FINITE VOLUME METHOD FOR SIMULATION OF VISCOELASTIC FLOW THROUGH A EXPANSION CHANNEL

A finite volume method for the numerical solution of viscoelastic flows is given. The flow of a differential Upper-Convected Maxwell (UCM) fluid through an abrupt expansion has been chosen as a prototype example. The conservation and constitutive equations are solved using the Finite Volume Method (FVM) in a staggered grid with an upwind scheme for the viscoelastic stresses and a hybrid scheme for the velocities. An enhanced-in-speed pressure-correction algorithm is used and a method for handling the source term in the momentum equations is employed. Improved accuracy is achieved by a special discretization of the boundary conditions. Stable solutions are obtained for higher Weissenberg number (We), further extending the range of simulations with the FVM. Numerical results show the viscoelasticity of polymer solutions is the main factor influencing the sweep efficiency.     

A HIGH RESOLUTION FINITE VOLUME METHOD FOR SOLVING SHALLOW WATER EQUATIONS

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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…     

HIGH ACCURATE SOLUTION OF INCOMPRESSIBLE VISCOUS FLOW WITH PRIMATIVE VARIABLE

This paper presents a higher order difference scheme for the computationof the incompressible viscous flows.The discretization of the two-dimensional incompress-ible viscous Navier-Stokes equations,in generalized curvilinear coordinates and tensor for-mulation,is based on a non-ataggered grid.The momentum equations are integrated intime using the four-stage explicit Runge-Kutta algorithm [1]and discretized in space us-ing the fourth-order accurate compact scheme[2]The pressure-Poisson equation is dis-cretized using the nine-point compact scheme.In order to satisfy the continuity constraintand ensure the smoothness of pressure field,an optimum procedure to derive a discretepressure equation is proposed [9][3]The method is applied to calculate the driven cavityflow on a stretched grid with the Reynolds numbers from 100 to 10000.The numerical re-sults are in very good agreement with the results obtained by Ghia et al [7]and includethe periodic solutions for high Reynolds numbers.     

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。     

Pressure-balanced Saint–Venant equations for improved asymptotic modelling of pipe flow

In urban drainage networks, steady free surface flows in circular-shaped pipes are commonly observed given low inflow discharges. Therefore, accurate computation of such steady states is of great practical significance, especially considering bent pipes. This requires numerical schemes to be capable of achieving a delicate balance between slope source terms and fluxes in the discrete framework. To this end, in the current study, a new method using pressure balanced Saint–Venant equations and positivity preserving Godunov-type finite volume scheme, is developed for 1D flow simulation in bent circular pipes. Using pressure balancing, a set of pre-balanced Saint–Venant equations is derived. The numerical discretization method uses an approximate Riemann solver and is capable of dealing with wetting–drying process stably in frictional pipes. As verified by several test cases, the proposed method shows better performances than existing methods in modelling the asymptotic flow behavior and preserving steady states in bent circular pipes.     

二维溃坝波遇障碍物的水流泥沙数值模拟

本文通过对浅水方程进行Godunov差分离散和对泥沙运动方程进行一阶迎风差分离散，建立了平面l二维溃坝水流泥沙数值模型。在算例中计算了溃坝波遇障碍物后的水流反射、绕射及泥沙冲淤，计算结果表明，溃坝波遇障碍物后会产生明显的反射和绕射，并在障碍物前形成壅水、障碍物的侧面会发生剧烈的冲刷，障碍物前后则会发生局部淤积。本模型能够较好地模拟溃坝间断水流的运动，结果符合水流泥沙运动的基本规律。     

Comparison of depth-averaged concentration and bed load flux sediment transport models of dam-break flow

This paper presents numerical simulations of dam-break flow over a movable bed. Two different mathematical models were compared: a fully coupled formulation of shallow water equations with erosion and deposition terms (a depth-averaged concentration flux model), and shallow water equations with a fully coupled Exner equation (a bed load flux model). Both models were discretized using the cell-centered finite volume method, and a second-order Godunov-type scheme was used to solve the equations. The numerical flux was calculated using a Harten, Lax, and van Leer approximate Riemann solver with the contact wave restored (HLLC). A novel slope source term treatment that considers the density change was introduced to the depth-averaged concentration flux model to obtain higher-order accuracy. A source term that accounts for the sediment flux was added to the bed load flux model to reflect the influence of sediment movement on the momentum of the water. In a one-dimensional test case, a sensitivity study on different model parameters was carried out. For the depth-averaged concentration flux model, Manning's coefficient and sediment porosity values showed an almost linear relationship with the bottom change, and for the bed load flux model, the sediment porosity was identified as the most sensitive parameter. The capabilities and limitations of both model concepts are demonstrated in a benchmark experimental test case dealing with dam-break flow over variable bed topography.     

污染物对流扩散方程的几种新的高阶QUICK组合显格式比较研究

本文运用组合式的有限差分QUICK格式,将对流扩散方程进行了高精度离散,通过对流项、时间项、扩散项几种高阶差分格式的优化组合,最终建立了一种时间三阶、对流三阶、扩散二阶的显式差分格式,通过经典的数值算例验证了本格式具有精度高、编程简单、计算速度快的特点。本文还详细介绍了由有限体积法建立的经典QUICK格式和通过有限差分法建立的QUICK格式的区别以及各自的精度,澄清了某些文章作者对QUICK格式的认识偏差。     

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。     

浅水流动的模拟方法比较

本文研究浅水模拟中几种具有代表性的计算格式,包括不同阶数的简单格式、迎风格式、利用不同通量控制器的TVD格式以及基于分子运动理论的KFVS格式。通过对具有多种不同水流以及间断的一维溃坝的模拟,这些格式的优劣从各种典型数值现象中体现出来。最后用筛选后的格式对一维溃坝物理实验以及二维扩展渠道水流进行模拟。由于KFVS格式符合基本的流体分子运动规律,虽然引入了一定的耗散误差,但此格式无论对一维问题还是二维问题总体模拟效果都较佳。     

FVS SCHEME FOR SEVERE TRANSIENT FLOW IN PIPE NETWORKS

1.INTRODUCTIONWater hammer problems are i mportant aspectin the designs and operations of piping systeminpower plant.In pipe networks,the influences ofaccidental events such as power outage and controladjust ment generate sudden transient conditionsthat could make great damages.Hence it is neces-sary to develop the numerical models to si mulatewater hammer problems andsuddentransient flowsin complex pipe networks in order to get the diag-noses gist.Computerized water hammer models[1-5]are…     

A TVD-WAF-based hybrid finite volume and finite difference scheme for nonlinearly dispersive wave equations

A total variation diminishing-weighted average flux(TVD-WAF)-based hybrid numerical scheme for the enhanced version of nonlinearly dispersive Boussinesq-type equations was developed. The one-dimensional governing equations were rewritten in the conservative form and then discretized on a uniform grid. The finite volume method was used to discretize the flux term while the remaining terms were approximated with the finite difference method. The second-order TVD-WAF method was employed in conjunction with the Harten-Lax-van Leer(HLL) Riemann solver to calculate the numerical flux, and the variables at the cell interface for the local Riemann problem were reconstructed via the fourthorder monotone upstream-centered scheme for conservation laws(MUSCL). The time marching scheme based on the third-order TVD RungeKutta method was used to obtain numerical solutions. The model was validated through a series of numerical tests, in which wave breaking and a moving shoreline were treated. The good agreement between the computed results, documented analytical solutions, and experimental data demonstrates the correct discretization of the governing equations and high accuracy of the proposed scheme, and also conforms the advantages of the proposed shock-capturing scheme for the enhanced version of the Boussinesq model, including the convenience in the treatment of wave breaking and moving shorelines and without the need for a numerical filter.     

黄河下游突发性污染事件数值模拟

建立黄河下游一维非恒定流水动力学数学模型,并在此基础上建立一维水质模型,采用有限体积法(TVD格式)离散基本方程,通过时间二阶之预测-校正二步格式对离散方程进行求解。该求解方法具有守恒性好、算法简单、通用性强,在预测一般洪水及溃坝洪水波演进方面有较好的实用性,并能对黄河下游突发性污染事件进行初步模拟。     

实际地形下溃坝波的有限近似解

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的结果比较,结果表明该模型能够较好地模拟自由面的变化规律,具有较强的间断捕捉能力。进而对实际地形下的二维溃坝问题进行了计算模拟,给出了精细的数值结果,揭示了复杂的运动特性,进一步显示了有限近似法模拟溃坝洪水波间断面的形状和位置的优良性能,是求解溃坝流动的有效方法之一。     

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.     

Implicit Finite-Volume Scheme to Solve Coupled Saint-Venant and Darcy–Forchheimer Equations for Modeling Flow Through Porous Structures

In hydrodynamic modeling of flow through porous structures, the solution domain might encounter discontinuities. These include, for example, porous structure-open channel interface, porous dam-break, and heterogeneous porous structures. The treatment of discontinuity is challenging within a numerical scheme as it can be a source of instabilities. This study proposes a finite-volume method to solve coupled Saint-Venant and Darcy–Forchheimer equations for simulating free-surface flow through porous structures. For capturing shocks arising at discontinuous regions, an upwind scheme is utilized to maintain the solution monotone. Fully implicit methods can allow the choice of longer time steps. Since the current problem involves two nonlinear systems, namely the open-channel and seepage flow equations, the Picard method is adopted to linearize the system of equations. Unlike typical implicit schemes of seepage flows, herein, both flow depth and velocity matrices appear within the iterative process, threatening the convergence criterion. To converge iteration, the continuity equation's flux term is treated using the dynamic wave equation under the relaxation method. The present model is applicable to simulate gradually and rapidly unsteady flow through homogeneous and heterogeneous porous media under laminar, transitional, and fully developed turbulent flow regimes within various closed and/or open boundary conditions.

     

波浪作用下悬移质泥沙运动的两相流数值模型

该文采用基于水沙两相紊流的数值模型对波浪作用下的悬移质泥沙运动进行研究。基本方程中将水相和颗粒相通过相间作用力进行耦合,合理地考虑了相间相对运动的影响。数值计算方法为有限体积法,对流项处理利用了三阶精度的QUICK格式,离散方程组求解采用的是TDMA迭代方法。计算得到的悬移质泥沙垂线时均计算值与不同尺度的水槽实验数据吻合很好,表明数学模型及其计算方法对于低浓度水沙两相问题是合理的。该研究还探讨了悬沙浓度、泥沙沉降速度以及各种相间作用力随时间的分布规律。     

基于非结构化网格建立求解具有复杂地形的浅水流动的数值模型

采用有限体积法,基于非结构化网格上建立求解具有复杂地形的浅水流动数值模型。采用Roe格式的计算界面通量,引入一种单元界面处近似水深的方法来处理地形变化源项,并证明了在非结构化网上满足和谐性条件,此外,此方法还能有效的应用到现存的激波捕捉方法,如HLL、HLLC和CU格式等。通过两个算例,验证了格式是和谐的并具有良好的间断捕捉能力。     

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。