On boundary conditions for velocity potentials in confined flows: Application to Couette flow
On boundary conditions for velocity potentials in confined flows: Application to Couette flow
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DOI：
10.1063/1.857726
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发表时间：
1990-05
影响因子：
4.6
通讯作者：
F. Marques
中科院分区：
文献类型：
--
作者：
F. Marques
用两个标量势表示螺线线场对于许多问题来说是非常有用的方法，特别是对于不可压缩的Navier-Stokes方程，尽管在有限的容器中边界条件可能不容易处理。势的微分方程比原来的纳维-斯托克斯方程高一个阶。因此，需要附加的边界条件来求解它们。导出了这些微分方程和相应的边界条件，并证明了它们与原问题的等价性。特别强调了具有非平凡几何的域，其中存在积分边界条件。作为一个例子，结果已应用于周期性Couette流。在这种情况下，可以通过适当改变变量来避免积分边界条件，从而降低得到的方程的阶数。
The representation of solenoidal fields by means of two scalar potentials can be a very useful method for a wide range of problems, in particular for the incompressible Navier–Stokes equations, though in finite containers boundary conditions may not be easily handled. The differential equations for the potentials are of an order higher than the original Navier–Stokes ones. As a consequence additional boundary conditions are needed to solve them. These differential equations and the corresponding boundary conditions for any geometry have been derived and the equivalence with the original problem has been proved. Special emphasis has been laid on domains with nontrivial geometry in which integral boundary conditions appear. As an example, the results have been applied to the periodic Couette flow. In this case the integral boundary conditions can be avoided by an appropriate change of variables, hence reducing the order of the equations obtained.