多功能淺水模型的建立及其應(yīng)用研究
發(fā)布時間：2019-06-19 22:36
【摘要】：本文以多功能性、干濕邊界處理通用性、二、三維耦合計算一體性、數(shù)值計算穩(wěn)定和可靠性為出發(fā)點,基于淺水水動力平臺并疊加輸運擴散模塊,建立了一個多功能淺水模型。該模型可應(yīng)用于陸域、河口和近岸水域的水動力(主要為流場)及水環(huán)境問題的二維、三維及其耦合的數(shù)值模擬。 模型建立過程中,從嚴格擬合天然的復(fù)雜邊界、網(wǎng)格密度自由控制、追求計算效率和精度角度出發(fā),選取模型的計算網(wǎng)格和控制體；從模型適應(yīng)復(fù)雜地形、水位劇烈變化、水位和流速間斷、干濕變化頻繁等實際需要出發(fā),在數(shù)值方法處理上,對流項、底摩擦阻項、斜壓項、擴散項等,分別采用現(xiàn)有最新研究成果；提出了一種與單元中心格式有限體積法計算過程相結(jié)合的干濕界面處理方法,該方法可以準確捕捉復(fù)雜地形上干濕邊界的位置,并在保證水體質(zhì)量守恒時不修改時間步長；為確保水平流速分層信息準確性,并避免疊加二、三維耦合計算時能量比降不連續(xù)造成的誤差,提出了一種新的處理復(fù)雜分層流的耦合方法。 第一,對于二維模型,基于非結(jié)構(gòu)混合網(wǎng)格技術(shù),利用加限制器的重構(gòu)過程得到變量在單元內(nèi)的線性分布,以HLLC近似Riemann算子計算對流通量,并采用半隱式方法處理摩阻源項,通過4步顯示RLunge-Kutta法積分,建立了在時間和空間上均為二階精度的高分辨率、無數(shù)值振蕩Godunov型有限體積法二維數(shù)值模型。通過一系列實例驗證表明,該模型具有計算精度高、格式強健以及良好的激波捕捉能力。 第二,對于三維模型,首先采用改進二維淺水方程時相同的方法,得到了三維淺水方程的和諧形式。利用垂向σ坐標變換,使得方程對起伏的自由表面和水底地形有自適應(yīng)能力,采用二階精度的TVD格式計算垂向?qū)α魍坎⑷[式處理垂向擴散項,可使得三維淺水模型在時空上均有二階精度。 第三,建立了二、三維耦合淺水模型。在二、三維模型的耦合界面上設(shè)定通量守恒為匹配條件,提出了一個新的、適用于復(fù)雜分層流動(如分層逆流、回轉(zhuǎn)流,垂向平均流速趨向零時除外)的耦合方法。耦合模型共用一套平面網(wǎng)格,在相同時間步上一體計算。通過對復(fù)雜分層流動的適用性檢驗和比較顯示,該方法區(qū)別于常規(guī)的設(shè)定三維流速分布為某種理論分布的耦合方法,在耦合邊界附近對復(fù)雜分層流動的計算結(jié)果更接近實際情況。 第四,將本文的建立多功能淺水模型分別應(yīng)用于潰壩后的洪水演進、海嘯波傳遞、風(fēng)生流、波生流、物質(zhì)輸運擴散和水體交換物理過程的大尺度模擬,結(jié)果表明,該淺水模型體現(xiàn)出在水利、港口、海岸和近海工程領(lǐng)域的水動力及環(huán)境問題數(shù)值模擬方面具有多功能性、干濕邊界處理的通用性、二、三維耦合計算一體性、數(shù)值計算穩(wěn)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.
【學(xué)位授予單位】：大連理工大學(xué)
【學(xué)位級別】：博士
【學(xué)位授予年份】：2014
【分類號】：TV131.61
本文編號：2502690
[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.
【學(xué)位授予單位】：大連理工大學(xué)
【學(xué)位級別】：博士
【學(xué)位授予年份】：2014
【分類號】：TV131.61
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