三维水沙运动及河床变形数学模型研究
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摘要
三维数学模型是解决复杂条件下水沙运动及河床变形问题的重要途径,对它的研究具有重要的理论意义和应用价值。本文建立了三维水沙运动及河床变形数学模型,并对天然河流中三维水沙问题的典型代表——坝区水流、泥沙运动和河床冲淤进行了模拟,其主要工作与成果如下。
在前人工作的基础上,提出了C-D无结构、z坐标网格上的非静水模型的构造方法,详细论述了其求解过程及特点,并对模型进行了测试。模型基于新兴的压力分裂模式建立,并较传统的C无结构网格上的非静水模型增加了对切向动量方程的求解。为此,对C-D网格与传统C网格上的非静水模型的计算效果、稳定性进行了检测和对比分析。前者的计算具有无噪音性,但当水流中存在较强的非线性动水压力分布时它容易产生非物理解并失稳。基于分析提出了一种联合使用的方法,克服了C-D网格的不稳定问题,使模型兼有C网格的稳定性和C-D网格的计算精度。使用改进方法,成功地模拟了开闸式盐水异重流。
采用数值实验和数学分析的方法,对本文模型所用到的欧拉-拉格朗日方法(ELM)的时间阻力现象进行了研究,基于分析解释了其本质并提出了改进方法。验证计算表明,改进方法虽不能彻底消除ELM中插值误差的影响,但在小时间步长模拟时能较显著地提高它的计算精度。另外,在无结构、σ坐标网格上建立了三维静水模型,通过计算证实了ELM时间阻力现象的普遍性。
建立了三维悬移质泥沙数学模型,验证表明计算结果与实验资料符合较好。在垂向使用亚网格技术,提高了模型计算精度,同时提出垂向网格融合技术消除了亚网格技术在河床发生冲淤时带来的不稳定影响。另外,提出了一种追踪不规则河岸动边界的方法,定性的检验计算表明它是合理的、有效的。
基于对孔口出流物理图形的分析,提出了一种在孔口出流情况下给定孔口处流量、动水压强边界条件的经验方法。另外,在模型中构建了水下坍塌模块。在此基础上,模拟了趋孔水流、急流异重流、概化水库异重流和在不同的坝前地形、水位条件下冲刷漏斗的形成过程,计算结果与实验资料符合较好。
Three-dimensional numerical model is an important approach to cope with the free-surface flow, sediment transport and the river bed deformation, especially in the complex situations, on which the study is valuable from the academic and practical views. A 3-D numerical model for free-surface flow and suspended-sediment transport is developed in this paper, and the typical 3-D flow and sediment transport in a reservoir are simulated. The main work and results are as follows.
On the basis of the former work, a 3-D non-hydrostatic pressure model for free surface flows on the C-D unstructured, z-level grid is built. The details and properties of model formulation are described, and the model is validated by benchmarks. The model is based on the newly developed pressure-split mode, and it augments the solution of the tangential momentum equation comparing to models on the C grid. Hence, the comparison and discussion about the non-hydrostatic pressure models on the C-D and C grid is done. Based on practice, simulations by using the former are free of noisy, but the model produce unphysical solutions and becomes unstable when a strong nonlinear distribution of non-hydrostatic pressure exists. Based on analysis, a combination of the two is proposed to avoid the instability of the C-D grid, which gives the model the stability of the C grid and the exactness of the C-D grid. By using the improved method, the lock-exchange salty density flow is simulated successfully.
By combining numerical experiments and formal analysis we investigate the artificial resistance of the Eulerian-Lagrangian Method (ELM) which is used in our model. The phenomena are explained and an improved method is proposed based on the illustrations and analysis. The validation indicates that though the new method does not eliminate the ELM interpolation error absolutely, it does improve the exactness for simulations at small time steps. More over, a 3-D hydrostatic pressure model for free surface flows on the C-D unstructured,σgrid is built. The artificial resistance is revealed to be ubiquitous for the ELM, though theσgrid is found to be able to reduce its influence.
A suspended-load transport model is built on the basis of the hydrodynamic model, and validations indicate that the simulations agree well with the experiment data. Then a method for tracking moveable, irregular river bank is proposed, the qualitative check indicate that it is applicable and effective. More over, the sub-grid technique is used in the model to make simulations more exact, and it is found that this technique may introduce instability due to the bed degradation and aggradation. And a grid-union method is proposed to make the sub-grid technique robust.
Based on the analysis of the physical process of the flow around an orifice, new experiential methods are proposed to determine the boundary conditions of discharge and hydrodynamic pressure at the orifice. More over, a module for simulating the block sliding under water is built. After that, the following projects are simulated: the orifice associated flow, the density flow after a hydraulic jump, the simplified reservoir density flow, the development of the filler just before the bottom orifice at different topography and water levels. The simulation results agree well with the experiment data.
在前人工作的基础上,提出了C-D无结构、z坐标网格上的非静水模型的构造方法,详细论述了其求解过程及特点,并对模型进行了测试。模型基于新兴的压力分裂模式建立,并较传统的C无结构网格上的非静水模型增加了对切向动量方程的求解。为此,对C-D网格与传统C网格上的非静水模型的计算效果、稳定性进行了检测和对比分析。前者的计算具有无噪音性,但当水流中存在较强的非线性动水压力分布时它容易产生非物理解并失稳。基于分析提出了一种联合使用的方法,克服了C-D网格的不稳定问题,使模型兼有C网格的稳定性和C-D网格的计算精度。使用改进方法,成功地模拟了开闸式盐水异重流。
采用数值实验和数学分析的方法,对本文模型所用到的欧拉-拉格朗日方法(ELM)的时间阻力现象进行了研究,基于分析解释了其本质并提出了改进方法。验证计算表明,改进方法虽不能彻底消除ELM中插值误差的影响,但在小时间步长模拟时能较显著地提高它的计算精度。另外,在无结构、σ坐标网格上建立了三维静水模型,通过计算证实了ELM时间阻力现象的普遍性。
建立了三维悬移质泥沙数学模型,验证表明计算结果与实验资料符合较好。在垂向使用亚网格技术,提高了模型计算精度,同时提出垂向网格融合技术消除了亚网格技术在河床发生冲淤时带来的不稳定影响。另外,提出了一种追踪不规则河岸动边界的方法,定性的检验计算表明它是合理的、有效的。
基于对孔口出流物理图形的分析,提出了一种在孔口出流情况下给定孔口处流量、动水压强边界条件的经验方法。另外,在模型中构建了水下坍塌模块。在此基础上,模拟了趋孔水流、急流异重流、概化水库异重流和在不同的坝前地形、水位条件下冲刷漏斗的形成过程,计算结果与实验资料符合较好。
Three-dimensional numerical model is an important approach to cope with the free-surface flow, sediment transport and the river bed deformation, especially in the complex situations, on which the study is valuable from the academic and practical views. A 3-D numerical model for free-surface flow and suspended-sediment transport is developed in this paper, and the typical 3-D flow and sediment transport in a reservoir are simulated. The main work and results are as follows.
On the basis of the former work, a 3-D non-hydrostatic pressure model for free surface flows on the C-D unstructured, z-level grid is built. The details and properties of model formulation are described, and the model is validated by benchmarks. The model is based on the newly developed pressure-split mode, and it augments the solution of the tangential momentum equation comparing to models on the C grid. Hence, the comparison and discussion about the non-hydrostatic pressure models on the C-D and C grid is done. Based on practice, simulations by using the former are free of noisy, but the model produce unphysical solutions and becomes unstable when a strong nonlinear distribution of non-hydrostatic pressure exists. Based on analysis, a combination of the two is proposed to avoid the instability of the C-D grid, which gives the model the stability of the C grid and the exactness of the C-D grid. By using the improved method, the lock-exchange salty density flow is simulated successfully.
By combining numerical experiments and formal analysis we investigate the artificial resistance of the Eulerian-Lagrangian Method (ELM) which is used in our model. The phenomena are explained and an improved method is proposed based on the illustrations and analysis. The validation indicates that though the new method does not eliminate the ELM interpolation error absolutely, it does improve the exactness for simulations at small time steps. More over, a 3-D hydrostatic pressure model for free surface flows on the C-D unstructured,σgrid is built. The artificial resistance is revealed to be ubiquitous for the ELM, though theσgrid is found to be able to reduce its influence.
A suspended-load transport model is built on the basis of the hydrodynamic model, and validations indicate that the simulations agree well with the experiment data. Then a method for tracking moveable, irregular river bank is proposed, the qualitative check indicate that it is applicable and effective. More over, the sub-grid technique is used in the model to make simulations more exact, and it is found that this technique may introduce instability due to the bed degradation and aggradation. And a grid-union method is proposed to make the sub-grid technique robust.
Based on the analysis of the physical process of the flow around an orifice, new experiential methods are proposed to determine the boundary conditions of discharge and hydrodynamic pressure at the orifice. More over, a module for simulating the block sliding under water is built. After that, the following projects are simulated: the orifice associated flow, the density flow after a hydraulic jump, the simplified reservoir density flow, the development of the filler just before the bottom orifice at different topography and water levels. The simulation results agree well with the experiment data.
引文
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