弯道水流的混合有限分析解

Hybrid finite analytic solutions to bend-flows

建立了基于曲线拟合坐标系下的平面二维弯道水流数学模型,采用混合有限分析法进行了离散,对强弱弯曲河道矩形断面水流进行了数值计算.弱曲率弯道主流速度沿弯道外岸逐渐增加,在离心力作用下主流最大流速由凸岸逐渐向凹岸转移;且弯道水流的水面为一扭曲面,凹岸的水位线常形成上凸曲线,凸岸的水位线常形成下凹曲线.水面形态和流速重分布与相关文献实验结果符合良好,表明混合有限分析法与曲线拟合坐标的结合是一种可适用于弯道水流计算的有效格式.

The depth-averaged 2-D mathematic model for bend-flow under orthogonal curvilinear coordinate system is proposed. The hybrid finite analytic method with non-staggered grid was applied to solve the flow in mildly and sharply curved channel. With centrifugal effect, there is a shift of the maximum main velocity along the mildly curved channel bend from the inner-bank region toward the outer-bank region, and the water level rises at the outer bank and falls at the inner bank. The experimental data and other numerical results are given to demonstrate the capabilities of the mathematical model. So the hybrid finite analytic method combined with orthogonal curvilinear coordinate system can satisfactorily simulate the variation of water surface pattern and redistribution of velocity in bend flow.