]*>","")" /> DAE的Runge-Kutta方法在不可压NS方程求解中的应用

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DAE的Runge-Kutta方法在不可压NS方程求解中的应用

伍亚丹,黄兰洁   

  1. 中国科学院计算数学与科学工程计算研究所,中国科学院计算数学与科学工程计算研究所
  • 出版日期:1997-03-14 发布日期:1997-03-14

伍亚丹,黄兰洁. DAE的Runge-Kutta方法在不可压NS方程求解中的应用[J]. 计算数学, 1997, 19(3): 277-286.

THE RUNGE-KUTTA METHODS OF DAE IN THE NUMERICAL SOLUTION OF THE INCOMPRESSIBLE NS EQUATIONS

  1. Wu Ya-Dan; Huang Lan Chieh(Institute of Computational Mathematics and Scientific/Engineering Computing,Chinese Academy of Sciences, Beijing )
  • Online:1997-03-14 Published:1997-03-14
The incompressible Navier-Stokes (INS) equations upon discretization on fixed meshes become a system of differential algebraic equations (DAE) of index 2. It is proved in this paper that for the general explicit and implicit Runge-Kutta (RK)methods, the time accuracy of velocity is the same as that for the ordinary differential equations, by taking into consideration of the special form of the resulting DAE; (the time accuracy of pressure can be lower). For the three-stage secondorder explicit RK method, algorithms with less (than three) Poisson solutions of pressure are proposed and verified by numerical experiments. However, in practical computation of complex flows it is found that the method must satisfy the so-called consistency condition for the components of the solution (here the velocity and the pressure) of the DAE for the method to be robust.
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