N-S方程有限分析数值研究

 本文将有限分析方法用于曲线座标系上紊流N-S方程的数值计算。分别计算了单列和串列叶栅内部流场,计算中采用了k-ε紊流模型和壁面函数。计算结果与试验结果相比较,吻合程度令人满意。有限分析方法在网格单元上对N-S方程进行线化处理,以解析边界条件作为约束,得出解析解,在解析解基础上构造离散代数方程。有限分析方法的最大特点是可以适应对流速度大小和方向,自动调整格式系数,因而具有数值扩散小和稳定性高等优点。

FINITE ANALYTIC NUMERICAL SOLUTION OF NAVIER-STOKES EQUATION

The finite analytic method is used in the present study to calculate the turbulent flow field described with Navier-Stokes equations in body-fitted curvilinear coordinate system. The finite analytic method invokes the analytic solution of governing partial differential equation in formulating the algebraic equation that relates a nodal value in an element to its neighbouring nodal values. The major feature of the finite analytic method is its ability to simulate automatically the upwind influence of neighbouring nodal values according to the direction and the magnitude of convection. It is shown that the finite analytic method has good numerical stability and accuracy. The turbulent flow fields through a single cascade of airfoil and a tandem cascade of airfoil are numerically simulated by using finite analytic method respectively in the paper. The k-e turbulence model and wall function method are employed in the present study. The agreement of numerical solution compared with experimental result is quite good.