【作者】 陈昞睿；

【导师】 朱建荣；

【作者基本信息】 华东师范大学 ， 河口海岸学， 2011， 博士

【摘要】 数值模拟在科学研究、工程应用与灾害预测分析等方面发挥着重要作用。海洋数值模式是对河流、海洋等水体在计算机上模拟的工具,正得到蓬勃发展。传统的海洋数值模式大多采用矩形结构网格,局部加密及拟合岸线能力有限,往往难以拟合河口、海湾或岛屿等区域复杂的岸线和工程结构。无结构网格能够在任意局部区域对网格加密并拟合岸线,从而克服了结构网格的缺陷。当前国际上知名的无结构网格海洋模式大多来自国外,而国内自主开发的模式尚缺少能达到国际先进水平的。所以需要研制具有完全自主知识产权的无结构网格河口海洋数值模式,以期通过不断改进发展最终达到国际先进水平。本文研制了一套无结构网格二维河口海洋数值模式。该模式采用三角形网格,基于有限体积法求解。在网格中心(重心)求解水位,在网格边的中点同时求解x-方向和y-方向流速的配置。这样的配置既不用水平坐标转换,能使用有限体积法直接对原始方程组进行求解,简洁高效且易于守恒,同时也能够较方便地处理移动潮滩边界。模式采用垂向平均的二维控制方程组,对连续方程、动量方程和盐度方程均采用有限体积法求解,以确保守恒性。求解连续方程和盐度方程时采用三角形网格作为控制体。求解动量方程时则采用围绕边中点的菱形作为控制体,并采用TVD格式处理流速平流项以增强稳定性。设计了两种方法求解正压梯度力,第一种方法为对水位插值,再在菱形控制体中用有限体积法求解,第二种方法为先构造4个以水位计算点为顶点的控制体,用有限体积法求解出水位梯度后,再将所得水位梯度平均。斜压梯度力求法与正压梯度力类似。求解盐度平流项时,根据Darwish和Moukalled在无结构网格下设计物质输运TVD平流项算法的经验,以及Li等对其不足的分析和改进,针对本文模式的无结构网格设计了一种计算上游r值的方法,并以此r值为基础构造了TVD格式。模式在时间上用预估修正法显式求解以增加水动力精度,并且包含了移动潮滩边界。通过在一个理想圆湖试验,验证了第二种正压梯度力求解方法更加精确,计算结果与解析解非常接近。而通过理想往复流数值试验测试TVD盐度平流项格式,测试结果表明该格式成功地消除了数值频散,并有效地降低了数值耗散,但使用Superbee限制函数会造成人为的锋面,故推荐使用Monotonic和Minimode限制函数。对黄浦江进行水动力验证,水位结果与实测结果基本一致。在长江口对模式作了率定验证。模式在不同区域取不同底摩擦曼宁系数值,通过计算2007年8月长江口的流场,对比实测水位、流速和流向率定,并通过计算2004年末2005年初的流场和盐度场,对比实测流速、流向和盐度验证。率定结果整体较好,验证的流速流向较为接近,但盐度偏差略大,这是由于二维模式无法再现三维盐水楔现象,以及盐度变化与初始场等有关。通过各种测试和率定验证,可得出结论：模式的正压梯度力计算和盐度平流项格式均具有较高的精度,可应用于河口与近海区域的数值计算。更多还原

【Abstract】 Numerical simulation plays an important role in scientific research, engineering application, and disaster forecast. Ocean numerical models, as the tool of simulating hydrodynamics of rivers, seas, and oceans on computers, are being well developed. Traditional ocean models usually use rectangular structured grid, which has limited capability of local refinement and coastline fitting, and is hard to fit complex coastlines and project structures in estuaries, bays, and islands. Unstructured grid can be refined at arbitrary local area and fit any coastline, which avoids the flaw of structured grid. Most of the distinguished unstructured grid ocean models in the world now are developed abroad. Domestic models which achieved the international advances are lacked. So there is need to develop an unstructured grid estuary and ocean numerical model with complete proprietary intellectual property rights, which could be further improved to achieve the international advances.In this thesis, an unstructured grid two-dimensional estuary and ocean numerical model is developed. The model uses triangular grid and finite-volume method. It solves elevation at centroid of grid cell, and solves velocities of x- and y- direction at mid-point of grid side. Such architecture needs no horizontal coordinate conversion, which is simple, efficient, and easy to conserve, while it’s convenient to address the moving tidal flat. The model uses vertically-integrated two-dimensional control equation set. Continuity equation, momentum equation, and salinity equation are solved by using finite-volume method to guarantee conservation. A control volume of triangular cell is used in solving continuity equation and salinity equation. A rhombic control volume is used to solve momentum, while TVD scheme is used in treating velocity advection to enhance stability. Two methods of solving barotropic force are designed. The first method interpolates elevation first and then solves barotropic in rhombic control volume. The second method constructs 4 control volumes whose vertices are elevation points, calculating elevation gradients by using control-volume, and then averages the elevation gradients. Solving baroclinic is similar to solving barotropic. In solving salinity advection, according to Darwish and Moukalled’s experience of constructing TVD advection scheme under unstructured grid, and Li’s analysis and improvement to it, a method of calculating upwind r value is designed for the unstructured grid of the model, and TVD advection is constructed based on this r value. Predictor-corrector temporal method is used in the model to promote accuracy of hydrodynamics. A moving tidal flat boundary is included in the model.By an ideal circular lake experiment, the second method of solving barotropic force is proved to be more accurate. The simulated result is highly close to analytic solution. The TVD scheme for salinity advection is tested by an ideal reversing current numerical experiment. Results show that it eliminates numerical dispersion while reduces numerical diffusion. The Superbee limiter would produce artificial sharp gradient. So the Monotonic limiter and Minimode limiter are recommended. The model’s hydrodynamics is validated in the Huangpu River, and elevation results are consistent with observed data.The model is calibrated and validated in Changjiang Estuary. Different Manning’s coefficients are taken at different areas of the model domain. By simulating the current in Changjiang Estuary in August 2007, the model result is calibrated by comparing with observed elevation, current velocity, and current direction. By simulating the current and salinity in late 2004 and early 2005, the model result is validated by comparing with observed current velocity, current direction, and salinity. The calibration results are good in general. In validation, the current velocity and current direction results are close, but salinity differences are slightly big, which is because three-dimensional saltwater wedge can’t be made in a two-dimensional model, and salinity variation is related to initial condition.Though various experiments, calibration, and validation, the conclusion could be drawn that in this model, the calculating method of barotropic force and salinity advection scheme are highly accurate, and the model is applicable in the simulation of estuarine and short sea areas.更多还原