基于自适应结构网格ale方法的研究.pdf

南京航空航天大学硕士学位论文 i 摘要在计算流体力学( CFD )界面追踪问题的数值模拟中, ALE ( Arbitrary Lagrangian-Eulerian )方法是目前国内外普遍应用的方法之一。这类方法由于涉及到 Lagrange 坐标系下计算网格的变形问题,目前的研究工作主要包括 Lagrange 坐标系下有限体积格式的构造和针对计算网格变形的守恒重映及网格重分问题。本文研究了一类新的 ALE 方法,主要进行了 Lagrange 网格下的有限体积格式的构造、积分守恒重映格式的构造和自适应结构网格的生成三方面的工作,相关内容如下: 1 、从积分形式的二维 Lagrange 流体力学方程组出发,采用已经在 Euler 方程求解中得到成功运用的高精度 ENO(Essentially Non-oscillatory) 有限体积格式的构造思想,推导了一类 Lagrange 网格下的有限体积格式; 2 、分别介绍了一类基于单元相交和基于面通量的守恒重映格式。然后通过 WENO(Weighted Essentially Non-oscillatory) 插值多项式重构密度分布的思想构造了一类基于 WENO 插值的守恒重映算法。最后通过一组算例验证了算法的可行性, 并分析了算法的精度; 3 、给出了一种结构网格的生成方法和两类网格自适应方法: 自适应加密网格方法( Adapative Mesh Refinement )和自适应运动网格方法( Moving Mesh Method ) 。由于在网格自适应方法中, 涉及到新网格上物理量的重构,这需要满足守恒性和单调性的要求,本文把积分守恒重映格式应用到网格的自适应方法中,并在最后给出了算例,验证了该方法的有效性。作者分别编写了三个部分的程序模块,最后把这三部分串联起来运行,形成了一类新的 ALE 方法。数值实验的结果表明,这是一种十分有效的界面追踪方法。关键字:界面追踪技术, ALE 方法,有限体积格式,重映技术, ENO 插值, WENO 插值, 网格自适应技术基于自适应结构网格的 ALE 方法研究 ii Abstract In the research of numerical simulation for front tracking problems in computational fluid dynamics, one of the most popular numerical algorithms is so called ALE (Arbitrary Lagrangian-Eulerian) method. For the reason of concerning with large mesh distortion, the research of this kind of methods mainly focuses on constructing of finite volume schemes in Lagrangian coor dination , mesh redistribution and remapping of physical quantities between mesh systems. In this paper, a new kind of ALE meth od is investigated , mainly including : constructing of finite volume schemes on structure grids in Lagrangian coordination; construc ting of a new kind of high order accurate conservative remapping algor ithm; generation of a kind of adaptive grids. It primarily concerns three following aspects: ( ⅰ)By use of ENO(Essentially N on-oscillatory) interpolating polynomials on structure grids, a high accurate finite volume scheme has been constructed through modifying a first order finite volume scheme on rectangular mesh. ( ⅱ)Two kinds of integration conservative remapping