流体力学方程组人为解应用研究

The Manufactued Solutions of Fluid Dynamics Equations and Its Applications

流体力学方程求解的应用程序已成为众多重大工程理论研究与设计的重要工具,其应用程序的正确性验证已成为研究的重要问题.人为解验证技术是基于偏微分方程建模与模拟、很难解析求解的复杂工程应用程序正确性验证的重要手段.文章对流体力学方程组人为解构造方法及在应用程序正确性验证方面的研究进行了综述总结.利用李群约化理论得到流体力学方程几类精确解,给出了人为解构造的准则及流程,三维理想流体力学方程组的人为解,二维平面、柱坐标系下流体方程组的人为解及在欧氏应用程序验证中的应用,流体力学拉氏方程组人为解及在拉氏应用程序验证中的应用.

The computer programs of solving fluid dynamics equations is an important tool in com- plex engineer research and design. It is very important problem of code verification. A key part of code verification is the method of manufactured solutions. This paper is a summary for the method of constructing manufactured solutions and applying to fluid dynamics equations. First, applying Lie group theory, we find some exact solutions of the equations. Second, we also provide the technological process and rules of constructing manufactured solutions. Last, we provide code verifications for several examples of fluid dynamics equations.