关于变形网格“几何守恒律”概念的讨论

Discussion about GCL for Deforming Grids

在国内外文献中应用包含有变形的动网格进行流动数值模拟时,要满足所谓的几何守恒律条件;通过对这一概念最早提出推导过程和近年来应用发展情况分析以后发现,逻辑上存在不适当之处。从流体力学基本理论出发,对包含有变形的动网格技术的理论基础进行讨论,证实几何守恒律是流体力学控制方程的伴随方程或退化方程;通过简单模型分析有限体积方法离散过程,发现计算过程中不满足几何守恒律所引起的非物理现象本质上是目前有限体积离散处理中微元体积计算方法不符合物理定律所致;因此在变形动网格计算方法中不存在必须要满足的几何守恒律。最后根据理论提出物理背景清晰的微元体积计算方法,数值验证可行。

According to many literatures, when using moving grids in numerical simulation, so-called Geometric Conservation Law（GCL） should be satisfied. After analyzing the process of coining this terminology and its applications these years, we consider that this law is not very appropriate logically. On the basis of primal theories in fluid dynamics, through discussing about moving and deforming grids＇ theoretical foundations, it＇s confirmed that GCL is the accompanying/degenerate equations of the fluid governing equations ; through analyzing the discretization process of finite volume methods （FVM） in brief,we found the non-physical phenomena induced by violating GCL is essentially because the calculation of infinitesimal region＇s volume doesn＇t accord with physical law;so,in deforming grid computational methods ,there isn＇ t any GCL to be satisfied. Finally, a new method with clear physical backgrounds of calculating volume is developed, and it is validated numerically.