可压缩流动激波装配在格心型有限体积法中的应用

Applications of shock-fitting technique for compressible flow in cell-centered finite volume methods

发展了一种基于格心型有限体积方法(FVM)的激波装配算法。通过定义网格节点属性可以灵活调用激波装配和激波捕捉计算方法。在使用激波装配方法时,激波节点运动速度和下游运动速度通过Rankine-Hugoniot(R-H)关系式获得,同时采用非结构动网格技术描述激波的运动以及调整其他网格节点的位置。流过激波面元的通量为上游单元的基本通量,物理概念更加清晰,通量计算也更为准确。在计算过程中,网格节点属性可以发生变化,以此实现对带有拓扑变化流场的描述。数值试验表明:本文提出的计算方法不但具有较高的计算精度,同时能有效地避免由于捕捉激波而出现的数值问题。

A shock-fitting technique for cell-centered Finite Volume Method（FVM）is developed in this work.It is flexible to switch among shock-fitting and shock-capturing methods by changing the nature of grid nodes,which are defined as shock nature and common nature.In the shock-fitting method,velocities of shock nodes and downstream states are obtained by solving Rankine-Hugoniot（R-H）relations.The unstructured dynamic grid technique is used for shock tracking and updating the positions of other common nodes.The flux across a shock face equals the basic flux of its upstream cell.During the computational process,the nature of the nodes is allowed to change.Thus,it is easier to apply this method in complex problems,even with topological change.The numerical results show the proposed method is not only of high accuracy,but also able to avoid the troubles in shock-capturing.