三维非定常可压缩理想气体的广义变分原理

广义变分原理是构造杂交有限元和流体力学各种杂交命题（包括反命题）的理论基础。如何从偏微分方程及初边值条件出发，构造广义变分原理，这是一个非常难的课题，历来是许多学者寻求的目标。本文提出了建立广义变分原理的新方法－凑合反推法。应用该法作者建立了三维非定常可压缩理想气流的亚广义变分原理及广义变分原理。本文的结果将给变分有限解法提供严密的理论基础。并对如何处理初边值条件作了简要的说明。

Generalized Variational Principles for 3 Dimensional Unsteady Inviscid Compressible Flow

The generalized variational principles are the basic for hybrid finite element method(FEM) and for hybrid/inverse problems for fluid mechanics. It has been the aim which has been searched by many scholars for how to arrive at a generalized variational principle from the known partial differential equations and boundary/initial conditions. A semi inverse method, which is very effective and convenient, is proposed to establish generalized variational principles. With such method, sub generalized variational principles (SGVPs) & generalized variational principles (GVPs) for 3 D unsteady compressible inviscid flow are formulated. This theory aims at rendering a general, rigorous theoretical basis for the finite element method and other direct variational methods. In addition, a simple method to deal with initial/finial conditions are suggested.