基于非协调边界元法和涡方法的黏性流场研究

VISCOUS FLOW FIELD BASED ON DISCONTINUOUS BOUNDARY ELEMENT METHOD AND VORTEX METHOD

基于非协调边界元方法和涡方法的联合应用,模拟了二维和三维黏性不可压缩流场.计算中利用离散涡元对漩涡的产生、凝聚和输送过程进行模拟,并将整体计算域分解为采用涡泡模拟的内部区域和用涡列模拟的数字边界层区域.计算域中涡量场的拉伸和对流由Lagrangian涡方法模拟,用随机走步模拟涡量场的扩散.内部区域涡元涡量场速度由广义Biot--Savart公式计算,势流场速度则采用非协调边界元方法计算.非协调边界元将所有节点均取在光滑边界处,从而避免了法向速度的不连续现象;而对于系数矩阵不对称的大型边界元方程组,引入了非常高效的预处理循环型广义极小残余(the generalized minimum residual,GMRES)迭代算法,使得边界元法的优势得到了充分发挥,同时,在内部涡元势流场计算中对近边界点采用了正则化算法,该算法将奇异积分转化为沿单元围道上一系列线积分,消除了势流计算中速度及速度梯度的奇异性.二维、三维流场算例证明了所用方法的正确性,也验证了该算法可以大幅度提高模拟精度和效率.

The two-dimensional, three-dimensional viscosity and incompressible flow fields are simulated bases on a .combination application of discontinuous boundary element method and vortex method in our present study. Discrete vortex elements are used to analogue the vorticity generation, accumulation and transport mechanisms of the unsteady separated flow fields. And it decomposes the computing domain into an interior domain of vortex blobs and a thin nu- merical boundary layer of vortex sheets. The convection and stretch of the vortical field is imitated by Lagrangian vortex method, and the random walk method is adopted to describe the diffusion process of the vortical field. Additionally, vortex element＇s vortical velocity is calculated by generalized Biot-Savart law, while discontinuous boundary element method is used to compute potential velocity. To avoid the discontinuous of normal velocity, all nodes of discontinuous boundary element are selected at smooth boundary. Since a large scale boundary element equation set with a nonsymmetrical coef- ficient matrix should be solved, the present study import a pre-conditioning the generalized minimum residual （GMRES） iterative algorithm, which takes full advantage of the boundary element method. Moreover, regularization algorithm that applies at interior points close to the boundary, which the nearly singular surface integrals are transformed into a series of line integrals along the contour of the element, help to eliminate the unacceptable results of potential velocity and velocity gradient in potential calculation. The accuracy of present method is verified in both examples of two-dimension and three-dimension flow field calculation, as well as the significant increased simulation precision and efficiency.