论基础

Parametric polynomial method for fast flow-field calculation

This paper studies the principles of the parametric polynomial method, a super fast method for flow field calculation by analyzing the relationship between the parametric polynomial method and the weighted residual method. The conclusions can be applied whether the number of control points is larger than or equal to the number of primary functions, or whether the number of control points is limited. The solution obtained by the parametric polynomial method is equal to the solution by the weighted residual method for corresponding conditions. The parametric polynomial method is further developed as a solid theoretical foundation for engineering applications.