【作者】 潘存鸿；

【导师】 戴世强；

【作者基本信息】 上海大学 ， 流体力学， 2007， 博士

【摘要】 涌潮、水跃、溃坝波、浅水变形后的波浪、闸门突然开启形成的涌波等浅水间断流动的数值模拟具有很高的学术价值和实际应用价值，一直是计算水动力学的热点和难点之一。本文在分析钱塘江涌潮和浅水流动方程基本性质的基础上，分别应用Godunov格式和KFVS(Kinetic Flux Vector Splitting)格式建立了一、二维浅水间断流动数值模型，应用WLTF(Water Level-bottom Topography Formulation)方法结合源项离散技术解决了守恒型计算格式的“和谐”性，应用改进的干底Riemann解处理动边界问题。模型在典型算例验证的基础上，模拟了钱塘江涌潮传播过程以及涌潮作用下的泥沙输移。本文的主要工作如下：(1)应用基于准确Riemann解的Godunov格式建立了一、二维浅水间断流动数值模型。为保证方程左边的压力项与方程右边底坡源项始终保持“和谐”，求解法向通量过程中采用了WLTF方法，同时对压力项和底坡源项采用相同的离散方法。对于三角形网格，采用两种方法达到计算格式的“和谐”，第一种方法底坡源项采用静水压力原理变换离散，第二种方法采用变换控制方程来实现模型的和谐。应用类似于MUSCLE方法，建立了三角形网格下二阶精度计算格式。(2)应用宏观和微观变量基本关系式，以平衡态的Boltzmann方程为基础，导出了基于Boltzmann方程的一维和二维浅水流动方程。应用有限体积法离散浅水流动方程，法向数值通量采用KFVS格式求解，建立了具有空间二阶精度的一维和二维浅水流动方程的KFVS格式。为保证计算格式的和谐性，除采用WLTF方法外，通量计算中考虑了底坡源项的作用。(3)钱塘江河口存在大片滩地，动边界处理好坏对涌潮计算结果有很大影响。本文应用改进的干底Riemann解处理动边界问题。根据WLTF思想，将经典干底Riemann解仅适用于平底情形进行了改进，使其能应用到非平底的情况。数值试验结果表明，该方法能模拟动边界条件下大梯度流动问题。(4)上述建立的基于Godunov格式和KFVS格式的两个二维数值模型在多个典型算例验证的基础上，模拟了钱塘江涌潮的形成、发展和衰减的过程，复演了交叉潮、一线潮和回头潮等潮景。经实测资料验证，计算结果反映了涌潮到达时刻潮位暴涨、流速迅速从落潮转为涨潮并达到极值的现象，解决了以前计算模型潮位涨幅偏小、涌潮流速大大偏小以及流量不守恒等问题。(5)在水流数值模型的基础上，应用Godunov格式建立了三角形网格下具有空间二阶精度的二维泥沙输移数值模型，模拟了钱塘江涌潮作用下泥沙输移规律，复演了涌潮前后含沙量突变的过程。计算结果表明涌潮对泥沙输移、河床演变有着深刻的影响，并揭示了钱塘江河口高含沙量区的成因、洪冲潮淤以及大冲大淤的机理。更多还原

【Abstract】 Numerical simulation of discontinuous shallow water flows, such as tidal bores, hydraulic jumps, dam-break waves, waves distorted due to shallow water, surge wave formed by suddenly-opened sluice, etc. is of great academic and practical significance, and thus has long been a hotspot and difficult issue in computational hydrodynamics.In this thesis, based on the analyses of basic characteristics of the tidal bores on the Qiantang River and of the related shallow water equations, 1D and 2D mathematical models were developed for simulating discontinuous shallow water flow by using the Godunov scheme and KFVS (Kinetic Flux Vector Splitting) scheme, in which the well-balanced problem of conservative computational schemes was solved by applying the WLTF(Water Level-bottom Topography Formulation) combined with the discretization technique for treating the source term generated by uneven bottom topography, and the wet/dry technique was invoked to improve the Riemann solution for the dry bed. On the basis of the verification of the above models by simulating typical examples, the models were employed to compute the propagation of the tidal bore on the Qiantang River and the sediment transportation under the effect of the tidal bore.The main results in this thesis are as follows.(1) The 1D and 2D mathematical models were established for simulating the discontinuous shallow water flow by using the Godunov scheme. In order to keep the well-balance between the pressure term on the left-hand side and the source term due to bottom topography on the right-hand side of the shallow water equations (SWE), the WLTF was applied in the process of solving the normal numerical flux, and the same discretization method was used for both the pressure term and the source terms. With the triangular grids, two methods were proposed to keep the models well-balanced. Firstly, the source term due to bottom topography was discretize by using hydrostatic pressure law. Secondly, the governing equations were transformed to reach the well-balance. With a technique similar to the MUSCLE, a 2nd-order accuracy scheme in space with triangular grids was developed.(2) Based on the Boltzmann equation for the equilibrium state, the 1D and 2D shallow water equations were derived from the basic relationship between macroscopic and microcosmic variables. The 1D and 2D KFVS schemes for solving the SWE were developed with the 2nd-order accuracy in space by using the finite volume method (FVM) to discretize the SWE and the KFVS method to compute normal numerical flux. In order to keep the scheme well-balanced, in addition to the WLTF, the effect of the source term due to bottom topography was considered in the computation of normal numerical flux.(3) There are extensive shoals at the Qiantang estuary, so the wet/dry technique has great impact on the computed results for the tidal bore. In this thesis, an improved Riemann solution on dry bed was proposed to deal with moving boundary. According to the idea of WLTF, the classical Riemann solution on dry bed only applicable to even bottoms was improved to be applied to uneven bottom. Numerical tests show that the method can be applied to simulate discontinuous flow in the condition of moving boundary.(4) The above two 2D mathematical models with the Godunov scheme and KFVS scheme were validated by some typical tests, and then employed to simulate the formation, evolution and dissipation of the tidal bore at the Qiantang estuary, and to replicate some bore sceneries, such as the crossed tidal bore, thread-shape bore and returned tidal bore. The computed results were verified by field data, showing the sudden and sharp rise of the tidal level, the rapid velocity conversion from ebb to flood and fast reaching to its extremum during the bore arriving. The models have overcome the problems which appeared in common mathematical models, such as unreasonably smaller water-level rise, velocity increase, and the nonconservatve computed discharge.(5) Based on the mathematical model of water flow, a 2D sediment transport mathematical model with the 2nd-order accuracy in space was developed by using the Godunov scheme with triangular grids. The model was used to simulate sediment transport under the tidal bore on the Qiantang River, and to replicate the abrupt variation process of the sediment concentration during the bore arriving. The computed results show that the tidal bore has great impact on sediment transport and fluvial process, and reveals the cause of formation of high sediment concentration region at the Qiantang estuary, the mechanism of erosion by runoff and deposit by tidal current, and the riverbed variation with large amplitude.更多还原