Development of Accurate Numerical Methods for Turbulent Open Channel Flows with Complex Geometries

本文研究了河流工程中流量计算数值方法的发展。主要成果包括改进湍流模型，改进对流格式，在边界拟合坐标系上重新表述基本方程，以及减少计算时间的计算机代码向量化。提出了一种新的湍流驱动二次流的代数应力湍流模型。湍流模型保持了与非线性kappa - epsilon模型相似的结构，但在变量模型系数上有所不同，使模型不受复杂边界几何的影响。与复合通道流动的实验数据比较，表明平均流速和雷诺数应力符合较好。总结了自由表面影响的模型，并讨论了自由表面附近湍流量的极限行为。边界拟合坐标的使用产生了新的平流。更多关于非保守形式的基本方程中的项。这导致数值结果对所采用的网格系统的敏感性。采用几何坐标系和速度场坐标系相结合的方法求解该问题。采用规则网格系统对压力振荡进行阻尼处理。基于这些思想，开发了两个计算机代码来验证预期的特征。提出了对流过程的高精度有界格式。在控制容积面引入限制器来控制对流通量，以抑制物理上无意义的振荡。在线性和非线性流动情况下，与最快方案相结合的限位器的性能都优于目前使用的限位器。从计算时间的角度比较了几种线性系统迭代求解方法的性能，发现修正强隐式过程和类共轭梯度求解方法适用于流动计算。设计并在超级计算机上测试了对许多迭代求解器进行矢量化的技术。少

The present study is concerned with the development of numerical methods for flow calculation in River Engineering. Main achievements consist of refining a turbulence model, improving convection schemes, reformulation of basic equations on boundary-fitted coordinate systems and vectorization of computer codes for the reduction of computational time.A new algebraic stress turbulence model was proposed for turbulence-driven secondary flows. The turbulence model keeps the similar structure as the non-linear kappa - epsilon models, but has difference in variable model coefficients which enable the model independent of complex boundary geometries. Comparisons with the experimental data available for compound channel flows showed good agreement as for mean velocities and the Reynolds stresses. Models for the effect of free surface were summarized and the limiting behaviors of turbulence quantities near free surface were also discussed.Usage of boundary fitted coordinates produces new advecti … More on terms in basic equations which have non-conservative forms. This results in the sensitiveness of numerical results to the grid system employed. Combination of two coordinate systems, one for geometry, the other for velocity field was adopted to meet the problem. A regular grid system with a damping technique for pressure oscillation was used. Based on these ideas two computer codes were developed to validate the expected feature.Highly accurate and bounded scheme was proposed for convection process. A limiter was introduced to control the convection flux at the control volume face to suppress the physically meaningless oscillations.The limiter coupled with the QUICKEST scheme showed superior performance to those used so far for both linear and non-linear flow cases.Performance of many iterative solvers for linear systems were compared in terms of computational time to find out that Modified Strongly Implicit Procedure and Conjugate Gradient-like solvers are suitable for flow calculations. Techniques to vectorize many iterative solvers were devised and tested on supercomputers. Less