TVD格式数值模拟水电站水击波新探

水电站有压管道水击波数值模拟十分重要,其计算方法一直都是重点研究方向,TVD格式是数值模拟水击波的新方法,特别适合数值模拟强间断问题。其限制函数是该格式的核心问题,具有四种不同形式,将其运用于水击方程,数值模拟阀门突然关闭时水击波压力变化,与解析解进行对比,以此探究限制函数类型对TVD数值模拟水击波结果的影响。结果表明:四种限制函数TVD格式的计算结果,在间断处避免了非物理振荡,Superbee型TVD格式的分辨率最高,推荐该限制函数数值模拟水电站水击波。更多还原     

阀门关闭速度对TVD格式数值模拟水击影响分析

采用总变差减小（TVD）格式模拟了一维有压管道水击过程,对管道中阀门突然关闭和缓慢关闭引起的水击压强进行了数值计算。通过改变阀门关闭速度,分析TVD格式对水击数值模拟精度的影响。结果表明,与传统经典差分二阶MC格式相比,阀门关闭速度越快,TVD格式捕捉激波间断的能力越强,模拟水击波效果越好;当阀门关闭速度缓慢到一定程度,TVD格式与MC计算方法所得结果基本吻合,与解析解最大误差不超过2%。说明TVD格式是数值模拟水击现象行之有效的方法之一。     

一维水击波的高精度数值模拟

用本质无振荡ENO、TVD格式以及MacCormark和Lax-Friedrichs格式对一维水击模型进行数值模拟。结果表明,Lax-Friedrichs和二阶MacCormark格式在间断处有较大的数值耗散,计算精度较低,后者还存在明显的虚假数值振荡;TVD格式在光滑区具有高阶精度,在间断附近能在2个计算网格步长的范围内被光滑化,数值耗散较小;ENO格式数值解在间断附近无虚假数值振荡,数值解耗散很小,对间断具有较强的分辨能力和捕捉能力,能够很好地模拟水击波的变化过程。另外,ENO格式对计算网格的要求较TVD格式低,数值计算性能稳定。     

TVD格式在上游调压室水击数值模拟中的应用

为了模拟含上游调压室水电站的水力过渡过程,采用TVD格式求解水击方程,并结合调压室系统的基本方程组和给定的边界条件来模拟水击压力变化。将此方法用于工程实例,其计算所得的水头与实测水头相吻合;并将计算所得的水头与MacCormark 格式和Lax-Friedrichs格式的计算结果比较,结果表明：TVD格式能有效模拟含上游调压室的水击现象,其结果具有耗散性低,不产生虚假数值震荡,计算精度高等优点。     

用一种新TVD有限体积格式模拟间断行进滚波的演化

基于圣维南方程组,该文开发了一种新TVD有限体积数值格式,对自由面微小干扰演化成行进滚波的完整过程进行了模拟。该格式采用有限体积法来构建离散化方程,改进后的显式Lax-Wendroff格式来求解黎曼问题,通量限制函数来避免非物理振荡。结果表明,模拟所得的瞬态波幅变化率与线性理论精确解基本吻合,模拟所得的完全发育后准恒定行进滚波也能很好地吻合精确解,证明了该数值格式模拟行进滚波的高分辨率性质。滚波数值解对控制单元尺寸比较敏感,但对库朗数敏感度较低。     

水击的数值模拟方法比较

选用计算流体力学中几种具有代表性的数值方法进行水击的分析计算,包括Lax-Friedrichs格式、Mac-Cormark格式,以及近年来广泛用于空气动力学和溃坝水力学中的TVD格式,并将计算结果与解析解进行比较,结果表明:Lax-Friedrichs格式在间断处有较大的耗散;而MacCormark格式则出现了明显的数值振荡;TVD格式具有耗散性低,且不产生虚假数值振荡的优点.     

用TVD显隐格式模拟一维溃坝洪水波的演进与反射

应用空气动力学中的TVD格式构造了用于溃坝水流计算的显隐格式，模拟瞬间全溃时洪水波的运动，给出了与分析解的比较及多种数值试验，结果表明这类格式精度高，稳定性好，不产生虚假的数值振荡，对溃坝涌波具有较强的捕捉能力。     

考虑迎风性的高精度水击数值模拟

水击问题会对水利枢纽的正常运行造成严重危害,模拟其过程至关重要。考虑TVD格式及水流的迎风性,应用于水击方程组中,模拟简单管道中的水击压力变化。并与Lax-Friedrichs(LF)、Mac Cormark(MC)、未考虑迎风性的TVD格式及解析解进行对比。结果表明:基于迎风性的TVD格式具有高分辨率、高精度、低耗散性等优点,相比于未考虑迎风性的TVD格式,其有更强的压制性,耗散性更弱。     

曲线坐标网格下二维涌波数值模拟的TVD型格式

针对水动力学中的涌波现象导出二维曲线坐标系下的守恒型方程，然后利用算子分裂法和TVD差分格式思想构造出计算格式，在此基础上建立起由实际流场区域至方形计算区域的全局同胚映射，对急流过缩窄河道产生的涌波结构进行数值模拟，结果表明，本文的数值方法能够很好地模拟附体涌波、交叉涌波等复杂结构现象，所得波系结构和有关物理量与理论分析结果非常吻合，表明本文的数值方法对于模拟水动力学中的涌波现象是可行的。     

DORA算法一维溃坝水流模拟

DORA(double order approximation)方法是近年提出的求解动力学方程的一种算法.DORA方法物理意义明显,不受库朗稳定性条件约束,无条件稳定.DORA方法和传统典型算法相比最大的优点是可以计算初始水深是零的情况.在溃坝模拟中,经与解析解相比较可知,DORA算法在间断波附近没有出现数值振荡,水位、流速和解析解均比较吻合.证明DORA算法能很好模拟溃坝波的运动.     

Time stepping in discontinuous Galerkin method

The time discretization in the Discontinuous Galerkin (DG) scheme has been traditionally based on the Total Variation Diminishing (TVD) second-order Runge-Kutta (RK2) scheme. Computational efficiency and accuracy with the Euler Forward (EF) and the TVD second-order RK2 time stepping schemes in the DG method are investigated in this work. Numerical tests are conducted with the scalar Burgers equation, 1-D and 2-D shallow water flow equations. The maximum Courant number or time step size required for stability for the EF scheme and RK2 scheme with different slope limiters are compared. Numerical results show that the slope limiters affect the stability requirement in the DG method. The RK2 scheme is generally more diffusive than the EF scheme, and the RK2 scheme allows larger time step sizes. The EF scheme is found to be more efficient and accurate than the RK2 scheme in the DG method in computation.     

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…     

Numerical simulation of the internal wave propagation in continuously densitystratified ocean

A numerical model is proposed to simulate the internal wave propagation in a continuously density-stratified ocean, and in the model, the momentum equations are derived from the Euler equations on the basis of the Boussinesq approximation. The governing equations, including the continuity equation and the momentum equations, are discretized with the finite volume method. The advection terms are treated with the total variation diminishing （TVD） scheme, and the SIMPLE algorithm is employed to solve the discretized governing equations. After the modeling test, the suitable TVD scheme is selected. The SIMPLE algorithm is modified to simplify the calculation process, and it is easily made to adapt to the TVD scheme. The Sommerfeld＇s radiation condition combined with a sponge layer is adopted at the outflow boundary. In the water flume with a constant water depth, the numerical results are compared to the analytical solutions with a good agreement. The numerical simulations are carried out for a wave flume with a submerged dike, and the model results are analyzed in detail. The results show that the present numerical model can effectively simulate the propagation of the internal wave.     

基于有限体积法Godunov格式的水锤计算模型

针对管道内水锤问题,基于一阶和二阶Godunov格式的有限体积法建立数学模型并进行模拟分析。采用Riemann求解器对离散通量进行求解,同时在计算中引入对流项;采用MUSCL-Hancock方法进行重构得到二阶精度的Godunov格式,为了避免虚假振荡引入MINMOD斜率限制器;提出了虚拟边界的处理方法,实现了计算区域的所有节点和边界的统一计算。计算分析表明,虚拟边界法既保证了计算结果的精确性,又避免了边界处理的复杂性;一阶Godunov格式与传统的特征线法计算结果一致;当库朗特数小于1时,一阶Godunov格式和特征线法的瞬变压力可能出现严重的数值耗散,但二阶Godunov格式可有效抑制数值衰减从而得到更为准确稳定的计算结果;在马赫数很小的情况下,对流项对模拟结果的影响可忽略。     

A New Total Variation Diminishing Predictor Corrector Approach for Two-Dimensional Shallow Water Flow

This paper presents a new efficient and robust hydrodynamic model for simulation of unsteady shallow water flow. The governing equations of shallow water flows in two dimensional forms are solved using a new total variation diminishing (TVD) MacCormack predictor corrector scheme. In this numerical technique an additional TVD term is added after the traditional predictor corrector steps. The advantage of the present TVD term is that it is very simple and gives accurate results at the same time removing the numerical oscillations. Further, application of semi implicit treatment of the friction slope term helps in flow simulation even with very low water depth. Finally the model is used to analyze a wide variety of hydraulic problems including quiescent water above irregular bed, steady flow over irregular bed, steady flow over irregular bed with a shock, dam break flow over dry bed and dam break flow over wet bed. For each of the cases numerical results are compared with available analytical solution and known experimental data. The agreements between the results are satisfactory.     

NUMERICAL SIMULATION OF TWO-PHASE GRAVITY CURRENTS OVER A POROUS SUBSTRATE

1 .　INTRODUCTIONGravitycurrentsoccurinmanysituationsaris inginbothindustrialandnaturalsettings[1 2 ] .Commonlythecurrentisdrivenbycompositionalortemperaturedifference ,toleadtoahomoge nouscurrent ,orbysuspended particulatematter ,toleadtoaparticle drivencurrent.Combinationsbybothparticleandcompositionalortemperaturedifferencecanalsooccur[3] .Mostoftheresearchesareconcentratedonthesituationswherethecur rentsflowaboveanimpermeableboundary .How evertherearemanyimportantcaseswheregravitycurr…     

A HIGH RESOLUTION FINITE VOLUME METHOD FOR SOLVING SHALLOW WATER EQUATIONS

1 .　ＩＮＴＲＯＤＵＣＴＩＯＮＩｔｉｓｎｅｃｅｓｓａｒｙｔｏｃｏｎｄｕｃｔｆｌｕｉｄｆｌｏｗａｎａｌｙｓｅｓｉｎｍａｎｙａｒｅａｓ ,ｓｕｃｈａｓｉｎｅｎｖｉｒｏｎｍｅｎｔａｌａｎｄｈｙｄｒａｕｌｉｃｅｎｇｉｎｅｅｒｉｎｇ .Ｎｕｍｅｒｉｃａｌｍｅｔｈｏｄｂｅｃｏｍｅｓｇｒａｄｕａｌｌｙｔｈｅｍｏｓｔｉｍｐｏｒｔａｎｔａｐ ｐｒｏａｃｈ .Ｔｈｅｃｏｍｐｕｔａｔｉｏｎｆｏｒｇｅｎｅｒａｌｓｈａｌｌｏｗｗａｔｅｒｆｌｏｗ ｐｒｏｂｌｅｍｓａｒｅｓｕｃｃｅｓｓｆｕｌ,ｂｕｔｔｈｅｓｔｕｄｉｅｓｏｆｃｏｍｐｌｅ…     

基于高阶和高分辨率格式的自然空泡流数值模拟

基于有限体积通量修正,应用了一类高阶迎风对流格式:二阶迎风格式、二次迎风插值格式、三次迎风插值格式及带TVD限制器的高分辨率格式,对于自然空泡湍流流动的数值计算方法进行了研究.计算模型为轴对称圆盘,计算结果表明所有高阶格式都能有效抑制一阶迎风格式产生的假扩散,并得到了更薄,更"透明"的汽-液界面,其中高分辨率TVD格式最好地捕捉到了空泡界面附近物理量的阶跃特性关键词: 自然空泡;高阶迎风对流格式;汽-液界面