非结构化网格下求解二维浅水方程的和谐Roe格式

为保证底坡源项和重力梯度项的平衡离散,采用把底坡源项分解为两不同部分单独处理的方法,在非结构化网格上建立了求解带复杂地形的二维浅水方程数值模型.采用Roe格式的计算界面通量,隐式求解摩擦力源项以增加格式的稳定性,并给出计算格式在非结构化网格上满足和谐性条件的证明.通过实例验证了此格式是和谐的,并具有良好的间断捕捉能力和稳定性.     

具有复杂计算域和地形的二维浅水流动数值模拟

本文采用非结构化网格的有限体积方法,对具有复杂计算域和地形的二维河道进行数值模拟。采用Roe格式的近似Riemann解计算界面通量,对地形变化源项采用特征分解平衡界面通量以保证格式的和谐性,对摩擦力源项采用隐式或半隐式求解以增加格式的稳定性。通过与混合流算例理论解比较,验证了格式是和谐性的并具有良好的间断捕捉能力与稳定性。应用此方法对地形复杂,存在多处险滩和深潭的某河段进行了实际模拟,数值计算结果和模型试验结果吻合较好。     

带有干湿界面的MUSCL型有限体积法

该文采用MUSCL型非结构化网格的有限体积法模拟有干湿界面的复杂地形的非恒定流动,以Roe格式的近似Riemann解为基础,两步Runge-Kutta法提高到时间二阶精度.对底坡源项采用特征分解保证和谐性,对摩擦力源项采用半隐式格式增加格式的稳定性.采用适当的干湿界面处理技术以满足静水问题,同时对有干湿界面的复杂地形的非恒定流动达到无质量误差.通过几个经典算例,验证了本文方法的守恒性,同时具有良好的间断捕捉能力和稳定性.     

基于修正Roe格式的有限体积法求解二维浅水方程

应用迎风有限体积法,对具有复杂地形的二维浅水方程进行数值模拟.基于非结构化网格,采用Roe格式的近似Riemann解计算非粘性界面通量.底坡源项采用简单的斜底模型离散,从而保证了地形的离散精度.为了保证该计算格式的压力项和底坡源项的和谐性,对经典的Roe格式计算数值通量中的静水压力项进行了修正,并证明了修正后的Roe格式具备和谐性.通过与超临界流倾斜水跃和有激波混合流算例理论解结果比较,验证了该模型具有良好的间断捕捉能力、计算稳定性和守恒性.     

无质量误差的具有复杂地形的浅水问题

本文提出了一种处理带有干湿界面的非恒定浅水流动的无质量误差方法.以Roe格式的近似Riemann解为基础,采用非结构化网格的有限体积法,对底坡源项采用特征分解保证和谐性,摩擦力源项采用半隐式格式增加格式的稳定性.采用适当的干湿界面处理技术以满足静水问题,同时对有干湿界面的复杂地形的非恒定流动达到无质量误差.应用的算例表明对于处理洪水演进及溃坝问题,本文的方法是行之有效的.     

基于非结构网格的二维溃坝洪水数值模型

基于三角形非结构网格,采用有限体积法建立了平面二维水动力学模型,用于模拟复杂边界和地形下溃坝洪水的运动过程。该文采用中心迎风格式求解界面数值通量,并通过引入限制器技术对界面两侧变量进行重构,使其在空间上具有两阶精度。采用局部改变河床高程方法对界面重构变量进行修正来提高模型的干湿处理能力。该模型既能保证数值格式的和谐性,又能够确保整个计算过程中水深是非负的。通过采用三个典型算例的验证和一个实例溃坝洪水过程的模拟分析,计算结果表明:该模型能很好地捕捉复杂地形和边界条件下洪水演进过程中的洪水锋面运动、干湿节点转化、水深和流量变化等过程,具有很强的稳定性、水量守恒性和激波捕捉能力,特别适用于具有复杂地形和阻水结构物的溃坝洪水演进案例分析。     

基于无结构化网格浅水方程的隐式解法

为提高有限体积法计算浅水方程的数值稳定性,采用Roe方法近似Riemann解计算界面通量,利用TVD-MUSCL格式对守恒变量进行重构,推导并建立了高效的隐式计算格式。该格式基于无结构化网格,将计算精度提高到二阶,使用面积加权计算流速梯度,对坡底梯度的处理满足静水平衡要求。为在时间积分上采用隐格式,又导出了控制方程的雅可比矩阵全解析形式,并采用牛顿-拉夫逊方法进行迭代求解。通过对溃坝算例的对比分析,验证该方法的稳定性、和谐性和高效性,同时也证明该算法具有捕捉溃坝激波问题的能力。     

基于非结构网格的非恒定浅水二维有限体积数学模型研究

建立了基于非结构三角网格系统的非恒定浅水二维水流数学模型.基本控制方程采用浅水二维水流方程;采用能够有效捕捉激波的HLLC近似黎曼算子求解界面通量,并对界面变量进行数据重构,模型具有二阶精度:将地形高程定义在三角单元节点上,使得单元间地形连续变化,结合处理底坡的DFB(mvergence form for bed slope source term)方法,保证了模型的和谐性,使其能够有效地模拟不规则地形条件上干湿边界变化过程中的水流过程;采用了隐式方法处理阻力项,从而保证了模型的稳定性.最后,通过四个经典算例对模型进行了系统地检验.结果表明:此模型具有很好的和谐性和稳定性,能够有效、准确地模拟复杂地形情况下水流运动,显示了广阔的应用前景.     

大名泛区洪水演进数值模拟

利用结构化网格的有限体积法,建立了二维浅水方程的高精度、低计算负荷的数值计算模型。对结构化网格的处理采用一种自适应网格加密方法,提出四叉树的网格构造,以提高网格对地形和水力变化的敏感度。推导出一种具有激波捕捉能力的二维浅水方程的守恒形式,采用单元中心式有限体积离散。方程的离散采用Godunov格式,利用近似Riemann解求解界面通量,并介绍和采用了具有二阶精度的HLLC算法。对在此基础上,建立大名泛区二维洪水演进模型,获取了不同时段的淹没范围栅格图像、不同时刻淹没水深、洪泛区的蓄水量变化过程以及泛区内点的水力要素信息,为泛区的防洪规划和实时洪水预报提供理论参考。     

一种Godunov算法及其在非平底流污染物传输中的应用

采用和谐的加权平均通量(Weighted Average Flux,简称WAF)算法,研究了浅水波方程的间断解及污染物传输问题。该算法采用WAF格式和HLLC Riemann求解器近似单元边界数值通量,中心差分格式离散地形源项,然后理论上证明了该算法是和谐的。最后利用WAF算法对非平底地形上浅水波间断解及污染物传输问题进行数值计算,精确地捕捉到了间断解和污染物运动过程,结果表明该算法满足守恒性,具有高分辨率、无振荡及捕捉污染物运动边界的能力。     

拓扑映射法划分结构化六面体网格在水利工程方面的应用

网格划分是数值模拟的前处理阶段,划分的网格主要有结构化与非结构化之分,结构化网格较非结构化网格在提高计算精度,加快收敛速度方面有一定的优越性。本文应用拓扑映射法对较复杂几何外形的计算域进行结构化网格划分,并将此方法应用于水利工程的实际模拟中,得到高质量结果化六面体网格,验证了此种网格划分方法在水利工程实际应用中的可行性。     

桥渡对河道水流影响的二维无结构网格模型

采用有限体积法建立平面二维水流运动的无结构网格数学模型,模型采用Roe格式的近似Riemann解计算界面通量和特征分解法处理底坡源项.通过无结构网格对桥墩形状进行精细拟合克服了局部糙率修正、局部地形修正等方法的困难.为研究桥墩、桥形等对水位、局部流速等建桥前后的变化提供了新的计算模式.最后,应用模型对河段上的圆形墩和圆端矩形墩壅水进行了模拟,结果表明模型能够较好的模拟建桥前后桥墩附近的水流变化.     

黄河大柳树河段河床演变的三维数值模拟

针对河岸冲刷、河床演变显著的河流,建立考虑河岸变形的三维水沙数值模型,对黄河大柳树河段的河势演变进行数值模拟分析研究。模型中利用三角形网格和局部网格移动及局部加密技术,采用有限体积法离散控制方程,以及基于非结构化同位网格中的SIMPLE算法进行数值求解。依据2011年11月至2012年10月黄河大柳树河段典型断面实测资料对数值模拟结果进行验证,模拟结果与实测结果吻合较好。结果表明该模型能够较好地模拟黄河大柳树河段的水流运动和河床演变,模型中提出的河岸修正技术和局部网格加密技术可有效提高模拟计算精度和效率。     

APPLICATION OF A MODIFIED QUICK SCHEME TO DEPTHAVERAGED k-( TURBULENCE MODEL BASED ON UNSTRUCTURED GRIDS

The modified QUICK scheme on unstructured grid was used to improve the advection flux approximation, and the depth-averaged turbulence model with the scheme based on FVM by SIMPLE series algorithm was established and applied to spur-dike flow computation. In this model, the over-relaxed approach was adopted to estimate the diffusion flux in view of its advantages in reducing errors and sustaining numerical stability usually encountered in non-orthogonal meshes. Two spur-dike cases with different defection angles (90oand 135o) were analyzed to validate the model. Computed results show that the predicted velocities and recirculation lengths are in good agreement with the observed data. Moreover, the computations on structured and unstructured grids were compared in terms of the approximately equivalent grid numbers. It can be concluded that the precision with unstructured grids is higher than that with structured grids in spite that the CPU time required is slightly more with unstructured grids. Thus, it is significant to apply the method to numerical simulation of practical hydraulic engineering.     

SIMULATION OF SEDIMENT-LADEN FLOW BY DEPTH-AVERAGED MODEL BASED ON UNSTRUCTURED COLLOCATED GRID

The 2-D depth-averaged mathematical model for sediment-laden flows has been widely used in river control and other related engineering problems, and now it is usually solved on structured grids. Since the natural river is usually very complicated in plane boundary, and unstructured grids are more attractive in solving the problems with complicated domains, the following questions about solving 2-D depth-averaged model were discussed in this article: (1) a modified Bowyer algorithm was suggested to generate unstructured grids for natural rivers, (2) the Finite Volume Method (FVM) is employed to discretize the governing equations of the 2-D depth-averaged model and an implicit scheme was suggested with unstructured collocated grids, (3) the observed hydrological data of the Chenglingji Reach in the Yangtze River are used for verification of the presented method. It seems that the suggested numerical scheme works very well, and the simulation results of both hydraulic characteristics and river bed deformation are in good agreement with the observed ones.     

APPLICATION OF A MODIFIED QUICK SCHEME TO DEPTH- AVERAGED κ-ε TURBULENCE MODEL BASED ON UNSTRUCTURED GRIDS

The modified QUICK scheme on unstructured grid was used to improve the advection flux approximation, and the depth-averaged κ-ε turbulence model with the scheme based on FVM by SIMPLE series algorithm was established and applied to spur-dike flow computation. In this model, the over-relaxed approach was adopted to estimate the diffusion flux in view of its advantages in reducing errors and sustaining numerical stability usually encountered in non-orthogonal meshes. Two spur-dike cases with different defection angles （90°and 135°） were analyzed to validate the model. Computed results show that the predicted velocities and recirculation lengths are in good agreement with the observed data. Moreover, the computations on structured and unstructured grids were compared in terms of the approximately equivalent grid numbers. It can be concluded that the precision with unstructured grids is higher than that with structured grids in spite that the CPU time required is slightly more with unstructured grids Thus, it is significant to apply the method to numerical simulation of practical hydraulic engineering.     

A CONSERVATIVE COUPLED FLOW/TRANSPORT MODEL WITH ZERO MASS ERROR

A fully conservative form applied to a coupled system of two-dimensional water flow and solute motion is presented. A cell-centred finite volume method based on Roe's approximate Riemann solver with unstructured grids is formulated. The bed slope source terms are discretized following an upwind approach and a semi-implicit treatment is used for the friction source terms. The centered discretization of the diffusion terms is in an implicit way. It is shown that this numerical technique reproduces almost exactly the steady state of still water and enables to achieve zero numerical errors in unsteady flow over configurations with strong variations on bed slope. The model ensures a global conservation and positive values of both water level and solute concentration. Numerical results show the effectiveness of the model in solute transport over real complex geometries.     

NUMERICAL SIMULATION OF SLOSHING IN RECTANGULAR TANK WITH VOF BASED ON UNSTRUCTURED GRIDS

A new method for sloshing simulation in a sway tank is present, in which the two phase interface is treated as a physical discontinuity, which can be captured by a well-designed high order scheme. Based on Normalized Variable Diagram (NVD), a high order discretization scheme with unstructured grids is realized, together with a numerical method for free surface flow with a fixed grid. This method is implemented in an in-house code General Transport Equation Analyzer (GTEA) which is an unstructured grids finite volume solver. The present method is first validated by available analytical solutions. A simulation for a 2-D rectangular tank at different excitation frequencies of the sway is carried out. A comparison with experimental data in literature and results obtained by commercial software CFX shows that the sloshing load on the monitor points agrees well with the experimental data, with the same grids, and the present method gives better results on the secondary peak. It is shown that the present method can simulate the free surface overturning and breakup phenomena.     

长江口北支基于混合网格的通量差分裂水流水质计算模式

本文建立了基于三角形四边形混合网格的二维水流水质耦合数值计算模式。网格通过推进阵面法自动生成，控制方程采用有限体积法对守恒变量进行离散，应用通量差分裂格式(FDS)计算边界上的水量、动量和污染物法向数值通量。模型应用于长江口北支崇海公路大桥修建后的流场浓度场的数值模拟。网格根据工程实际需要分区布置．在工程外区域采用有结构的四边形网格布置，既可贴合实际岸线边界，又便于组织数据结构；在工程附近区域采用无结构的三角形网格布置，利用三角形网格的灵活性实现复杂地形边界和局部小尺度流场浓度场的精细模拟。模型计算出的流场和浓度场与实测值对比令人满意，较好地解决了复杂边界和工程网格尺度问题。     

Unstructured finite volume method for water impact on a rigid body

A new method is presented for the water impact simulation, in which the air-water two phase flow is solved using the pressure-based computational fluid dynamics method. Theoretically, the air effects can be taken into account in the water structure interaction. The key point of this method is the air-water interface capture, which is treated as a physical discontinuity and can be captured by a well-designed high order scheme. According to a normalized variable diagram, a high order discrete scheme on unstructured grids is realised, so a numerical method for the free surface flow on a fixed grid can be established. This method is implemented using an in-house code, the General Transport Equation Analyzer, which is an unstructured grid finite volume solver. The method is verified with the wedge water and structure interaction problem.