基于扩散波和双向波的感潮河段水位演算研究

针对感潮河段水流情势复杂、不易获得河道地形资料的问题,考虑充分应用已有水位实测资料,采用扩散波和双向波方法建立感潮河段水位演算模型,扩散波方法以水位为研究对象,求解线性扩散波方程定解问题的解析解,双向波方法将洪水过程分解为上游洪水波和下游潮水波,分别应用水位演算方法将这两种波独立演算至计算断面,再将其演算结果进行线性叠加得到计算断面的水位过程.将上述两类模型应用于新沂河和楠溪江感潮河段水位演算中,模拟精度良好.     

溃坝洪水波在天然梯级水库中的传播

将双曲型方程的ＴＶＤ和ＥＮＯ格式推广于一维浅水方程组，构造了一种守恒算法，将其用于天然河溃坝波传播计算，算得结果和解析解符合好，分辨率高，实际天然梯级水库溃坝洪水波传播的数值模拟表明该格式稳定，适应性强。     

多支流河道洪水演算方法的研究

本文借助虚拟单元河段概念研制了适用于多支流河道洪水演算的水力学方法。该法基于描述河道水流运动的St.Venant方程组的数值解,可以解决水文学洪水演算法不能解决的一些问题。     

扩散波方程的一种数值计算方法

根据扩散波的基本方程，推导仅含水位情况下扩散波的特殊方程；采用控制体积法，有限元法，导出这两种方法的扩散波数值计算模型，并证明在一定条件下两者的一致性，地非一隐式方程组给出牛顿迭代法的一性方程组及一般的解法     

扩散波模型在城市坡面汇流中的应用

为分析一维扩散波水动力方程在模拟城市地表降雨径流过程中的可行性,针对典型概化城市流域,采用一维扩散波水动力方程的数值解法模拟了一短历时强降雨事件,并对比SWMM模型模拟结果与扩散波模型模拟结果。结果表明,扩散波模型可以较好地体现降雨作用下地表径流过程的动力特点,但无法适用于过缓的地表坡度,解释了两者连续性方程的差异对模拟结果的影响,最后分析了扩散波模型下边界条件的确定方法。研究成果可为城市坡面汇流模拟提供参考。     

河道洪水演算的MC-RCM模型及其比较研究

MC-RCM模型是一种在马斯京根法的基础上引入水位流量曲线的洪水演算方法,为进一步验证MC-RCM模型在实际河段中及不同演算条件下的精确性,分别采用试错法、最小二乘法、马斯京根—康吉法及MC-RCM模型四种演算方法对长江李庄至泸县段的10例天然洪水进行流量演算分析,并引入五种评价指标,比较了MC-RCM模型与其他演算方法在不同演算时段下流量演算精度、演算可靠性、演算洪峰流量精度等方面的优劣。结果表明,MC-RCM模型在流量演算精度、演算可靠性、演算洪峰流量精度上相比其他方法均具有一定优势,且在较长演算时段中优势更为明显。因此,MC-RCM模型作为河道洪水演算的可靠方法,可在水文资料充分的情况下修正或校验马斯京根法的演算成果。     

洪水扩散波实时水位预报模型及其算法

运用洪水扩散波理论建立了河道水水位实时预报模型，改进了Ｔ．Ｋ．Ｆｏｒｔｃａｃｎｅ时变遗忘因子最不二乘估计时变参数的递推算法，经淮河河段的洪水实时水模拟预报应用，表明所建立的模型和实时递推算法对于河道洪水水位短期预报是有效的。     

马斯京根模型变参数洪水演算

针对在已有的河道洪水演算中通常不考虑场次洪水过程中不同时段流量下的马斯京根模型参数差异性的问题,通过分析马斯京根模型参数的物理意义,发现时段流量不同时参数为变化的,进而基于富拉尔基-江桥段的洪水资料,率定了不同时段流量下的马斯京根模型参数,对洪水进行了变参数动态演算,并与以洪峰流量分级进行分类演算的方法做了对比分析。结果表明,该方法明显提高了洪水演算的精度,具有可行性。     

洪水预报误差在河道演算中的传递分析

考虑入流过程洪水预报误差的随机性,基于Nash汇流理论建立了河道洪水演算的随机模型,在预报误差近似独立且服从正态分布时,推导了出流过程的计算公式和方差函数,定义了洪水预报误差随机性的传递函数,分析了洪水预报误差的随机性在河道洪水演算过程中的传递特征。实例应用结果表明,上游入流的洪水预报误差经过河槽调蓄或经由Nash汇流模型演算后,其不确定性会大为降低。同时,根据建立的河道洪水演算随机模型,还可以确定出流过程的置信区间,从而为估计河道防洪控制断面可能出现的风险提供理论依据。     

基于随机分形搜索算法的马斯京根模型参数优选

马斯京根模型在河道洪水演算中发挥着重要作用,该模型参数优选对提高洪水演算准确性至关重要。提出利用随机分形搜索算法(SFS)解决非线性马斯京根模型参数优选问题,同时将混沌序列替代SFS更新操作中的随机数。对算例进行洪水演算仿真分析并与多种优化算法比较,结果表明,随机分形搜索算法对非线性马斯京根法模型参数优选问题求解行之有效,且算法实施过程简便、参数解算精度高。     

Analytical solution of the advection–diffusion transport equation using a change-of-variable and integral transform technique

This paper presents a formal exact solution of the linear advection–diffusion transport equation with constant coefficients for both transient and steady-state regimes. A classical mathematical substitution transforms the original advection–diffusion equation into an exclusively diffusive equation. The new diffusive problem is solved analytically using the classic version of Generalized Integral Transform Technique (GITT), resulting in an explicit formal solution. The new solution is shown to converge faster than a hybrid analytical–numerical solution previously obtained by applying the GITT directly to the advection–diffusion transport equation.     

滁河流域洪水计算模型探讨

本文采用水文学和水力学相结合的途径,建立了滁河流域洪水计算模型,并率定了模型参数。在多支流河道洪水演算方法的研制中,本文建议用虚设单元河段法考虑支流交汇、分洪蓄洪和堰闸控制对洪水波运动的影响。本模型计算方便,精度令人满意。本文提出的建模思想具有较好的通用性。     

一维—二维耦合的水库下游地区洪水演进数学模型及应用

针对水库下游地区河道洪水与漫堤洪水模拟需求,建立了一维—二维耦合的洪水演进数学模型。一维模型采用Pressimann格式离散求解,二维模型采用能够适应复杂几何形状和多种流态的Osher格式求解,一维—二维连接处采用堰流公式实现水流交互。应用该模型模拟白溪流域2015年"苏迪罗"台风实际洪水,可得到洪水在计算区域的演进过程和淹没情况。对比模拟结果与实际情况可知,该模型计算合理、准确,计算结果可为防汛部门防洪预案制定、防汛调度决策提供技术支撑。     

Propagation Characteristics of Elasto-Thermodiffusive Surface Waves in Semiconductor Material Half-Space

The paper is aimed at an investigation of the propagation of elasto-thermodiffusive (ETN) surface waves in homogenous isotropic, thermally conducting, semiconductor material half-space with relaxation of heat and charge carrier fields. Secular equations, in isolated mathematical conditions and compact form, for the thermoelastic diffusive surface waves in semiconducting material half-space are derived. Some particular forms of the general secular equation are also deduced and investigated. The secular equations for thermoelastic (ET) and elastodiffusive (EN) surface waves have been obtained and discussed as special cases. The surface displacements during the wave propagation have also been obtained and discussed. The paths of surface particles of ETN, ET, and EN surface waves are found to be elliptical in nature. Numerical solution of various secular equations and other relevant relations is carried out for silicon (Si) semiconductor material with the help of functional iteration numerical technique. In order to illustrate and compare the analytical results, the dispersion curves, attenuation coefficient, and specific loss profiles of the waves are computed and presented graphically.     

Simulation of propagating fronts in geothermal reservoirs with the implicit Leonard total variation diminishing scheme

Geothermal reservoir engineering requires accurate numerical solution of the advective–diffusive transport equations for strong advective flows of multiphase nonisothermal fluids. Conventional interface weighting schemes such as upstream weighting cause numerical dispersion. Numerical dispersion can be reduced by grid refinement, but this increases execution times and computer memory requirements. As an alternative, higher-order differencing schemes can be used to reduce numerical dispersion, but they often lead to spurious oscillations. These limitations have led to the development of higher-order schemes called total variation diminishing (TVD) schemes. For geothermal reservoir engineering, these schemes must be capable of handling flows that may not be physically total variation diminishing. We have implemented TVD schemes into the implicit geothermal reservoir simulator TOUGH2. We verify the Leonard TVD (LTVD) scheme by comparison to an analytical solution for two-dimensional flow and transport. The LTVD scheme reduces numerical dispersion for tracer transport in a two-phase geothermal reinjection problem. One-dimensional simulations show that the LTVD scheme works well even if the saturation variation increases with time. Because the location of the phase front is strongly coupled to temperature, phase front propagation is sensitive to grid resolution insofar as it affects the temperature field. Phase front propagation in a composite porous medium Buckley–Leverett flow problem, where phase saturations increase upon encountering a second medium, are slightly more accurate for the LTVD scheme as compared to upstream weighting. We find that the LTVD scheme only performs well if the weighting and limiter are applied to saturation rather than to relative permeability. While there is some increased computational cost with the LTVD scheme due to increased linear equation solution time and smaller time-step size, the LTVD scheme is a practical and robust method for reducing numerical dispersion in complex flow problems relevant to geothermal reservoir engineering.     

Wave concepts in the theory of heatLe concept d'ondes en theorie de la chaleurWillenkonzept in der wärme theorieBoлнoвыэ лpэдcтaвлeния в тeopии тeплa

The known fundamental solution of the heat-conduction equation in the form of Poisson's integral is obtained by summing-up particular similarity solutions derived with the help of a similarity group. As these similarity solutions do not satisfy the initial data, then the integral condition is obtained from which the arbitrary constant of a general solution is determined. Then the solution in the form of Poisson's integral is shown to satisfy approximately the initial condition in the form of the discontinuous step function approximating the initial function. This is one of the drawbacks of the fundamental solution of the classical heat-conduction equation.The paradox on an infinite “heat propagation velocity” is discussed.Analysing the isotherm behaviour and using Green's theorem, the general non-linear wave equation is derived here in which the speed of isotherm propagation along the normal is used as an experimental parameter. The relationship between this speed and thermal diffusivity is shown. The different particular cases of this wave equation are studied. Some wave equation solutions are shown to correspond to those of the non-linear parabolic equation.Then, the derivation is given of the wave heat conduction equation from the point of view of molecular kinetic considerations. The conception on time relaxation is generalized using the Maxwell method and taking into account the correlation between components of a heat velocity of atoms of molecules.     

Analysis and solution of the ill-posed inverse heat conduction problem

The inverse conduction problem arises when experimental measurements are taken in the interior of a body, and it is desired to calculate temperature and heat flux values on the surface. The problem is shown to be ill-posed, as the solution exhibits unstable dependence on the given data functions. A special solution procedure is developed for the one-dimensional case which replaces the heat conduction equation with an approximating hyperbolic equation. If viewed from a new perspective, where the roles of the spatial and time variables are interchanged, then an initial value problem for the damped wave equation is obtained. Since the formulation is well-posed, both analytic and numerical solution procedures are readily available. Sample calculations confirm that this approach produces consistent, reliable results for both linear and nonlinear problems.