Muskingum法及其分段连续演算的若干理论探讨

根据水力学原理和洪水波运动理论,通过对Muskingum法的关键参数X与特征河长、扩散波动力方程和运动波数值扩散之间关系的分析,给出了X更为全面的物理解释;证明了Muskin gum法槽蓄方程是扩散波动力方程近似的表达;指出了Muskingum法演算公式在一定条件下是扩散波方程的二阶精度解。讨论了Muskingum法的使用条件和分段连续演算的必要性;应用Z 变换方法导出了Muskingum法的分段连续演算的汇流系数公式。     

下边界条件为水位流量关系的扩散波洪水演算方法研究

经大量的理论分析和实际洪水演算表明,扩散波可较好地反映洪水波的运动特点。本文基于河道下断面的水位流量关系和连续方程的联立求解,导出了水位流量关系型的下边界条件。利用Laplace变换,得到了扩散波方程在该边界条件下的解析解。文中的求解过程表明,可利用该法进行洪水演算,关键在于如何与实际洪水结合,这个问题有待进一步地分析研究。     

具有预见期的洪水演算方法研究

利用线性运动波方程数值解的数值扩散,在一定条件下可以模拟扩散波物理扩散的观点来建立洪水演算方法,是一条不同于通过槽蓄理论建立洪水演算方法的新途径.本文采用一种新的差分格式,导出了一种新的本身具有预见期的洪水演算方法,不仅给出了用数值扩散模拟物理扩散的条件,而且给出了保证计算成果稳定性的条件.提供的计算实例表明,该法可取得具有一定预见期的令人满意的预报成果     

线性扩散波洪水演算模型研究

扩散波概念的提出至今已有近半个世纪。在前人研究的基础上,着重讨论如何把扩散波解析解用到天然河道的洪水演算中去,即通过把入流过程离散成带常系数的单位矩形入流之和,将单位线概念引入具有自由下边界的线性扩散波洪水演算模型,并给出了确定天然河道Ｃｋ和μ的实用方法。用于黄河下游６个河段的洪水演算获得了令人满意的成果。扩散波洪水演算模型,继承了水力学方法的长处,又具有水文学方法的优点,可能有罗好的开发应用前景     

扩散波水位解析解模型的应用研究

扩散波方程被广泛地应用于河道洪水演算之中。考虑下边界的回水作用以及旁侧入流的影响，建立了扩散波水位解析解模型。由该模型可知，河道任一断面处的水位变化分别由上边界水位变化所造成的影响量、下边界回水控制的影响量以及由于旁侧流量加入的影响量三项叠加而成，这三项分别由它们所对应的响应函数来描述。将该模型应用于沂河水位演算之中，得到了较高的计算精度。     

Matlab遗传算法工具GUI率定马斯京根模型参数

本文针对传统及改进马斯京根洪水演算模型,利用简单易行的Matlab遗传算法工具(gatool)GUI进行模型参数最优估计,获得不同优化准则下的模型参数,并进行检验.结果表明用Matlab遗传算法工具GUI优选改进后的马斯京根模型参数,收敛能力强、计算时间短、所得演算流量更接近实际.     

涨落差法原理浅析及其在洪水预报中的应用

从河道洪水运动波方程的有限差分解入手,推导出了涨落差法的计算公式,进而证明该计算公式为河道洪水扩散波方程二阶精度的有限差分解。该洪水预报方法参数少,计算方法简单,有预见期。实际应用表明,涨落差法的特点是实用性强,而且具有较高的洪水预报精度,但同时也存在误差累积的缺点。     

水环境模型参数识别的一种新方法

通过在格雷码遗传算法进化过程中加入单纯形搜索算子,并利用格雷码遗传算法和单纯形法所得到的优秀个体群,作为变量新的变化范围,逐步缩小搜索空间,自动向最优解收缩,提出了水环境模型参数识别的一种新方法——格雷码混合加速遗传算法(GCHAGA),给出了实施该算法的详细步骤。对GCHAGA的收敛性和全局优化性进行了理论和实例分析,并在确定河流横向扩散系数等参数识别问题中,GCHAGA得到了精度较高的全局最优解。与格雷码遗传算法(GCGA)和常规优化方法相比,GCHAGA具有精度高、速度快和适用性强等特点,是一种既可以较大概率搜索全局最优解,又能进行局部细致搜索的较好的非线性优化方法,可广泛应用于各种水环境优化问题中。     

马斯京根法的龙格—库塔数值积分解

马斯京根法(以下简称M法)是一种基于槽蓄方程和水量平衡方程的河道流量演算法。由于使用方便,精度也较高,在生产实践中得到了广泛的应用。在方法上,由整河段演算发展到了分河段连续演算;在理论上,成功地证明了M法演算方程系为对流扩散方程具有二阶精度的差分格式。从而使M法有了坚实的水力学基础,同时也使M法参数K和x有了明确的物理意义。由此可知,M法线性演算不过是对     

扩散波的时空反演与洪水实时预报技术

以扩散波方程描述天然河道中的洪水波运动规律。将数学物理反问题理论和离散反演算法与河道流量演算相结合提出了扩散波实时预报的方法。该法的特点是在求解流量场Ｑ（ｘ,ｔ）的同时反演计算扩散波波速Ｃ（ｘ,ｔ）和扩散系数Ｄ（ｘ,ｔ）,根据不断监测的新信息系列,直接利用原偏微分方程进行参数的实时校正和预报过程实时修正。     

Inverse solution to the wave equation using the Laguerre transform

An inverse solution to the 1D wave equation is obtained using the spectral Laguerre transform to find the distribution of wave velocities at some point of the medium. The problem is solved as optimization in which the function of Laguerre harmonics is minimized by the conjugate gradient or Newton’s algorithms.Reported are velocities of a wave defined by a stepwise constant function. The accuracy of the inverse solution for the Laguerre harmonics is investigated against the approximation accuracy in the boundary problem. The accuracy and efficiency of the Laguerre method are compared to those in the Fourier method.     

Accuracy and efficiency of time integration methods for 1D diffusive wave equation

The diffusive wave approximation of the Saint-Venant equations is commonly used in hydrological models to describe surface flow processes. Numerous numerical approaches can be used to solve this highly nonlinear equation. Nonlinear time integration schemes—also called methods of lines (MOL)—were proven very efficient to solve other nonlinear problems in geosciences but were never considered to deal with surface flow modeling with the diffusive wave equation. In this paper, we study the relative performance of different time and space integration schemes by comparing the results obtained with classical approaches and with nonlinear time integration approaches. The results show that (i) the integration method with a higher order in space shows high accuracy regarding an integrated indicator such as the global mass balance error but is less accurate regarding local indicators, and (ii) nonlinear time integration techniques perform better than classical ones. Overall, it seems that integration techniques combining nonlinear time integration and a low spatial order need to be considered when developing hydrological modeling tools owing to their simplicity of implementation and very good performance.     

等时叠加波动方程叠前正演

非零炮检距地震正演模拟在复杂区叠前地震资料处理和解释中有着重要意义。通常使用射线追踪法和全程波动方程法来实现这一模拟。通过提出等时叠加原理和数学检波器表达式，形成了非零炮检距地震正演的新一类方法——单程波动方程法。该方法与射线追踪法相比能保持波的动力学特征，正演结果与实际地震记录相似性好。并且在计算过程中，人工干预的程度低，操作简便。与全程波动方程法相比，该方法计算效率高，且不产生直达波、多次波等干扰，信噪比高，与目的层相对应的一次波突出，波型识别难度不大。因此，单程波动方程法特别适合于复杂油气藏反射地震资料的正、反演研究。     

A solution for the transition zone isosats in two-phase primary drainage in the presence of gravity

Primary drainage in a water-wet saturated medium in the absence of capillarity is typically a combination of shock (discontinuous) and rarefaction (continuous) waves. Using nonlinear relative permeability functions for the host fluid and the invading fluid leads to the existence of a shock wave front, and the degree of nonlinearity of the relative permeability functions has an inverse relationship with the size of the shock wave (i.e., difference of saturation between upstream and downstream of the shock wave), whereas for linear relative permeability functions, the shock wave size approaches 0. Injection of a lower-viscosity immiscible phase such as gas or solvent into a water-wet porous medium in the presence of large capillary pressure leads to development of an extended and growing saturation transition zone that follows the discontinuous shock wave front. In this article, a semianalytical solution for the position of equisaturation contours (isosats) in the transition zone in the presence of gravity is obtained for a set of linearized relative permeability functions. The capillary (diffusive) and buoyancy terms are neglected, and the generalized convective equation for mass conservation is obtained. The set of equations is then reduced to a one-dimensional steady-state differential equation through forcing the isosat formulation to obey mass conservation. This scheme allows the isosat distribution to be solved, and the case of injection into an axisymmetric geometry for a confined planar configuration is solved and presented. A finite element model was developed to demonstrate the reasonable agreement between analytical and numerical solutions.     

改进的遗传算法在单孔电磁波法中全息重现的应用

对基本遗传算法进行了改进，并运用改进的遗传算法对单孔电磁波法的数值模型进行了全息重现，计算结果与实际模型非常接近，表明改进的遗传算法能够很好地解决反演问题，同时也说明改进的遗传算法在反演问题中有着非常广阔的应用前景。     

低应变下变阻抗薄壁管桩动力响应频域解析解

管桩低应变完整性检测时,桩顶一点受到瞬态集中荷载的作用,其动力响应问题是一个三维波动问题。基于三维波动理论,建立了任意段变阻抗薄壁管桩动力响应的计算模型和波动方程,结合初边值条件,采用Laplace变换法求得了该波动方程的频域解析解,采用Fourier逆变换求得了时域响应。将计算结果与三维有限元结果进行了对比分析,解析解的计算结果和三维有限元结果较为接近,两者在入射波峰、缺陷反射峰和桩底反射峰处都较为吻合,两种方法位移响应曲线基本相同。给出了桩顶不同点的动力响应,并探讨了高频干扰问题。对变截面桩和变模量桩的动力响应特性进行了分析。     

Nearly perfectly matched layer boundary conditions for operator upscaling of the acoustic wave equation

Acoustic imaging and sensor modeling are processes that require repeated solution of the acoustic wave equation. Solution of the wave equation can be computationally expensive and memory intensive for large simulation domains. One scheme for speeding up solution of the wave equation is the operator-based upscaling method. The algorithm proceeds in two steps. First, the wave equation is solved for fine grid unknowns internal to coarse blocks assuming the coarse blocks do not need to communicate with neighboring blocks in parallel. Second, these fine grid solutions are used to form a new problem which is solved on the coarse grid. Accurate and efficient wave propagation schemes also must avoid artificial reflections off of the computational domain edges. One popular method for preventing artificial reflections is the nearly perfectly matched layer (NPML) method. In this paper, we discuss applying NPML to operator upscaling for the wave equation. We show that although we only apply NPML to the first step of this two step algorithm (directly affecting the fine grid unknowns only), we still see a significant reduction of reflections back into the domain. We describe three numerical experiments (one homogeneous medium experiment and two heterogeneous media examples) in which we validate that the solution of the wave equation exponentially decays in the NPML regions. Numerical experiments of acoustic wave propagation in two dimensions with a reasonable absorbing layer thickness resulted in a maximum pressure reflection of 3–8%. While the coarse grid acceleration is not explicitly damped in our algorithm, the tight coupling between the two steps of the algorithm results in only 0.1–1% of acceleration reflecting back into the computational domain.     

非线性波动的几个基本问题

将非线性波动理论的研究划分为观察和分析、方程建立、初边值问题、解析解和数值解、非线性波动特征以及实际应用等六个大的研究方向，详细评述了各个方向的研究情况。提出了多层介质中的非线性波传播等尚未研究的问题，发现了用通常方法求取的解析解复杂、不易应用等问题，并提出了在定性的基础上省略与已知物理特征不符项的方法来求取解析解等思路。认为介质的非线性、各向异性、多相性应统一研究。