基于改进干湿算法的洪水演进三维水动力学模型开发与应用

发布时间：2018-04-01 18:07

  本文选题：干湿交替　切入点：三维模型　出处：《天津大学》2015年博士论文

【摘要】：洪水是主要的环境灾害之一,与人们的生活密切相关,且直接关系到人们的生命财产安全。研究洪水的演进过程有助于进一步了解洪水的发生和响应机制。洪水的水动力学模拟可以提供洪水演进过程的详细信息,如洪水的位置、水深、速度等,因此在洪水的风险评估中起着重要作用;并且要得到可靠的洪水风险评估结果,需要有准确的洪水模拟结果作为基础。目前洪水的水动力学模型大部分是一维、二维、或一维-二维耦合模型,这些模型成功的解决了许多工程问题。然而,基于一维/二维浅水方程的洪水模型无法真实描述洪水的运动。原因在于,如二维水动力学数值模型中,各变量沿竖直方向按均匀分布考虑,忽略了竖直方向的流速和加速度,水压力处理为静水压力分布,但在实际情况中,洪水水流的运动都是随纵向、侧向及垂向三个方向变化的,水流在运动过程中呈现明显的三维特征,并伴随各种副流产生。因此,对于实际条件下的洪水流动,二维模型无法真实全面地反映洪水的水动力学特性,于是引发了人们对三维模型研究的兴趣。尽管目前三维洪水模型在文献中仍然比较鲜见,但是近年随着超级计算机和并行计算技术的发展,人们开始逐步尝试三维水动力学模型研究,国际上对该课题的兴趣也大大提高。在这一背景下,本论文开展了对洪水的三维水动力学数值模型研究。论文的主要研究内容和创新成果如下:(1)通过在Navier-Stokes方程中引入竖直方向的稳定项,解决了干湿过程计算中宽高比大导致数值求解困难的问题,改进了干湿算法。在洪水的数值模拟中,干湿过程的处理一直是难点。原因之一是在干湿过程中,有限单元的宽高比一般较大,这会导致求解过程中矩阵方程的条件数增大,使得矩阵方程变为“病态”而难以求解。为解决这个问题,本文提出了四个控制离散方程组条件数的条件,通过引入合适的竖直吸收项控制矩阵方程(压强/自由面高度相结合的Laplacian方程)的条件数,以提高迭代求解器的稳定性和收敛速度,从而保证矩阵方程的良置性和模型的稳定性。(2)基于改进的干湿算法,开发了洪水演进的三维水动动力学数值模型,提高了数值模型的计算效率和稳定性。结合改进的干湿算法,开发新的洪水三维水动力学数值模型。该模型采用有限元法,在任意非结构化的四面体网格上求解Navier-Stokes方程,允许将自由面高度处理为全隐式,从而允许使用较大的时间步长;同时,它在水平和竖直方向使用完全非结构网格时可以保证数值一致性,因为自由面高度(尤其是其导数)不需要从自由表面内插到计算域的体积内部。当一个区域变干时,在自由表面设置无法向流(No-normal flow)的边界条件;当水深变得很小,如1 cm时,自由表面高度设定为一个指定的值。本文在一系列洪水演进情景下,检验了模型的效率、鲁棒性,分析模型参数的敏感性。(3)对比分析了洪水演进进过程的三维和二维水动动力学特性,并通过与实验数据比较,验证了新开发的洪水演进三维水动动力学数值模型的可靠性。将三维模型结果与实验数据对比,分析新开发的三维水动力学洪水模型的可靠性;通过与二维模型结果对比,分析模型的三维特点。研究发现,三维模型结果在竖直方向惯性力大的情况下,表现出与二维模型结果明显的差异;而随着水深变浅,竖直方向惯性力减弱,二者差异逐步减小。另外,三维模型捕捉到了流动中非常详细和复杂的细节信息,并能够生成平滑的干湿锋面。(4)建立了城市洪水地表径流的三维模型,分析了城市洪水的三维水动动力学特性。深入研究了城市洪水的三维水动力学特性。研究了不同网格精度对模型结果和CPU时间的影响,对Glasgow市一个高度城市化区域的一场洪水进行三维水动力学模型研究。通过比较三维模型与其他二维模型计算结果,发现在积水区二者非常相近;而在坡度较大的区域(3%),二者计算所得的水深差距更显著,且三维模型结果出现较大的竖直方向的速度(0.2 m/s)。另外,考虑城市洪水分为地表径流和地下管流,开发了SWMM模型与基于Fluidity的三维洪水模型的接口,为实现一维地下管流-三维地表径流耦合模拟打下了基础。本文系统地研究了洪水的三维水动力学数值模型,实现了实际条件下洪水事件的三维模拟,阐明了三维模拟技术有望改进洪水水动力模型精度并能提供更加详细的洪水过程信息,这有助于更好地估算洪灾损失和防洪设施的抗洪能力。同时,揭示了一些三维与二维洪水水动力模型的不同之处。
[Abstract]:Flood is one of the major environmental disasters, and closely related to people's life, and is directly related to people's life and property safety. The study of flood evolution process is beneficial to the further understanding of the occurrence of flood and water flooding response mechanism. The dynamics simulation can provide detailed information of flood evolution process, such as the location of the flooding, water depth, speed, so in the flood risk assessment plays an important role in flood risk; and to get reliable results, need to have accurate results as the basis for flood simulation. Water dynamics model of large part of the flood current is one-dimensional, two-dimensional, one-dimensional or two-dimensional - coupling model, the model successfully solved many engineering problems. However, one-dimensional / flood model of two-dimensional shallow water equations can describe the motion based on the real flood. The reason for this is that as a 2-D numerical model of water dynamics, the variables along the vertical The direction according to the uniform distribution, ignoring the velocity and acceleration in the vertical direction, the water pressure for the hydrostatic pressure distribution, but in reality, the flood water movement is along the longitudinal direction, the direction of the three lateral and vertical changes, the flow presents obvious three-dimensional features in the process of movement, and with a variety of secondary flow produce. Therefore, for the actual conditions of flood flow, two-dimensional model cannot fully reflect the real dynamic characteristics of water flooding, and sparked the interest of 3D model research. Although 3D flood models in the literature is still relatively rare, but in recent years with the super computer and the development of parallel computing technology, people began to try study on the three-dimensional hydrodynamic model, on the topics of interest is also greatly improved. In this background, this paper carried out the 3D numerical model of flood water dynamics The type of research. The main research contents and innovations are as follows: (1) through the introduction of a stable vertical direction in the Navier-Stokes equation, solved the calculation process of dry and wet due to the large numerical aperture ratio problem, improved algorithm. Numerical simulation of flood in the wet and dry quasi, dry process is always difficult. One reason is that in the wet process, finite element aspect ratio is generally large, this will lead to increased matrix equation in the process of solving the condition number, the matrix equation is "sick" and difficult to solve. In order to solve this problem, this paper proposes four control discrete equations of condition number conditions, absorption control matrix by introducing a suitable equation (Laplacian equation of vertical pressure / free surface height combination) condition number, in order to improve the stability and convergence of iterative solvers, thus ensuring the matrix equation Stability posed and model. (2) and algorithm based on the improved 3-D hydrodynamic numerical model is developed for the dynamics of flood routing, improves the computational efficiency and stability of the numerical model. The improved algorithm combined with wet and dry, flood 3-D hydrodynamic numerical model is developed. The new model by using the finite element method for solving Navier-Stokes the equation in arbitrary unstructured tetrahedral mesh, allowing the free surface height is fully implicit, thus allowing the use of large time step; at the same time, it is in the horizontal and vertical direction using completely unstructured meshes can guarantee the numerical consistency, because the free surface height (especially its derivative) does not require internal volume from the free surface interpolation to the computational domain. When a region is dried, the free surface is provided to flow (No-normal flow) boundary conditions; when water becomes very small, such as 1 cm, the free surface The surface height is set to a specified value. In this paper a series of flood scenarios, testing the model's efficiency, robustness, sensitivity analysis of model parameters. (3) the two-dimensional and three-dimensional hydrodynamic dynamics analysis of flood evolution process, and with the experimental data, verify the reliability the new development of the flood water dynamic three-dimensional numerical model. Comparing the three-dimensional model results and experimental data, the reliability analysis of three dimensional hydrodynamic model of flood new development; through the comparison with two-dimensional model results, three dimension analysis model. The study found that the three-dimensional model results in the vertical direction of inertial force under the condition of large show obvious differences in results of two-dimensional model; and with the shallow depth, the vertical direction of the inertial force is weakened, the difference between the two gradually decreased. In addition, the 3D model to capture the flow in a very detailed and complex The details of miscellaneous information, and can generate smooth dry fronts. (4) to establish the three-dimensional model of city flood runoff, flood water and analysis of three-dimensional city dynamical characteristics. The three-dimensional hydrodynamic characteristics of in-depth study of the city flood. The effects of different mesh on the accuracy of the model results and the CPU time, a the flood of Glasgow city a city area to study the height of a 3D hydrodynamic model. By comparing the 3D model and other two-dimensional model calculation results, found in the two water area is very similar; while in the slope area (3%), two of the calculated gap depth is more significant, and the vertical 3D model the direction of greater speed (0.2 m/s). In addition, consider the city flood into surface runoff and underground pipe flow, SWMM model and Fluidity model of 3D flood interface based on development, for the realization of one dimension Underground pipe flow simulation of 3D surface runoff coupling foundation. This paper systematically studied the 3-D numerical model of water dynamics of flood, the three-dimensional simulation under actual conditions of flood events, the 3D simulation technology is expected to improve the accuracy of flood water dynamic model and can provide more detailed information of flood process, which helps to better estimate the capability of flood control flood damage and flood control facilities. At the same time, reveals the difference between some three-dimensional and two-dimensional hydrodynamic model of flood.

【学位授予单位】：天津大学
【学位级别】：博士
【学位授予年份】：2015
【分类号】：TV122
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本文编号：1696671