基于GIS的二维水沙数学模型及其在黄河下游应用的研究
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摘要
针对黄河下游河道水沙运动的特点,以“IT”技术为平台,研制了基于GIS的黄河下游二维水沙数学模型。
通过对现有国内外水沙模型的比较,选取了适合多沙河流水沙特点的方程离散格式及数值方法:采用Osher及LSS格式计算对流项水沙数值通量,借助高斯积分确定扩散项中控制体形心处的梯度矢量,通过预测、校正二步格式求解方程组,以保证水流计算格式的解具有良好的物理基础,符合解的特征构造,并具有守恒性、逆风性、单调保持性和对间断的高分辨率等优良特性。对于由水压力与底坡项不平衡所导致的动量不守恒问题,采用三点高斯积分法来计算各边的平均法向通量。本文对非均匀沙沉速、床沙级配调整、横向冲刷坍塌变形等关键技术问题进行了深入分析,研制的二维水沙模型不但适用于低含沙水流的计算,而且适用于多沙河流的模拟计算。通过对ArcGIS软件的二次开发,设计和开发出了基于GIS的二维数学模型的前后处理系统。基于GIS的前后处理系统,不仅极大的提升了前期工作效率,而且在地形高程的生成精度、信息查询速度和可视化程度方面有了明显提高。
为检验所建模型的合理性和精度,利用国内外试验资料对其进行了测试,测试案例包括恒定流、非恒定流、溃坝、压缩水流、弯道、复式河道及复杂边界等不同情况。此外,利用黄河下游不同时期的实测资料和专题测验资料,对泥沙沉速模块、动床阻力模块、分组挟沙力模块等进行了测试,在此基础上,又将所建立的模型应用于黄河下游实测调水调沙洪水的模拟计算,结果表明,计算精度满足防洪调度的实际要求。
A 2D water and sediment numerical model in the lower Yellow River was developed aimed at flow and sediment transport characteristics and based on GIS platform.By comparing the development of numerical modeling technologies in the world, equation discrete schemes and methodologies suited for hyper-concentration flow are selected .The Osher and LSS schemes are used to calculate the convection term of water and sediment. The Gauss theory is adopted to induce the control volume central gradient of the diffusion term. Solutions of the equations with forecasting and adjusting two-steps method may ensure results have real physical means and fit well with characteristic construction of solution, which has flux conservation, upwind, monotonic keeping and high resolving power for discontinuity . As for the unbalance momentum induced from water pressure non-uniform with river bed slope, the Gauss theory is used to calculate averaged flux of each side, which not only avoids the error flow phenomena for steep water depth gradient, but also shows the distribution of status vectors correctly. The paper studies the key problems including non-uniform sediment settling velocity, suspend sediment transport capacity, bed sediment composition adjustment, movable bed roughness variety, turbulence viscous coefficient, sediment viscous coefficient and transverse bank scour simulating. By using ArcGIS and secondary developing with GIS, the model's pre-processes and post processes include grid generation system, digital elevation generation system and flow field visualization system.A typical testing procedure is used to test the flow module and sediment module, including processes of steady and unsteady flow, dam break flow, impressed flow, compounded river channel and complex boundary conditions. Data of conventional measurement in the Lower Yellow River and special observations for this study are used to calibrate the sediment settling velocity, movable bed roughness coefficient and gradations sediment transport capacity etc. Sets of scenario studies are carried out. Several typical flood processes are verified and results prove that the model can be satisfied for the flood management in the Lower Yellow River.The innovation achievements of the paper may be summarized as follows: Based on numerical method and sediment transport law with developed IT technology, realized the combination of IT technology with water science; Numerical methodologies of hyper-concentration flow and research on key problems of hyper-concentration flow fundamental theory improve the modeling precision for hyper-concentration flow. Based on GIS platform, not only improve the efficiency but also improve the precision of digital elevation generation, information searching speed and visualization technology obviously.
通过对现有国内外水沙模型的比较,选取了适合多沙河流水沙特点的方程离散格式及数值方法:采用Osher及LSS格式计算对流项水沙数值通量,借助高斯积分确定扩散项中控制体形心处的梯度矢量,通过预测、校正二步格式求解方程组,以保证水流计算格式的解具有良好的物理基础,符合解的特征构造,并具有守恒性、逆风性、单调保持性和对间断的高分辨率等优良特性。对于由水压力与底坡项不平衡所导致的动量不守恒问题,采用三点高斯积分法来计算各边的平均法向通量。本文对非均匀沙沉速、床沙级配调整、横向冲刷坍塌变形等关键技术问题进行了深入分析,研制的二维水沙模型不但适用于低含沙水流的计算,而且适用于多沙河流的模拟计算。通过对ArcGIS软件的二次开发,设计和开发出了基于GIS的二维数学模型的前后处理系统。基于GIS的前后处理系统,不仅极大的提升了前期工作效率,而且在地形高程的生成精度、信息查询速度和可视化程度方面有了明显提高。
为检验所建模型的合理性和精度,利用国内外试验资料对其进行了测试,测试案例包括恒定流、非恒定流、溃坝、压缩水流、弯道、复式河道及复杂边界等不同情况。此外,利用黄河下游不同时期的实测资料和专题测验资料,对泥沙沉速模块、动床阻力模块、分组挟沙力模块等进行了测试,在此基础上,又将所建立的模型应用于黄河下游实测调水调沙洪水的模拟计算,结果表明,计算精度满足防洪调度的实际要求。
A 2D water and sediment numerical model in the lower Yellow River was developed aimed at flow and sediment transport characteristics and based on GIS platform.By comparing the development of numerical modeling technologies in the world, equation discrete schemes and methodologies suited for hyper-concentration flow are selected .The Osher and LSS schemes are used to calculate the convection term of water and sediment. The Gauss theory is adopted to induce the control volume central gradient of the diffusion term. Solutions of the equations with forecasting and adjusting two-steps method may ensure results have real physical means and fit well with characteristic construction of solution, which has flux conservation, upwind, monotonic keeping and high resolving power for discontinuity . As for the unbalance momentum induced from water pressure non-uniform with river bed slope, the Gauss theory is used to calculate averaged flux of each side, which not only avoids the error flow phenomena for steep water depth gradient, but also shows the distribution of status vectors correctly. The paper studies the key problems including non-uniform sediment settling velocity, suspend sediment transport capacity, bed sediment composition adjustment, movable bed roughness variety, turbulence viscous coefficient, sediment viscous coefficient and transverse bank scour simulating. By using ArcGIS and secondary developing with GIS, the model's pre-processes and post processes include grid generation system, digital elevation generation system and flow field visualization system.A typical testing procedure is used to test the flow module and sediment module, including processes of steady and unsteady flow, dam break flow, impressed flow, compounded river channel and complex boundary conditions. Data of conventional measurement in the Lower Yellow River and special observations for this study are used to calibrate the sediment settling velocity, movable bed roughness coefficient and gradations sediment transport capacity etc. Sets of scenario studies are carried out. Several typical flood processes are verified and results prove that the model can be satisfied for the flood management in the Lower Yellow River.The innovation achievements of the paper may be summarized as follows: Based on numerical method and sediment transport law with developed IT technology, realized the combination of IT technology with water science; Numerical methodologies of hyper-concentration flow and research on key problems of hyper-concentration flow fundamental theory improve the modeling precision for hyper-concentration flow. Based on GIS platform, not only improve the efficiency but also improve the precision of digital elevation generation, information searching speed and visualization technology obviously.
引文
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