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

• 论文 •

### DAE的Runge-Kutta方法在不可压NS方程求解中的应用

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

### 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.
()
 [1] Van Kan, A second-order accurate pressure-correction scheme for viscous incompressibleflow, SIAM J Sci. Stat. Comput., 7 (1986), 870-891. [2] L.C. Huang, On the boundary treatmeat for the numerical solution of the incompressibleNavier-Stokes equations with finite difference methods, J Comput- Math., 14: 2 (1996),135-142. [3] L. Petzold et al., Numerical solution of nonlinear differential equations with algebraicconstraints II: practical implications, SIAM J Sci. Stat. Comput., 7 (1986), 720-733. [4] E. Hairer et al, The Numerical Solution of Differeatial Algebraic Systems by Runge-KuttaMethod, Lecture Notes in Mathematics 1409, Springer-Verlag, 1989. [5]伍亚丹,黄兰洁,非均匀交错网格上的 Temam方法及驱动方腔流动的数值模拟,计算物理, 11: 2 (1994),141-148. [6]黄兰洁,包兰丹,非定常不可压NS方程的高效和稳健的差分格式II,计算数学,19:1(1997) , 58—72. [7] U. Ghia et. al., High-Re solutions for incompressible flow using the Navier-Stokes equationsand a multigrid method, J Comput. Phys, 48, (1982), 387-411. [8]伍亚丹,非定常不可压NS方程的高效和稳健的差分格式II,数值计算与计算机应用,18:1(1997), 53—63.
 No related articles found!