Homotopy perturbation method for solving the space–time fractional advection–dispersion equation

In this paper we present a reliable algorithm, the homotopy perturbation method, to construct numerical solutions of the space–time fractional advection–dispersion equation in the form of a rapidly convergent series with easily computable components. Fractional advection–dispersion equations are used in groundwater hydrology to model the transport of passive tracers carried by fluid flow in a porous medium. The fractional derivatives are described in the Caputo sense. Some examples are given. Numerical results show that the homotopy perturbation method is easy to implement and accurate when applied to space–time fractional advection–dispersion equations.     

Prestack reverse-time depth migration of arbitrarily wide-angle wave equations

Based on arbitrarily wide-angle wave equations,a reverse-time propagation scheme is developed by substituting the partial derivatives of depth and time with central differences. The partial derivative of horizontal direction is replaced with high order difference. The imaging condition is computed by solving the eikonal equations. On the basis of above techniques,a prestack reverse-time depth migration algorithm is developed. The processing exam-ples of synthetic data show that the method can remove unwanted internal reflections and decrease the migration noise. The method also has the advantage of fidelity and is applicable of dip angle reflector imaging.     

Unification Of Non-Dimensional Solutions To Asymptotic Equations For Plumes Of Different Shape

A model of buoyant fluid rise is developed in aLagrangian framework. Results from the model arevalidated by comparison with laboratory and fieldexperiments. The model is sufficiently general toinclude geometries of any cross-sectional shape. Exact solutions to the asymptotic equations forcontinuous discharges from line and point sources andfor an instantaneous discharge from a point source areconsidered. Prismatic, cylindrical andspherical shapes approximate these three geometries,respectively. Accommodation of these shapes withinthe same general model allows for direct comparison. It is shown that, for discharges into a cross-flowthat may be stratified or unstratified, thenon-dimensional trajectory, thickness and dilution canbe uniquely specified using three parameters. Theseare the non-dimensional size of the source, therelative importance of the initial fluxes of momentumand buoyancy and the number of orthogonal axes throughwhich entrainment can occur. Such non-dimensionalresults are particularly useful for examining thosescenarios for which there are limited experimentaldata.     

岩石的临界孔隙度反演及横波预测(英文)

临界孔隙度模型是利用岩石的临界孔隙度来计算岩石骨架的弹性模量,岩石的临界孔隙度值受到很多因素的影响,而实际应用中通常无法获得准确的临界孔隙度值,只能选取经验临界孔隙度值,就会给岩石物理建模带来误差。本文提出了一种利用纵波速度反演岩石的临界孔隙度的方法,并且把它应用于横波预测中。实验室和测井数据应用结果表明本文提出的方法可以降低以往选取经验值带来的不确定性,并且能够为横波预测提供准确的临界孔隙度值,提高了横波预测的精度。     

Analytical modelling of a large‐scale dynamic testing facility

An analytical model, which aims at reproducing the response of a large‐scale dynamic testing facility, that is a system composed of the specimen/shaking table/reaction‐mass/airbags/dampers/soil is developed. The Lagrangian of the system is derived, under the assumption of large displacements and rotations. A set of four nonlinear differential equations is obtained and solved with numerical methods. Preliminary verifications of the derived model are carried out by reproducing both well‐known results in the literature as well as those of a lumped model employed in the design of an existing dynamic testing facility. The case‐study for validating the nonlinear equations of motion is the shaking table of the EUCENTRE Laboratory. Copyright © 2011 John Wiley & Sons, Ltd.     

Numerical simulation of irregular wave overtopping against a smooth sea dike

Based on the filtered Navier-Stokes equations and Smagorinsky turbulence model,a numerical wave flume is developed to investigate the overtopping process of irregular waves over smooth sea dikes.Simulations of fully nonlinear standing wave and regular wave’s run-up on a sea dike are carried out to validate the implementation of the numerical wave flume with wave generation and absorbing modules.To model stationary ergodic stochastic processes,several cases with different random seeds are computed for each specified irregular wave spectrum.It turns out that the statistical mean overtopping discharge shows good agreement with empirical formulas,other numerical results and experimental data.     

Wave height transformation and set-up between a submerged permeable breakwater and a seawall

In this study,we investigated wave transformation and wave set-up between a submerged permeable breakwater and a seawall.Modified time-dependent mild-slope equations,which involve parameters of the porous medium,were used to calculate the wave height transformation and the mean water level change around a submerged breakwater.The numerical solution is verified with experimental data.The simulated results show that modulations of the wave profile and wave set-up are clearly observed between the submerged breakwater and the seawall.In contrast to cases without a seawall,the node or pseudo-node of wave height evolution can be found between the submerged breakwater and the seawall.Higher wave set-up occurs if the nodal or pseudo-nodal point appears near the submerged breakwater.We also examined the influence of the porosity and friction factor of the submerged permeable breakwater on wave transformation and set-up.     

Evaluation of gene expression programming approaches for estimating daily evaporation through spatial and temporal data scanning

Evaporation of water from free water surfaces or from land surfaces is one of the main components of the hydrological cycle, and its occurrence is governed by various meteorological and physical factors. There is a multitude of models developed for estimating daily evaporation values by using weather data. This paper evaluates a Gene Expression Programming (GEP) model for estimating evaporation through spatial and temporal data scanning techniques. It is by using ‘leave‐one‐out’ procedures, a complete scan of the possible train and test set configurations is carried out according to temporal and spatial criteria. Comparison of the GEP model with empirical‐physical models shows that daily evaporation values computed by the GEP model are more accurate. Further, local calibration of the GEP model may not be needed, if enough climatic data are available at other stations. The performance of the GEP model fluctuates throughout the period of study and between stations. A suitable assessment of the model should consider a complete temporal and/or spatial scan of the data set used. Copyright © 2012 John Wiley & Sons, Ltd.     

基于内变量和张量函数表示定理的本构方程

针对各向同性材料,基于张量函数表示定理,建立了本构关系的张量不变性表示,其中,3个不可约基张量取决于应力的0～2次幂,且相互正交,3个系数由塑性应变增量和应力的不变量表示。基于塑性应变增量的不变量定义内变量,本构关系归结为确定内变量的演化。使用张量函数表示定理,给出了内变量演化方程的一般表达式,它取决于应力不变量的增量,因而与主轴旋转无关。讨论了如何根据试验资料和引入适当的假定,确定具体的演化方程。通过与塑性势理论和多重屈服面理论进行比较,表明所建模型是这些理论的最一般表示,且简捷直观、使用方便。     

饱和地基上条形弹性基础的摇摆振动

基于Biot动力方程,研究了饱和均质弹性半空间上弹性条形基础的摇摆振动问题。通过Fourier积分变换求解了饱和土的动力控制方程,然后结合基础底部为混合边界的条件得到了弹性条形基础的摇摆振动对偶积分方程,利用正交多项式将对偶积分方程转化为求解一组线性代数方程组,同时利用复合Simpson法则,得到了动力柔度系数的表达式,通过算例得出了不同参数时地基动力柔度系数随无量纲频率的关系曲线。