摘要
应用坐标变换，把可变动的物理平面，在映像平面上转化成为十分规则的矩形区域，这给有限元计算带来了极大的方便。在映像平面上巧妙地把控制方程转化为守恒形式，从而定义了两个新型函数——迹线长度函数Ｙ和能量函数Ω，并巧妙地构造了约束方程。应用凑合反推法非常方便地建立了一维变截面非定常可压缩均熵流动的广义变分原理及其相应的杂交命题的广义变分原理。并对如何处理初终值条件作了简要的说明。
In the imagine plane τψ (defined τ time, ψ path function),two special functions pathline length function Y and energy function Ω have been defined due to the fact that the governing equations can be changed into conservative ones by space translation.The calculation domain in the image plane has the defined rectangle form,which gives much advantages to use finite element method(FEM) to solve the flow problem,while the calculation domain in the physical plane is changed with time or even unknown (hybrid or inverse problems),so the imagine plane is very convenient for one to establish GVPs for hybrid problems without using variable domain variational principle.A constraint equation (eq.13) has been constructed in order to establish GVP more easily via semi inverse method,which is one of the most effective and convenient ways to establish sub generalized variational principles and generalized variational principles with multi variables without any variational crisis(some Lagrange multipliers are equal to zero) which always come across when using Lagrange multiplier method.As a result two families of generalized variational principles for 1 dimensional unsteady compressible flow in a varying cross section and their hybrid problems have been deduced.In addition,a simple method to deal with initial/final conditions are given. The semi inverse method will make great affects not only in fluid mechanics,but also in elasticity.This theory aims at rendering a general,rigorous theoretical basis for the finite element method for 1 D unsteady flow.
出处
《空气动力学学报》
CSCD
北大核心
1998年第3期352-357,共6页
Acta Aerodynamica Sinica
关键词
一维
非定常流
广义变分原理
有限元
杂交命题
dimensional unsteady flow
image plane
generalized variational principle
finite element method
semi inverse method
hybrid problem
