多功能浅水模型的建立及其应用研究

发布时间：2019-06-19 22:36

【摘要】：本文以多功能性、干湿边界处理通用性、二、三维耦合计算一体性、数值计算稳定和可靠性为出发点,基于浅水水动力平台并叠加输运扩散模块,建立了一个多功能浅水模型。该模型可应用于陆域、河口和近岸水域的水动力(主要为流场)及水环境问题的二维、三维及其耦合的数值模拟。模型建立过程中,从严格拟合天然的复杂边界、网格密度自由控制、追求计算效率和精度角度出发,选取模型的计算网格和控制体；从模型适应复杂地形、水位剧烈变化、水位和流速间断、干湿变化频繁等实际需要出发,在数值方法处理上,对流项、底摩擦阻项、斜压项、扩散项等,分别采用现有最新研究成果；提出了一种与单元中心格式有限体积法计算过程相结合的干湿界面处理方法,该方法可以准确捕捉复杂地形上干湿边界的位置,并在保证水体质量守恒时不修改时间步长；为确保水平流速分层信息准确性,并避免叠加二、三维耦合计算时能量比降不连续造成的误差,提出了一种新的处理复杂分层流的耦合方法。第一,对于二维模型,基于非结构混合网格技术,利用加限制器的重构过程得到变量在单元内的线性分布,以HLLC近似Riemann算子计算对流通量,并采用半隐式方法处理摩阻源项,通过4步显示RLunge-Kutta法积分,建立了在时间和空间上均为二阶精度的高分辨率、无数值振荡Godunov型有限体积法二维数值模型。通过一系列实例验证表明,该模型具有计算精度高、格式强健以及良好的激波捕捉能力。第二,对于三维模型,首先采用改进二维浅水方程时相同的方法,得到了三维浅水方程的和谐形式。利用垂向σ坐标变换,使得方程对起伏的自由表面和水底地形有自适应能力,采用二阶精度的TVD格式计算垂向对流通量并全隐式处理垂向扩散项,可使得三维浅水模型在时空上均有二阶精度。第三,建立了二、三维耦合浅水模型。在二、三维模型的耦合界面上设定通量守恒为匹配条件,提出了一个新的、适用于复杂分层流动(如分层逆流、回转流,垂向平均流速趋向零时除外)的耦合方法。耦合模型共用一套平面网格,在相同时间步上一体计算。通过对复杂分层流动的适用性检验和比较显示,该方法区别于常规的设定三维流速分布为某种理论分布的耦合方法,在耦合边界附近对复杂分层流动的计算结果更接近实际情况。第四,将本文的建立多功能浅水模型分别应用于溃坝后的洪水演进、海啸波传递、风生流、波生流、物质输运扩散和水体交换物理过程的大尺度模拟,结果表明,该浅水模型体现出在水利、港口、海岸和近海工程领域的水动力及环境问题数值模拟方面具有多功能性、干湿边界处理的通用性、二、三维耦合计算一体性、数值计算稳定和可靠性等特性。
[Abstract]:In this paper, a multifunctional shallow water model is established based on shallow hydrodynamic platform and superimposed transport and diffusion module, which is based on versatility, universality of dry and wet boundary treatment, integration of two and three dimensional coupling calculation, stability and reliability of numerical calculation. The model can be applied to the numerical simulation of hydrodynamic (mainly flow field) and water environment problems in land, estuary and coastal waters. In the process of model establishment, the computational grid and control body of the model are selected from the point of view of strict fitting of natural complex boundary, free control of grid density and pursuit of computational efficiency and accuracy. According to the actual needs of the model to adapt to the complex terrain, the sharp change of water level, the discontinuity of water level and velocity, and the frequent change of dry and wet, the latest research results are adopted in numerical method treatment, such as convective term, bottom friction resistance term, baroclinic term, diffusion term and so on. In this paper, a dry and wet interface treatment method combined with the finite volume method of element center format is proposed, which can accurately capture the position of dry and wet boundary on complex terrain and do not modify the time step while ensuring the conservation of water quality. In order to ensure the accuracy of horizontal velocity stratification information and avoid the error caused by the discontinuity of energy ratio drop in superposition of two-dimensional and three-dimensional coupling calculation, a new coupling method for dealing with complex layered flow is proposed. First, for the two-dimensional model, based on the unstructured hybrid grid technique, the linear distribution of variables in the element is obtained by using the reconstruction process of the limiter, the convolution flux is calculated by HLLC approximate Riemann operator, and the friction source term is treated by semi-implicit method. The two-dimensional numerical model of high resolution and innumerable oscillatory Godunov finite volume method with second-order accuracy in time and space is established by showing the integration of RLunge-Kutta method in four steps. A series of examples show that the model has high calculation accuracy, strong format and good shock capture ability. Secondly, for the three-dimensional model, the harmonious form of the three-dimensional shallow water equation is obtained by using the same method when the two-dimensional shallow water equation is improved. The vertical 蟽 coordinate transformation is used to make the equation adaptive to the undulating free surface and underwater topography. The second order precision TVD scheme is used to calculate the vertical convective flux and the vertical diffusion term is dealt with implicitly, which can make the three dimensional shallow water model have second order accuracy in time and space. Thirdly, a two-dimensional and three-dimensional coupled shallow water model is established. Based on the matching condition of flux conservation on the coupling interface of two-dimensional and three-dimensional models, a new coupling method is proposed, which is suitable for complex layered flows (such as delamination countercurrent, rotary flow, vertical average velocity tends to 00:00). The coupling model shares a set of planar grids and calculates them at the same time step. Through the test and comparison of the applicability of the complex layered flow, it is shown that this method is different from the conventional coupling method which sets the three-dimensional velocity distribution to a certain theoretical distribution, and the calculation results of the complex layered flow near the coupling boundary are closer to the actual situation. Fourth, the multifunctional shallow water model established in this paper is applied to the large-scale simulation of flood evolution, tsunami wave transmission, wind-induced current, wave-generated current, material transport and diffusion and water exchange physical process after dam break, respectively. the results show that the shallow water model is multifunctional in the numerical simulation of hydrodynamic and environmental problems in the fields of water conservancy, port, coastal and offshore engineering, and is universal in dry and wet boundary treatment. Three-dimensional coupling calculation integration, numerical calculation stability and reliability and other characteristics.
【学位授予单位】：大连理工大学
【学位级别】：博士
【学位授予年份】：2014
【分类号】：TV131.61

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