二维明渠非恒定水流BGK数值模型

本文根据BGK波尔兹曼方程及明渠水流中波尔兹曼变量与宏观变量之间的基本关系，导出了明渠水流运动方程，验证了BGK波尔兹曼方程与明渠水流运动方程的一致性，并从理论上证明，圣维南方程是BGK明渠水流模型在局部平衡状态下的一个特例。以BGK波尔兹曼方程为基本方程，利用有限体积离散方法，建立了满足熵原理的二维明渠非恒定水流的BGK数值模型。通过对典型的明渠水流现象的模拟，并与其它计算方法获得的解以及实验结果相比较，表明BGK模型勿须人为的熵修正，能准确地模拟存在不连续运动的明渠水流运动，是一种较好的明渠非恒定水流模型。     

以波尔兹曼方程建立明渠水流模型的理论基础

针对传统模拟明渠水流方法所存在的问题，提出了应用ＢＧＫ模拟方法模拟明渠水流运动的可能性。根据ＢＧＫ波尔兹曼方程及明渠水流中微、宏观变量之间的基本关系，导出了明渠水流运动的控制方程。理论推导证明，圣维南方程是ＢＧＫ模型在局部平衡状态下的一个特例。通过对熵方程分析表明，ＢＧＫ波尔兹曼方程严格满足熵条件，从而阐释了ＢＧＫ模拟方法满足熵条件。利用一个恒定水跃的例子说明了熵条件的重要性，同时也表明，仅仅以质量和动量守衡律为基础的圣维南方程可能会得出不唯一的解，即不满足熵条件的解。在论证ＢＧＫ波尔兹曼方程与明渠水流守衡律的一致性的基础上，提出了建立ＧＢＫ明渠水流模型之基本思路和步骤并分析了该方法与传统模拟方法之区别。从理论上论证了利用ＢＧＫ模拟方法模拟明渠水流的可行性，为建立ＢＧＫ明渠水流模型奠定了理论基础。     

溃坝波的简单计算方法

为了避免和减少大坝溃决对下游的影响，开发了一种应用范围大，容易掌握，可供大坝安全管理者使用的溃坝波简化计算软件：ＣＡＳＴＯＲ。ＣＡＳＴＯＲ假定水流为均匀流，推算出最大流量与最高水位和最大溃坝波速的关系，并可计算溃坝波到达坝址的时间。用溃坝实例对ＣＡＳＴＯＲ计算结果与圣维南方程（ＲＵＢＡＲ３）计算结果进行了统计检验，结果表明，二者水力要素平均值吻合较好。     

地下水流与河网水流的耦合模型

从河道水流一维不稳定流(扩展的圣维南方程组)有限差分的递代方程和地下水的有限元数值方法出发，通过河道四周地下水流与河道水流的交换流量把两个模型数值计算的矩阵方程从理论上耦合起来.理想水文流域系统的计算结果表明，模型的设计是合理的     

用槽蓄关系联解圣维南方程组模拟洪水演进的方法探讨

采用槽蓄关系联解圣维南方程组模拟洪水演进的水力学方法,首次发现了在Δt时段可将圣维南方程组简化后绘制两种不同形式的河段槽蓄增量图形:一是根据水流连续方程可绘制槽蓄增量1,二是根据水流运动方程也可绘制槽蓄增量2。由于河段槽蓄增量1、2应相等,因此,可以用槽蓄增量为纽带求解圣维南方程组。     

水库动库容调洪计算方法研究

基于非恒定流理论的圣维南方程组的求解是河道型水库动库容调洪计算的常用方法，该法能较好地反映河槽水流的非恒定流状态。但在一些实际的水库动库容量计算中，圣维南方程组的一些假定对计算结果将产生不可忽视的影响，对圣维南方程组的求解方法进行了改进，通过分析采用修正区间流量的方法来解决在求解圣维南方程组时出现的蓄水量不平衡问题，逐时段对库区的水量不平衡进行修正，该法较以往的算法计算精度更高，并已应用于某大型水库的动库容调洪计算。     

相应涨差实时洪水预报模型

一、相应涨差模型的建立 河道洪水演算方法众多,但基本上都是基于对圣维南(Saint-Venant)方程组的简化和近似。1891年圣维南导出的描述洪水波运动规律的方程组是一阶拟线性双曲型微分方程组,即非恒定流的连续方程和动力方程:     

城市排水管网明满交替非恒定流数学模型的研究

该文针对城市排水管网系统存在的明满流共存的计算难点,从一维水流的圣维南方程组的物理意义入手,推导了适用于有压管流的方程组表达形式,提出了当量宽度的概念和计算方法,修正了Preissmann窄缝假定方法中的窄缝宽度公式,将明渠和有压管道两种情况下的方程组写成统一的形式,实现了对明满过渡流的有效数值模拟。通过数学模拟,与经验数据和SWMM模型的对比验证,揭示了当量宽度法的合理性、可行性及其实际应用价值。     

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。     

一维不恒定流河网数学模型研究与应用

河道中洪水数值模拟主要用求解描述洪水波运动的圣维南方程组，依数值计算解法不同而产生了不同的模型．在海河流域大清河北支及中下游河道洪水数值模拟的实际工作中，应用了一维河网模型进行洪水的模拟计算，并根据实际情况加入了蓄滞洪区调度、泄洪闸控制调度以及近年来北方河道入渗的特点等条件，计算效果良好．现对模型的理论基础和解法以及实际应用经验作一简述。     

Numerical Models for the Simulation of Overland Flow in Fields Within Surface Irrigation Systems

Discharges in a network of drainage ditches generated by intense rainfall are influenced by overland flow dynamically interacting with infiltration. Therefore a detailed estimation of the overland flow, especially in agricultural fields prepared for surface irrigation, is essential to the design of drainage ditches. In order to simulate overland flow, which in that case may be considered unsteady and one dimensional, numerical models were developed based on the numerical solution of the Saint-Venant equations, externally coupled with the Green-Ampt equation to account for the dynamic interaction between surface flow and infiltration. The numerical solution of the Saint Venant equations in their complete form (dynamic model) and in the simplified forms of the diffusion (diffusion model) and the kinematic wave equations (kinematic model) was obtained by applying the MacCormack explicit computational scheme. Overland flow models’ simulations were conducted in order to study the effect of the soil surface parameters on the hydrographs at the downstream end of the fields, as well as the accuracy of the diffusion and kinematic equations. It was found that the kinematic wave equations were unable to describe overland flow, while the diffusion model results were close to the results of the dynamic model.     

基于PINNs的圣维南方程组数据同化方法

为提高河道水位流量数据同化的智能化水平,基于物理信息神经网络(PINNs)提出了圣维南方程组的数据同化方法。采用双输出网络结构解决双输出方程组的同化问题,以模拟的实测数据作为边界条件和初始条件,通过消融试验验证网络中加入时空映射缩放和平衡权重系数对同化模型的有效性,以及所提出同化方法在部分测值缺失情况下的鲁棒性。结果表明,一维非恒定流圣维南方程组的数据同化结果与Preissmann四点隐式差分法结果一致,且随着同化断面数量的增加,所获得的同化精度也稳步提升;基于PINNs的圣维南方程组数据同化方法有效,对非恒定流模拟具有较强的适应性。     

A SPLIT-CHARACTERISTIC FINITE ELEMENT MODEL FOR 1-D UNSTEADY FLOWS

An efficient and accurate solution algorithm was proposed for 1-D unsteady flow problems widely existing in hydraulic engineering. Based on the split-characteristic finite element method, the numerical model with the Saint-Venant equations of 1-D unsteady flows was established. The assembled finite element equations were solved with the tri-diagonal matrix algorithm. In the semi-implicit and explicit scheme, the critical time step of the method was dependent on the space step and flow velocity, not on the wave celerity. The method was used to eliminate the restriction due to the wave celerity for the computational analysis of unsteady open-channel flows. The model was verified by the experimental data and theoretical solution and also applied to the simulation of the flow in practical river networks. It shows that the numerical method has high efficiency and accuracy and can be used to simulate 1-D steady flows, and unsteady flows with shock waves or flood waves. Compared with other numerical methods, the algorithm of this method is simpler with higher accuracy, less dissipation, higher computation efficiency and less computer storage.     

基于连续性扩散流的湿地表面水流动力学模型

受表面密生植被的影响,湿地表面流总是处于高阻力、低流速状态。湿地表面流的水流动力学方程中,其水流加速度项相对于地表高密度植被造成的高阻力项相比,可以忽略。由此,以水流连续性方程和忽略加速度项的水流动力学方程为基础,构建基于连续性扩散流的湿地表面流动力学模型。该模型是一个抛物型偏微分方程,相对于描述一般径流流态的圣维南双曲型偏微分方程组而言,其求解过程相对容易。模型中的表面流流量采用修正的曼宁方程描述,表面糙率采用已有经验公式,数值计算方法采用六点差分格式。模拟结果表明,该模型能够体现湿地表面流的高阻力、低流速特征。水深越浅,水流模式变化越慢,水深越大,表面流受植被阻力越小,水流模式变化越快。     

A NEW APPROACH TO THE SIMULATION OF UNSTEADY SUBCRITICAL FLOW

ＡＮＥＷＡＰＰＲＯＡＣＨＴＯＴＨＥＳＩＭＵＬＡＴＩＯＮＯＦＵＮＳＴＥＡＤＹＳＵＢＣＲＩＴＩＣＡＬＦＬＯＷ￥ＭａｏＺｅ－ｙｕ（ＤｅｐａｒｔｍｅｎｔｏｆＨｙｄｒａｕｌｉｃＥｎｇｉｎｅｅｒｉｎｇ，ＴｓｉｎｇｈｕａＵｎｉｖｅｒｓｉｔｙＢｅｉｊｉｎｇ１０００８...     

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.

     

LARGE EDDY SIMULATION FOR PLUNGING BREAKER WAVE

1 .　INTRODUCTIONInthenear shoreregion ,aswavespropagateintoshallowwater ,theprocessofshoalingleadstotheincreaseofwaveheight ,however ,thisprocesscannotcontinue ,andatacertain positionthewavebreaks .Inpractice ,breakingwavesarepow erfulagentsforgeneratingturbulence ,whichplaysanimportantroleinmostofthefluiddynamicalprocessesthroughoutthesurfzone ,suchaswavetransformation ,generationofnear shorecurrent ,diffusionofmaterials ,andsedimenttransporta tion .Manynumericalstudieshavebeenconductedt…     

Application of CLEAR-VOF method to wave and flow simulations

A two-dimensional numerical model based on the Navier-Stokes equations and computational Lagrangian-Eulerian advection remap-volume of fluid (CLEAR-VOF) method was developed to simulate wave and flow problems. The Navier-Stokes equations were discretized with a three-step finite element method that has a third-order accuracy. In the CLEAR-VOF method, the VOF function F was calculated in the Lagrangian manner and allowed the complicated free surface to be accurately captured. The propagation of regular waves and solitary waves over a flat bottom, and shoaling and breaking of solitary waves on two different slopes were simulated with this model, and the numerical results agreed with experimental data and theoretical solutions. A benchmark test of dam-collapse flow was also simulated with an unstructured mesh, and the capability of the present model for wave and flow simulations with unstructured meshes, was verified. The results show that the model is effective for numerical simulation of wave and flow problems with both structured and unstructured meshes.