垂向基于谱方法的三维弯道水流模型

3-D hydrodynamic model using the spectral method in the vertical direction for bend flow simulations

传统平面二维水动力模型模拟弯道水流时，将流速垂向分布固定化，不能随边界变化和二次流发展进行调整，而垂向完全自动调整的三维水动力模型计算效率低。该文采用谱方法将平面流速的垂向分布用正交多项式表示，通过加权余量法建立简易三维模型，对流项采用基于Gauss点的半Lagrangian法（semi-Lagrangianscheme，SLS）计算。由急弯弯道水流试验验证可知，多项式阶数大于1时模拟结果较好。弯道主流线位置预测整体误差不超过7％，精度和传统的三维水动力学模型相当。对涡黏性系数简单求解，但考虑了垂向和水平方向的差异性，能够得到合理的弯道水流结构。垂向基于谱方法建立的三维模型，无垂向网格离散，计算量明显减少，获得了与平面二维模型相当的计算效率。

The traditional depth-averaged 2-D hydrodynamic models for bend flow simulations assume velocity profiles for the secondary flow terms in the momentum equations which are unable to adjust to dynamic conditions. More flexible three-dimensional models are not very efficient. A simplified 3-D model using a spectral method in the vertical direction was developed with the flow velocity components modeled by orthogonal polynomials in the vertical direction using polynomial coefficient equations obtained using the weighted residuals method with the advection terms defined at the vertical Gauss points by the semi-Lagrangian scheme. Simulated flow structures in a sharp bend open channel match well with measured data for polynomials having degrees larger than l with reasonable flow structures, The mean error of the predicted main flow location is less than 7%, equivalent to other 3-D hydrodynamic models. The eddy viscosity is solved in a simple way with consideration of the turbulence anisotropy between the vertical and horizontal directions, Since this method does not have a vertical grid, the caleulational efficiency is proved to be to 2-D models.