Outflow boundary conditions for the incompressible non-homogeneous Navier-Stokes equations-猫眼课题宝

不可压缩非齐次纳维-斯托克斯方程的流出边界条件

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2006

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作者：

F. Boyer;P. Fabrie

在本文中，我们提出了分析的不可压缩具有非线性外流的非齐次Navier-Stokes方程边界条件这种边界条件似乎是，在某些情况下，进行数值计算的一种有用的方法非定常Navier-Stokes方程的解， Dirichlet数据不是由计算域边界的一部分。边界条件下，我们提出，继以前的作品中的同质情况下，是应力的法向分量之间的关系以及考虑惯性效应的流出动量通量。我们证明了该模型弱解的整体存在性， 2D和3D。特别是，我们表明，非线性边界条件下的研究成立这样一个解决方案在弱意义上，即使应力和密度的法向分量可能没有通常意义上的痕迹。

In this paper we propose the analysis of the incompressible non-homogeneous Navier-Stokes equations with nonlinear outflow boundary condition. This kind of boundary condition appears to be, in some situations, a useful way to perform numerical computations of the solution to the unsteady Navier-Stokes equations when the Dirichlet data are not given explicitly by the physical context on a part of the boundary of the computational domain. The boundary condition we propose, following previous works in the homogeneous case, is a relationship between the normal component of the stress and the outflow momentum flux taking into account inertial effects. We prove the global existence of a weak solution to this model both in 2D and 3D. In particular, we show that the nonlinear boundary condition under study holds for such a solution in a weak sense, even though the normal component of the stress and the density may not have traces in the usual sense.

Outflow boundary conditions for the incompressible non-homogeneous Navier-Stokes equations

不可压缩非齐次纳维-斯托克斯方程的流出边界条件

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