Viscous Fluid Mechanics
Viscous Fluid Mechanics
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DOI：
10.1007/978-3-642-83683-1_8
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发表时间：
1989
影响因子：
23.9
通讯作者：
D. Bonneau;G. Bezine
中科院分区：
文献类型：
--
作者：
D. Bonneau;G. Bezine
首先给出了不可压缩粘性牛顿流体的控制方程和边界条件，提出了二维Stokes流动的积分方程方法，即求解双调和方程，并给出了双调和方程的直接边界积分公式。所得到的流函数及其导数的表达式涉及边界上定义的所有量.在Stokes流的情况下，这些表达式的离散化导致一个线性方程组.当考虑惯性效应时，这些项的计算是必要的.在后一种情况下，定义了四个内部参数：速度的两个分量和涡度的两个梯度。通过对区域进行离散，得到了非线性代数方程组，对于小的Bronchold数，该方程组可以用经典方法求解，但当惯性效应很重要时，需要更精细的方法，最后给出了一些例子，与其他方法的结果相比，证明了该公式的数值效率。
First we give the governing equations for an incompressible viscous newtonian fluid completed with boundary conditions.An integral equation method for two-dimensional Stokes flows is presented which consists in solving the biharmonic equation.A direct boundary integral formulation is developed for the biharmonic equation. The representation of the stream function and its derivative obtained involves all the quantities defined on the boundary.In the case of Stokes flow the discretization of these representations leads to a linear system of equations.When the inertia effects are taken into account, the evaluation of these terms is necessary. In this latter case four internal parameters are defined: the two components of the velocity and the two gradients of the vorticity. By discretizing the domain we obtain nonlinear algebraic equations which can be solved by classical method for small Reynold’s numbers, but much elaborated methods are necessary when the inertia effects are important.Finally we present some examples which prove the numerical efficiency of this formulation compared with results given by other methods.