非结构动网格上的多介质流数值模拟方法研究
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摘要
本文主要研究了在非结构动网格上求解含有可自由运动的介质界面的可压缩多介质流场的一套数值模拟方法。
首先采用阵面推进法生成了二维三角形和三维四面体非结构网格,在生成过程中为了提高网格生成效率,采用双向链表和堆的数据结构,加快插入、删除和查找等单元操作。在三维阵面推进法中,提出了线、面、体几何相交判断规则,将复杂几何体的相交判断看作为几个简单几何体的相交判断的合成,同时加入了边交换和面交换技术,提高了网格质量。
本文尝试在非结构动网格上通过运用HLLC格式求解ALE方程(ArbitraryLagrangian-Eulerian Formulation)来数值模拟多介质流,将介质界面定义为一种可以自由运动的网格内部边界,它将整个流场分成了若干个区域,分别对应不同的介质。该边界由网格边组成,界面两侧对应两种不同介质中的网格,界面节点上的流动状态矢量都有着两种定义,分别对应界面两侧不同的介质状态。通过求解介质界面上的Riemann问题来追踪介质界面上网格节点的运动。通过公式推导求出了刚性气体状态方程(Stiffened Gas EOS)下多介质Riemann问题的解析解,而对其他拥有复杂形式的状态方程则采用双波近似方法求得Riemann问题的近似解。同时研究了两种介质界面数值通量的求解方法:Lagrange方法和虚拟流体方法(Ghost FluidMethod,GFM),通过算例比较,认为虚拟流体方法比Lagrange方法更适合求解介质界面上存在大压力梯度的多介质流问题。
在动网格的处理上,对于小变形多介质界面以及简单多介质流场,非结构网格的变形运用弹簧原理来处理;而对于大变形介质界面和复杂多介质流场,采用局部重构技术来处理。同时,介质界面上的网格节点可能会在界面上进行滑移,导致界面上网格体积为负,因此将介质界面定义为网格变形边界,如果节点滑移幅度过大,则会自动调整界面上的节点和网格,避免造成负体积网格的出现。另外,本文在运用动网格技术求解含有运动弹丸的膛口流场过程中,将整个流场分为两个区域,它们由特殊的内部边界联系,从根本上解决了弹丸从膛内到膛外运动时流场结构发生变化的问题。
最后通过水下爆炸、激波诱导水中气泡变形以及机翼与海面相互作用等多介质模型的数值模拟,证明本文的ALE方法是可行的,而且与国内外流行的基于静止网格的Euler方法有如下优点:(1)能够时刻追踪介质界面上每个节点的运动状态,界面形状描述更加精确;(2)能够捕捉含有微小位移的介质界面。
Numerical methods based on unstructural moving grids are developed to solve compressible multi-material flows where an arbitrarily moving interface exists between two immiscible fluids.
Unstructural 2D triangle and 3D tetrahedron grids are generated using advancing front technology. The bidirectional chains are applied to accelerate some operations such as inserting, deleting and searching. A simple rule is proposed to judge the intersection of segment, facet and volume during generating tetrahedron grids. Besides, edge swaping and face swaping methods are also applied to improve the quality of tetrahedron grids.
Arbiratry Lagrangian-Eulerial (ALE) formulation based on unstructual moving grids is used to solve multi-material flows. The material interface is looked upon as a lagrangian interface which can move freely and is composed of a number of edges of the unstructured grids. The state vectors of the points on the interface have two different definitions corresponding to the two different fluids. Then, Riemann problem is solved to track the interface accurately and the grids are moving automatically with the motion of the interface. The analytic solution of Riemann problem for stiffened gas equation of state (EOS) is deduced in this article. And two-shock approximation method is implemented for general EOS. Two different methods, Lagrange methods and ghost fluid method (GFM) are discussed here to compute the numeical flux through the material interface. 1D double-material shock tube problems are solved to indicate that GFM still work well when large pressure grads exists near the interface.
Spring analogy and local remeshing technology is respectively applied to deal with small and large deforming grids. At the same time, points at the material interface may slip in tangent direction of the interface resulting in negative volume grids. To resolve this problem, the material interface is defined as deforming boundary where the points and grids can adaptively adjust their positions.
Underwater explosion model, shock bubble model and supersonic aerofoil over water model are computed using ALE method, which indicates that ALE method is feasible in the computing of multi-material flows and holds these advantages comparing with Euler mehods: (1) real-time tracking of the material interface; (2) ability of capturing mirco-deforming interface.
首先采用阵面推进法生成了二维三角形和三维四面体非结构网格,在生成过程中为了提高网格生成效率,采用双向链表和堆的数据结构,加快插入、删除和查找等单元操作。在三维阵面推进法中,提出了线、面、体几何相交判断规则,将复杂几何体的相交判断看作为几个简单几何体的相交判断的合成,同时加入了边交换和面交换技术,提高了网格质量。
本文尝试在非结构动网格上通过运用HLLC格式求解ALE方程(ArbitraryLagrangian-Eulerian Formulation)来数值模拟多介质流,将介质界面定义为一种可以自由运动的网格内部边界,它将整个流场分成了若干个区域,分别对应不同的介质。该边界由网格边组成,界面两侧对应两种不同介质中的网格,界面节点上的流动状态矢量都有着两种定义,分别对应界面两侧不同的介质状态。通过求解介质界面上的Riemann问题来追踪介质界面上网格节点的运动。通过公式推导求出了刚性气体状态方程(Stiffened Gas EOS)下多介质Riemann问题的解析解,而对其他拥有复杂形式的状态方程则采用双波近似方法求得Riemann问题的近似解。同时研究了两种介质界面数值通量的求解方法:Lagrange方法和虚拟流体方法(Ghost FluidMethod,GFM),通过算例比较,认为虚拟流体方法比Lagrange方法更适合求解介质界面上存在大压力梯度的多介质流问题。
在动网格的处理上,对于小变形多介质界面以及简单多介质流场,非结构网格的变形运用弹簧原理来处理;而对于大变形介质界面和复杂多介质流场,采用局部重构技术来处理。同时,介质界面上的网格节点可能会在界面上进行滑移,导致界面上网格体积为负,因此将介质界面定义为网格变形边界,如果节点滑移幅度过大,则会自动调整界面上的节点和网格,避免造成负体积网格的出现。另外,本文在运用动网格技术求解含有运动弹丸的膛口流场过程中,将整个流场分为两个区域,它们由特殊的内部边界联系,从根本上解决了弹丸从膛内到膛外运动时流场结构发生变化的问题。
最后通过水下爆炸、激波诱导水中气泡变形以及机翼与海面相互作用等多介质模型的数值模拟,证明本文的ALE方法是可行的,而且与国内外流行的基于静止网格的Euler方法有如下优点:(1)能够时刻追踪介质界面上每个节点的运动状态,界面形状描述更加精确;(2)能够捕捉含有微小位移的介质界面。
Numerical methods based on unstructural moving grids are developed to solve compressible multi-material flows where an arbitrarily moving interface exists between two immiscible fluids.
Unstructural 2D triangle and 3D tetrahedron grids are generated using advancing front technology. The bidirectional chains are applied to accelerate some operations such as inserting, deleting and searching. A simple rule is proposed to judge the intersection of segment, facet and volume during generating tetrahedron grids. Besides, edge swaping and face swaping methods are also applied to improve the quality of tetrahedron grids.
Arbiratry Lagrangian-Eulerial (ALE) formulation based on unstructual moving grids is used to solve multi-material flows. The material interface is looked upon as a lagrangian interface which can move freely and is composed of a number of edges of the unstructured grids. The state vectors of the points on the interface have two different definitions corresponding to the two different fluids. Then, Riemann problem is solved to track the interface accurately and the grids are moving automatically with the motion of the interface. The analytic solution of Riemann problem for stiffened gas equation of state (EOS) is deduced in this article. And two-shock approximation method is implemented for general EOS. Two different methods, Lagrange methods and ghost fluid method (GFM) are discussed here to compute the numeical flux through the material interface. 1D double-material shock tube problems are solved to indicate that GFM still work well when large pressure grads exists near the interface.
Spring analogy and local remeshing technology is respectively applied to deal with small and large deforming grids. At the same time, points at the material interface may slip in tangent direction of the interface resulting in negative volume grids. To resolve this problem, the material interface is defined as deforming boundary where the points and grids can adaptively adjust their positions.
Underwater explosion model, shock bubble model and supersonic aerofoil over water model are computed using ALE method, which indicates that ALE method is feasible in the computing of multi-material flows and holds these advantages comparing with Euler mehods: (1) real-time tracking of the material interface; (2) ability of capturing mirco-deforming interface.
引文
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