本文選題：干濕交替　切入點(diǎn)：三維模型　出處：《天津大學(xué)》2015年博士論文

【摘要】：洪水是主要的環(huán)境災(zāi)害之一,與人們的生活密切相關(guān),且直接關(guān)系到人們的生命財(cái)產(chǎn)安全。研究洪水的演進(jìn)過(guò)程有助于進(jìn)一步了解洪水的發(fā)生和響應(yīng)機(jī)制。洪水的水動(dòng)力學(xué)模擬可以提供洪水演進(jìn)過(guò)程的詳細(xì)信息,如洪水的位置、水深、速度等,因此在洪水的風(fēng)險(xiǎn)評(píng)估中起著重要作用;并且要得到可靠的洪水風(fēng)險(xiǎn)評(píng)估結(jié)果,需要有準(zhǔn)確的洪水模擬結(jié)果作為基礎(chǔ)。目前洪水的水動(dòng)力學(xué)模型大部分是一維、二維、或一維-二維耦合模型,這些模型成功的解決了許多工程問題。然而,基于一維/二維淺水方程的洪水模型無(wú)法真實(shí)描述洪水的運(yùn)動(dòng)。原因在于,如二維水動(dòng)力學(xué)數(shù)值模型中,各變量沿豎直方向按均勻分布考慮,忽略了豎直方向的流速和加速度,水壓力處理為靜水壓力分布,但在實(shí)際情況中,洪水水流的運(yùn)動(dòng)都是隨縱向、側(cè)向及垂向三個(gè)方向變化的,水流在運(yùn)動(dòng)過(guò)程中呈現(xiàn)明顯的三維特征,并伴隨各種副流產(chǎn)生。因此,對(duì)于實(shí)際條件下的洪水流動(dòng),二維模型無(wú)法真實(shí)全面地反映洪水的水動(dòng)力學(xué)特性,于是引發(fā)了人們對(duì)三維模型研究的興趣。盡管目前三維洪水模型在文獻(xiàn)中仍然比較鮮見,但是近年隨著超級(jí)計(jì)算機(jī)和并行計(jì)算技術(shù)的發(fā)展,人們開始逐步嘗試三維水動(dòng)力學(xué)模型研究,國(guó)際上對(duì)該課題的興趣也大大提高。在這一背景下,本論文開展了對(duì)洪水的三維水動(dòng)力學(xué)數(shù)值模型研究。論文的主要研究?jī)?nèi)容和創(chuàng)新成果如下:(1)通過(guò)在Navier-Stokes方程中引入豎直方向的穩(wěn)定項(xiàng),解決了干濕過(guò)程計(jì)算中寬高比大導(dǎo)致數(shù)值求解困難的問題,改進(jìn)了干濕算法。在洪水的數(shù)值模擬中,干濕過(guò)程的處理一直是難點(diǎn)。原因之一是在干濕過(guò)程中,有限單元的寬高比一般較大,這會(huì)導(dǎo)致求解過(guò)程中矩陣方程的條件數(shù)增大,使得矩陣方程變?yōu)椤安B(tài)”而難以求解。為解決這個(gè)問題,本文提出了四個(gè)控制離散方程組條件數(shù)的條件,通過(guò)引入合適的豎直吸收項(xiàng)控制矩陣方程(壓強(qiáng)/自由面高度相結(jié)合的Laplacian方程)的條件數(shù),以提高迭代求解器的穩(wěn)定性和收斂速度,從而保證矩陣方程的良置性和模型的穩(wěn)定性。(2)基于改進(jìn)的干濕算法,開發(fā)了洪水演進(jìn)的三維水動(dòng)動(dòng)力學(xué)數(shù)值模型,提高了數(shù)值模型的計(jì)算效率和穩(wěn)定性。結(jié)合改進(jìn)的干濕算法,開發(fā)新的洪水三維水動(dòng)力學(xué)數(shù)值模型。該模型采用有限元法,在任意非結(jié)構(gòu)化的四面體網(wǎng)格上求解Navier-Stokes方程,允許將自由面高度處理為全隱式,從而允許使用較大的時(shí)間步長(zhǎng);同時(shí),它在水平和豎直方向使用完全非結(jié)構(gòu)網(wǎng)格時(shí)可以保證數(shù)值一致性,因?yàn)樽杂擅娓叨?尤其是其導(dǎo)數(shù))不需要從自由表面內(nèi)插到計(jì)算域的體積內(nèi)部。當(dāng)一個(gè)區(qū)域變干時(shí),在自由表面設(shè)置無(wú)法向流(No-normal flow)的邊界條件;當(dāng)水深變得很小,如1 cm時(shí),自由表面高度設(shè)定為一個(gè)指定的值。本文在一系列洪水演進(jìn)情景下,檢驗(yàn)了模型的效率、魯棒性,分析模型參數(shù)的敏感性。(3)對(duì)比分析了洪水演進(jìn)進(jìn)過(guò)程的三維和二維水動(dòng)動(dòng)力學(xué)特性,并通過(guò)與實(shí)驗(yàn)數(shù)據(jù)比較,驗(yàn)證了新開發(fā)的洪水演進(jìn)三維水動(dòng)動(dòng)力學(xué)數(shù)值模型的可靠性。將三維模型結(jié)果與實(shí)驗(yàn)數(shù)據(jù)對(duì)比,分析新開發(fā)的三維水動(dòng)力學(xué)洪水模型的可靠性;通過(guò)與二維模型結(jié)果對(duì)比,分析模型的三維特點(diǎn)。研究發(fā)現(xiàn),三維模型結(jié)果在豎直方向慣性力大的情況下,表現(xiàn)出與二維模型結(jié)果明顯的差異;而隨著水深變淺,豎直方向慣性力減弱,二者差異逐步減小。另外,三維模型捕捉到了流動(dòng)中非常詳細(xì)和復(fù)雜的細(xì)節(jié)信息,并能夠生成平滑的干濕鋒面。(4)建立了城市洪水地表徑流的三維模型,分析了城市洪水的三維水動(dòng)動(dòng)力學(xué)特性。深入研究了城市洪水的三維水動(dòng)力學(xué)特性。研究了不同網(wǎng)格精度對(duì)模型結(jié)果和CPU時(shí)間的影響,對(duì)Glasgow市一個(gè)高度城市化區(qū)域的一場(chǎng)洪水進(jìn)行三維水動(dòng)力學(xué)模型研究。通過(guò)比較三維模型與其他二維模型計(jì)算結(jié)果,發(fā)現(xiàn)在積水區(qū)二者非常相近;而在坡度較大的區(qū)域(3%),二者計(jì)算所得的水深差距更顯著,且三維模型結(jié)果出現(xiàn)較大的豎直方向的速度(0.2 m/s)。另外,考慮城市洪水分為地表徑流和地下管流,開發(fā)了SWMM模型與基于Fluidity的三維洪水模型的接口,為實(shí)現(xiàn)一維地下管流-三維地表徑流耦合模擬打下了基礎(chǔ)。本文系統(tǒng)地研究了洪水的三維水動(dòng)力學(xué)數(shù)值模型,實(shí)現(xiàn)了實(shí)際條件下洪水事件的三維模擬,闡明了三維模擬技術(shù)有望改進(jìn)洪水水動(dòng)力模型精度并能提供更加詳細(xì)的洪水過(guò)程信息,這有助于更好地估算洪災(zāi)損失和防洪設(shè)施的抗洪能力。同時(shí),揭示了一些三維與二維洪水水動(dòng)力模型的不同之處。
[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.

【學(xué)位授予單位】：天津大學(xué)
【學(xué)位級(jí)別】：博士
【學(xué)位授予年份】：2015
【分類號(hào)】：TV122
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本文編號(hào)：1696671