SOLUTION OF SPATIAL VISCOUS FLOW BASED ON HAMILTONIAN SYSTEM
SOLUTION OF SPATIAL VISCOUS FLOW BASED ON HAMILTONIAN SYSTEM
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发表时间：
2002
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通讯作者：
Ma Jian-wei
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作者：
Ma Jian-wei
传统的流体力学求解方法是基于一类变量描述的，属于拉格朗日体系表述下的欧几里得空间。处理一些复杂的域是困难的。本文提出了一种新的流体力学求解策略。利用变分原理引入对偶变量和哈密顿函数，将问题提升到辛几何空间中，在守恒哈密顿体系下求解。进一步推导了基于Hamilton算子矩阵特征向量展开的求解方法。直接求解了低雷诺数的三维粘性流动问题。通过求解零特征值解及其约当规范形，得到了流体力学的几个基本解。最后，利用Papkovitch-Neuber一般解，通过求解非零特征值和叠加非零特征向量，研究了流场的边缘效应。
The traditional solution methods of fluid mechanics, which were described based on one kind of variable, belong to the Euclidian space under the Lagrange system formulation. It is difficult to deal with some complex domain. In this paper, a new solution strategy for fluid mechanics is put forward. Dual variables and Hamiltonian function are introduced by variational principle such that a problem is promoted to symplectic geometrical space under the conservative Hamiltonian system. Furthermore, the solution based on the expansion of eigenvectors of Hamiltonian operator matrix is derived. The problem of three dimensional viscous flow with low Reynolds number is solved directly. Several basic solutions of fluid mechanics are obtained by virtue of solving the zero eigenvalue solutions and their Jordan normal forms. Finally, using the general solution named Papkovitch-Neuber, the edge effect of flow field is studied via solving the non-zero eigenvalue and superposing non-zero eigenvectors.