非结构变形网格和离散几何守恒律

数值模拟流固耦合问题或多体分离问题的非定常流动时，常采用基于任意拉格朗日-欧拉（ALE）方程的有限体积法，涉及到变形网格和离散几何守恒律。在对变形网格算法进行综述时，按照构造思想分为物理比拟、椭圆光顺、插值、运动子网格（MSA）及其混合法共5类，分别介绍了基本原理、研究现状和适用范围，通过算例比较表明，径向基函数（RBFs）和运动子网格相结合的混合方法既有很好的变形能力，也有较高的计算效率，值得进一步发展和推广。在介绍了离散几何守恒律（DGCL）概念之后，采用二维几何模型进行分析，指出其机理是离散过程中体积增量与网格面元扫过的体积不相等造成的，把目前国内外应用的算法分为面积修正法、给定速度的面积修正法、速度修正法和体积修正法共4类，对其应用范围和存在的问题进行讨论，认为提出的体积修正算法既可以保证流固界面条件，也可以用于时间多层格式。

Unstructured deforming mesh and discrete geometric conservation law

A popular method for simulating unsteady flow of fluid-structure interaction or multi-body separation is finite volume method based on arbitrary Lagrangian-Eulerian (ALE) equations, which involves mesh deformation and discrete geometric conservation law. The fundamental principle, state of the art and boundaries of validity of mesh deformation are reviewed following 5 categories of constructing ideas, e.g., physics analogy, ellipse smoothing, interpolation, moving submesh approach (MSA) and hybrid method. A hybrid method which combines the benefits of MSA and radial basis functions (RBFs) interpolation is proved to be robust and efficient via several numerical examples. After the concept of discrete geometric conservation law (DGCL) is introduced, the intrinsic mechanism of DGCL is analyzed through 2D model, which is the inequality between volume increment and the volume sweeping by the surfaces enclosing of mesh cell. The different implementations of DGCL which could be mainly categorized as area correction, area correction via assuming velocity of surface, velocity correction and volume correction are surveyed and their range of application and the existing problems are discussed. We found that the proposed volume correction method can satisfy the fluid-structure interface condition, and is also appropriate for multi-step temporal discrete schemes.