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首页> 外文期刊>Mathematical Engineering in Industry >A variational principle for the Navier-Stokes equations incorporating finite element approximation to high-Re flows
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A variational principle for the Navier-Stokes equations incorporating finite element approximation to high-Re flows

机译：Navier-Stokes方程的变分原理，将有限元逼近合并到高分辨率流中

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摘要

The work described here shows that the known variational principle for the Navier-Stokes equations and the adjoint system can be modified to produce a set of Euler-Lagrange variational equations, which have the same order and same solution as the Navier-Stokes equations, provided the adjoint system has a unique solution. The variational principle, in conjunction with finite element discretization, is then applied to lid-cavity driven flow problem in he steady state using primitive variables. An upwind differencing approximation is used for the solution of the boundary value problem. The discrete equations are solved using a multigrid method. Solutions are obtained for Reynolds number in the range 1000 < Re <10 000 on a uniform rectangular mesh consisting Of 120×120 grid points. The results are compared with the work of Ghia et al. (1982) and good Agreement is obtained with their high-re solutions.
机译：此处描述的工作表明，可以修改Navier-Stokes方程和伴随系统的已知变分原理，以生成一组Euler-Lagrange变分方程，该方程具有与Navier-Stokes方程相同的阶数和相同的解。伴随系统具有独特的解决方案。然后，将变分原理与有限元离散化结合起来，使用原始变量将其应用于稳态下盖腔驱动的流动问题。迎风微分逼近用于解决边值问题。离散方程使用多重网格法求解。在由120×120网格点组成的均匀矩形网格上，获得雷诺数在1000

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