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A Novel Method for the Numerical Solution of the Navier- Stokes Equations in Two -Dimensional Flow Using a Pressure Poisson Equation

机译:用压力泊松方程求解二维流动中Navier-Stokes方程的新方法

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A new finite-difference method is presented for the numerical solution of the Navier-Stokes equations of motion of a viscous incompressible fluid in two (or three) dimensions and in the primitive-variable formulation. Introducing two auxiliary functions of the coordinate system and considering the form of the initial equation on linesrnpassing through the nodal point (x0, Jo) anc* parallel to the coordinate axes, we can separate it into two parts that arernfinally reduced to ordinary differential equations, one for each dimension. The final system of linear equations in n-unknowns is solved by an iterative technique and the method converges rapidly giving satisfactory results. For the pressure variable we consider a pressure Poisson equation with suitable Neumann boundary conditions. Numerical results, confirming the accuracy of the proposed method, are presented for configurations of interest, like Poiseuille flow and the flow between two parallel plates with step under the presence of a pressure gradient.
机译:提出了一种新的有限差分方法,用于求解二维(或三维)和原始变量公式的粘性不可压缩流体的Navier-Stokes运动方程的数值解。引入坐标系的两个辅助函数,并考虑通过平行于坐标轴的节点(x0,Jo)anc *的直线上的初始方程的形式,我们可以将其分为两部分,最后简化为常微分方程,每个维度一个。通过迭代技术解决了n个未知数中的线性方程组的最终系统,该方法迅速收敛,给出了令人满意的结果。对于压力变量,我们考虑具有合适诺伊曼边界条件的压力泊松方程。数值结果证实了所提方法的准确性,并针对感兴趣的配置(如泊瓦流和在压力梯度存在下带有台阶的两个平行板之间的流)进行了介绍。

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