用有限近似法求解二维溃坝波的演进

为了对水库和堤防的失事影响作出定量评价,以便合理确定水库或堤防的防洪标准以及采取恰当的避险措施。采用有限近似法5点格式离散二维浅水波方程组,建立平面二维溃坝洪水波模型。通过与平底无摩擦二维非对称部分溃坝问题其他数模结果的比较,表明该模型能够较好地模拟自由面的变化规律,具有较强的间断捕捉能力。进而模拟有障碍物水槽中的二维溃坝波绕流现象,给出了精细的数值结果,揭示了水流复杂的运动特性。研究结果表明了有限近似法在模拟溃坝洪水波间断的形状和位置方面的优良性能,是求解溃坝流动的有效方法之一。     

基于2D FEVM-SWEs的局部底床变形溃坝水流模拟

为研究局部底床变形对溃坝波传播的影响,该文采用有限元法和有限体积法联合离散控制水流运动的二维浅水方程(2D FEVM-SWEs)建立了溃坝水流运动的数学模型。溃坝模型验证算例的结果与前人实体模型试验结果基本一致,利用该模型研究了局部底床变形条件下溃坝波传播的特性,结果表明该模型能够简便、快速、有效地模拟局部变形底床上的溃坝波传播过程,并且得到了不同时刻的溃坝水流水位变化以及反射波向上游的传播历程。     

用混合有限分析法求解二维溃坝洪水波的演进

在交错网格上，基于混合有限分析法离散浅水方程组和水深平均k-ε两方程湍流模型，并运用SIMPLE算法求解离散后的代数方程组，建立平面二维溃坝洪水波演进模型，对比典型算例——平底无摩擦二维非对称部分溃坝问题，数值模拟结果表明该模型能够较好地模拟自由面的变化规律，具有较强的捕捉间断的能力，充分显示了混合有限分析法模拟溃坝洪水波间断面的形状和位置的优良性能。     

溃坝水流在复杂河道中传播的三维数值模拟

为研究河道弯曲和障碍物对溃坝波传播的影响,采用有限体积法对描述水流运动紊流模型和描述自由水面运动的VOF方程进行离散,建立了溃坝水流运动的三维数学模型,并对急弯河道进行了数值模拟计算。急弯河道溃坝波传播过程的模拟结果与前人实体模型试验结果基本一致。利用该模型研究了丁坝附近溃坝波传播的特性和溃坝水流的内部结构,数值模拟结果表明,溃坝波的传播受河道弯曲或障碍物的影响,产生反射和绕射,使得局部溃坝水流呈明显的三维特性。上游丁坝迎水面受到溃坝波波前的直接冲击,其动水压力远大于作用于下游丁坝的动水压力。另外,障碍物对溃坝水流的影响主要局限在障碍物上游和下游一定范围内,在此范围外,水流呈二维或一维特性。     

坝体溃决过程与溃坝洪水演进耦合数值模拟

研究坝体的溃决过程与溃坝洪水演进对于处置由溃坝引起的洪水灾害、提升水利安全具有重要的意义。鉴于目前大多模型均将坝体溃决过程与溃坝洪水演进分别进行模拟,不能反映土体与水流相互耦合的特点,模拟结果精度有限。基于对土体有限抗冲能力的考虑,选取双曲线型冲蚀速率表达式描述坝体冲蚀、采用简化Bishop法搜索临界滑裂面描述溃口边坡坍塌和具有总变差不增特性的MacCormack有限体积法离散控制方程,建立了坝体溃决过程与溃坝洪水演进耦合的平面二维数值模型。实际算例表明模型合理地模拟了溃口的发展过程与洪水演进过程,在溃口急缓流转换区展现了较强稳定性,守恒性良好,可作为溃坝洪水风险评估与洪灾预报的有力工具。     

溃坝洪水对构筑物冲击荷载的数值模拟

洪水巨大的冲击力对坝区及堤岸构筑物造成很大的破坏,准确计算溃坝洪水对构筑物的冲击荷载对于建筑物的安全设计是十分必要的。采用有限体积法和中心迎风格式建立了二维数值模型,用于计算溃坝洪水对构筑物的作用力,并将该模型应用于全局溃坝和局部溃坝的物理模型试验。计算结果表明:该模型能够准确地模拟全局溃坝工况下洪水对构筑物冲击荷载的变化情况,而对于局部溃坝工况,本模型的计算结果较为平滑,无法模拟实际水流紊动的过程,但其最大冲击荷载的计算值与试验测量值相接近。相比于三维数值模型,本文所建立的二维数值模型程序简单、计算效率高、计算结果与实测结果总体吻合较好,能够有效地用于预测溃坝洪水对构筑物的冲击荷载。     

溃口近区二维数值模拟与溃坝洪水演进耦合

基于黏土心墙砂石坝的溃决过程,以及溃坝洪水传播和运动的特性,建立黑河金盆水库大坝溃口近区二维数值模型和下游地区溃坝洪水演进耦合数学模型。使用DAMBRK法计算逐渐溃坝,并应用其结果进行后续模拟。采用Abbott-Ionescu六点隐式有限差分格式求解一维模型,采用单元中心的有限体积法求解二维模型方程。采用侧向连接方式,将黑河两岸计算水位点与二维网格单元相连,实现一、二维模型的耦合。采用所建立的二维模型对溃口近区进行计算与模拟,得到计算区域某一时刻的水深及流速分布。应用所建耦合模型对黑河金盆水库万年一遇入库洪水漫顶致溃坝洪水进行数值模拟,得到一维河道内各断面的水位和流量变化过程,以及二维计算区域内不同时刻的水深分布图、流速矢量图和淹没范围变化过程。溃口的形成过程不仅包括漫顶水流的直接作用,同时包括溃口形成过程中两侧漩涡状水流的反冲刷作用。耦合模型可以同时兼顾河道内的水流变化以及河道外计算区域内的洪水演进过程,从而减少由于计算结果偏大或偏小所带来的防洪资源浪费和防洪措施不利等不良影响。     

局部断面收缩的溃坝水流三维数值模拟

为研究局部断面收缩对溃坝水流传播的影响,采用压力隐式算子分割法求解雷诺时均方程和RNG k-ε紊流模型,建立了模拟三维局部断面收缩情况下溃坝洪水演进过程的数学模型。采用有限体积法对溃坝水流的控制方程进行离散,利用流体体积函数法处理自由水面,物理变量采用交错网格布置,对局部断面收缩溃坝水流进行数值模拟计算,模拟结果与实体模型试验结果吻合较好。利用该模型研究了溃坝洪水负波的形成和传播过程,得到了负波形成和传播的规律以及溃坝水流的水位变化特征。     

基于高精度WENO格式的二维溃坝波数值模拟

以浅水波方程组建立二维溃坝洪水模型,对经典WENO格式计算模板重新选取,得到各计算模板上重构多项式,对各个模板的局部光滑因子进行组合得到更高阶的全局光滑因子,建立相应的非线性权,将各模板上重构多项式加权处理得到计算单元界面数值通量的一个新高精度WENO格式,泰勒级数展开证明了该格式的非线性权比经典WENO格式的非线性权更接近理想权。将该格式、Lax-Friedrich通量分裂方法和局部特征分解方法相结合用于二维浅水方程的离散求解,模拟二维局部溃坝流和圆形溃坝流洪水的演进过程,模拟结果与实际流动符合较好,表明采用高精度WENO格式所建立的高分辨率溃坝模型能很好地模拟溃坝波的演进过程。     

用守恒元和解元法数值模拟二维溃坝洪水波

本文采用守恒元和解元方法（简称CE／SE法）来求解二维浅水方程，该方法从守恒积分型方程出发，严格遵守物理意义上的守恒律，通过设立守恒元和解元，从而提出一种新的数值模拟方法。用该方法计算得到的全溃的溃坝洪水波的数值解和理论解与文献中的实验值符合的较好。在此基础上，进一步对二维局部溃坝洪水波的演进过程进行模拟，结果表明，CE／SE法精度较高，稳定性较好，其溃坝洪水波的间断具有很高的分辨率，能很好的模拟溃坝洪水波的运动过程。     

动床条件下溃坝水流的二维水沙耦合模型

现有大部分溃坝水流模型仅适用于模拟定床条件下的水流演进，但溃坝水流经常可在动床条件下演进。因此非常有必要同时模拟溃坝洪水演进时的水沙输移及床面冲淤过程。本文首先建立了动床条件下溃坝水流的二维水沙耦合模型。该模型主要由二维浑水控制方程、非均匀沙不平衡输移方程及河床冲淤方程组成，采用水沙耦合解法以及基于无结构三角网格下的有限体积法离散。同时利用Roe-MUSCL方法以及时间方向的预测-校正格式，使模型在时空方向具有二阶计算精度。然后采用已有算例及水槽试验资料对模型进行了初步验证。最后采用该模型研究了均匀沙及非均匀沙床面对典型溃坝水流演进的影响。模拟结果表明溃坝水流在定床及动床条件下的演进过程明显不同。溃坝水流因流速大，床面变形较快，且床面冲淤速率可与水流变化速率相当，故需要采用浑水控制方程及耦合解法。     

Numerical simulation of flow and bed morphology in the case of dam break floods with vegetation effect

The purpose of this study is to establish a depth-averaged 2-D hydrodynamic and sediment transport model for the dambreak flows with vegetation effect. The generalized shallow water equations are solved using an explicit finite volume method with unstructured quadtree rectangular grid, and in the hydrodynamic model, a Harten-Lax-Van Leer(HLL) approximate Riemann solver is used to calculate the intercell flux for capturing the dry-to-wet moving boundary. The sediment transport and bed variation equations in a coupled fashion are calculated by including the bed variation and the variable flow density in the flow continuity and momentum equations. The drag force of vegetation is modeled as the sink terms in the momentum equations. The developed model is tested against lab experiments of the dam-break flows over a fix bed and a movable bed in vegetated and non-vegetated channels. The results are compared with experimental data, and good agreement is obtained. It is shown that the reduced velocity under vegetated conditions leads to a decrease of the peak discharge and a rise of the water level of rivers and also an enhancement of the sediment deposition.     

用最小二乘无网格有限差分方法求解二维浅水方程

近年来兴起的无网格方法摆脱了网格约束,在计算区域内能自由布点,快速灵活,并且离散节点能更好地拟合复杂的边界,求解精度较高。运用最小二乘无网格有限差分（MLSFD）方法,求解二维非守恒形式浅水方程。支撑域内点采用两种方法结合的方式进行选取。为避开繁琐的矩阵奇异、病态的检验过程,选用了最小二乘技术对矢量做最优化近似,并使用MLSFD对圆形溃坝模型进行计算。为了更好地处理边界条件,在无网格的四周,向内分别布置三层直角网格。对数值模拟结果进行分析比较,验证了该方法在计算二维浅水流动的数值模拟方面有着较高的精确度,进而说明无网格方法运用于求解浅水方程是可行的。     

FINITE-VOLUME TVD ALGORITHM FOR DAM-BREAK FLOWS IN OPEN CHANNELS

1 .　INTRODUCTIONThepropagationofborewavesorthemove mentoffreesurfaceflowscausedbydambreak ing ,orsuddenopeningorclosingofasluiceinachannelhasincreasedinterestinenvironmentalandhydraulicengineering .Generallyitcanbede scribedbytheShallowWaterEquations (SWE )throughtheintegrationoftheNavier Stokesequationsoverdepthwiththeassumptionsofhydrostaticpressuredistributionandmildchannel bedslope .ManyclassicaltechniquesthatwereusedforsolvingtheSWEcanbefoundinthepaststudies .However ,whendiscon…     

MODELING DAM-BREAK FLOOD OVER NATURAL RIVERS USING DISCONTINUOUS GALERKIN METHOD

A well-balanced numerical model is presented for two-dimensional, depth-averaged, shallow water flows based on the Discontinuous Galerkin (DG) method. The model is applied to simulate dam-break flood in natural rivers with wet/dry bed and complex topography. To eliminate numerical imbalance, the pressure force and bed slope terms are combined in the shallow water flow equations. For partially wet/dry elements, a treatment of the source term that preserves the well-balanced property is presented. A treatment for modeling flow over initially dry bed is presented. Numerical results show that the time step used is related to the dry bed criterion. The intercell numerical flux in the DG method is computed by the Harten-Lax-van Contact (HLLC) approximate Riemann solver. A two-dimensional slope limiting procedure is employed to prevent spurious oscillation. The robustness and accuracy of the model are demonstrated through several test cases, including dam-break flow in a channel with three bumps, laboratory dam-break tests over a triangular bump and an L-shape bend, dam-break flood in the Paute River, and the Malpasset dam-break case. Numerical results show that the model is robust and accurate to simulate dam-break flood over natural rivers with complex geometry and wet/dry beds.     

NUMERICAL SIMULATION OF TWO-DIMENSIONAL DAM-BREAK FLOWS IN CURVED CHANNELS

Two-dimensional transient dam-break flows in a river with bends were theoretically studied. The river was modeled as a curved channel with a constant width and a flat bottom. The water was assumed to be an incompressible and homogeneous fluid. A channel-fitted orthogonal curvilinear coordinate system was established and the corresponding two-dimensional shallow-water equations were derived for this system. The governing equations with well-posed initial and boundary conditions were numerically solved in a rectangular domain by use of the Godunov-type finite-difference scheme, which can capture the hydraulic jump of dam-break flows. The comparison between the obtained numerical results and the experimental data of Miller and Chaudry in a semicircle channel shows the validity of the present numerical scheme. The mathematical model and the numerical method were applied to the dam-break flows in channels with various curvatures. Based on the numerical results, the influence of river curvatures on the dam-break flows was analyzed in details.     

基于加权本质无振荡格式的二维溃坝水流数值模拟

将加权本质无振荡WENO(Weighted essentially nonoscillatory)格式和Runge-Kutta时间离散的思想应用于二维浅水控制方程的求解中，建立了模拟大坝瞬间全溃或局部溃倒所致的洪水演进过程的数学模型。应用该模型对一维矩形明渠中大坝瞬间全溃所致的水流运动进行了数值计算，并与理论解进行了比较，证实了方法的可靠性。最后用该模型预测了矩形河道中大坝瞬间局部溃倒时的洪水演进过程，模拟结果与实际相符。算例表明采用WENO格式所建立的高分辨率溃坝模型能够很好地模拟溃坝波的演进过程。     

1-D coupled non-equilibrium sediment transport modeling for unsteady flows in the discontinuous Galerkin framework

A high-resolution,1-D numerical model has been developed in the discontinuous Galerkin framework to simulate 1-D flow behavior,sediment transport,and morphological evaluation under unsteady flow conditions.The flow and sediment concentration variables are computed based on the one-dimensional shallow water flow equations,while empirical equations are used for entrainment and deposition processes.The sediment transport model includes the bed load and suspended load components.New formulations for Harten-Lax-van Leer(HLL) and Harten-Lax-van Contact(HLLC) are presented for shallow water flow equations that include the bed load and suspended load fluxes.The computational results for the flow and morphological changes after two dam break events are compared with the physical model tests.Results show that the modified HLL and HLLC formulations are robust and can accurately predict morphological changes in highly unsteady flows.     

移动边界的有限体积KFVS方法在一维溃坝波计算中的应用

本文从Boltzmaun方程出发，采用有限体积KFVS（Kinetic flux-vector splitting）方法，对微观粒子的速度分布进行组合，给出了模拟河道洪水演进时干湿交界处移动边界的一种新方法。并成功地模拟了大坝下游为干河道的一维溃坝模型，通过和精确解的比较得出，此方法在处理河道移动边界问题上是成功和有效的。