Abstract：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 1 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 calculational efficiency is proved to be to 2-D models.
杨飞, 傅旭东. 垂向基于谱方法的三维弯道水流模型[J]. 清华大学学报（自然科学版）, 2018, 58(10): 914-920.
YANG Fei, FU Xudong. 3-D hydrodynamic model using the spectral method in the vertical direction for bend flow simulations. Journal of Tsinghua University(Science and Technology), 2018, 58(10): 914-920.
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