Petrov‐Galerkin methods on multiply connected domains for the vorticity‐stream function formulation of the incompressible Navier‐Stokes equations
Petrov‐Galerkin methods on multiply connected domains for the vorticity‐stream function formulation of the incompressible Navier‐Stokes equations
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不可压缩纳维-斯托克斯方程涡流函数公式的多重连通域 Petrov-Galerkin 方法
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发表时间：
1988
期刊：
影响因子：
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通讯作者：
J. Liou
中科院分区：
文献类型：
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作者：
T. Tezduyar;R. Glowinski;J. Liou
总结在本文中，我们提出了流线迎风/Petrov-Galerkin有限元程序的基础上的不可压缩Navier-Stokes方程的涡量流函数制定的二维流体动力学计算。我们解决的困难与对流项的涡输运方程，缺乏边界条件的涡在无滑移边界，并确定流函数的值在多连通域的内部边界。所提出的技术，块迭代方法的框架内实施，已成功地应用于各种问题，涉及简单和多连通域。用不可压Navier-Stokes方程的涡量流函数公式进行二维计算有一些优点。与速度-压力公式相比，涡量-流函数公式可自动计算出满足不可压缩性条件的流场，未知函数由3个减少为2个，涡量场由速度场微分直接计算。如果人们需要研究涡量场，因而希望尽可能精确地表示涡量场，那么最后一个优点就变得很重要。我们提出了合适的有限元程序的时间依赖的涡度输运方程和泊松方程的流函数的涡度的解决方案。与涡度输运方程中对流项有关的困难，
SUMMARY In this paper we present streamline-upwind/Petrov-Galerkin finite element procedures for two-dimensional fluid dynamics computations based on the vorticity-stream function formulation of the incompressible Navier-Stokes equations. We address the difficulties associated with the convection term in the vorticity transport equation, lack of boundary condition for the vorticity at no-slip boundaries, and determination of the value of the stream function at the internal boundaries for multiply connected domains. The proposed techniques, implemented within the framework of block-iteration methods, have successfully been applied to various problems involving simply and multiply connected domains. There are some advantages in using the vorticity-stream function formulation of the incompressible Navier-Stokes equations for two-dimensional computations. Compared to the velocity-pressure formulation, the vorticity-stream function formulation leads to computed flow fields which satisfy the incompressibility condition automatically; also the number of unknown functions is reduced from three to two and the vorticity field is computed directly instead of being obtained by differentiation of the velocity field. The last advantage becomes important if one needs to study the vorticity field and therefore wants that this field be represented as accurately as possible. We propose suitable finite element procedures for the solution of the time-dependent vorticity transport equation and the Poisson’s equation which relates the stream function to the vorticity. The difficulties associated with the convection term in the vorticity transport equation, lack of