求解对流占优地下水水质模型的有限元高精度广义迎风单元均衡格式及应用

根据水质模型的具体特点，对不同的方程采用不同方法，水流问题用有限元法；对流弥散方程先用算子分裂的方法分解为两个方程，即对流方程和弥散方程，前者用高精度广义迎风格式求解，对弥散方程则采用多单元均衡格式法求解，最后合成为高精度广义迎风均衡格式求出溶质浓度。通过对数值实验例子的计算和实验溶质迁移的模拟，可以看出在求解对流弥散定解问题时，广义迎风均衡格式克服了有限元数值波动和浓度出现负值的问题，与有限元相比有较大改进。     

基于NAD算法的声波方程时间四阶差分解法

波动方程数值模拟是研究地震波传播机理的重要工具,有限差分求解波动方程是当前地震波数值模拟的主要方法之一。当地下介质中的地震波速度较低或地震波高频成分丰富时,常规有限差分技术常常产生严重的数值频散误差,这种误差会降低数值模拟的精度,影响对地震波传播机理的分析。为压制地震波数值模拟时产生的数值频散误差,提高波场模拟精度,提出了基于NAD算子的时间四阶精度波动方程差分格式。根据对应的差分格式,分析了该差分格式的数值频散关系。与常规四阶精度差分算法的频散曲线相比,基于NAD时间四阶精度差分方法不但能够实现时间频散的有效压制,同时其基于更多网格点的位移分量和位移梯度分量空间微分求解方法还能够实现空间频散的有效压制。另外在相同模型条件下,基于NAD算法的声波方程时间四阶差分解法可采用大网格对模拟空间进行差分离散,减少网格数,提高计算效率。     

非饱和渗流模拟中非均匀空间网格的改进方法

Richards方程在非饱和渗流模拟及其他相关领域应用广泛。在数值求解过程中,可以采用有限差分方法进行数值离散并迭代求解,为了获得较可靠的数值解,常规的均匀网格空间步长往往是较小的。在一些不利数值条件下,如入渗于干燥土壤,迭代计算费时甚至精度也不能得到很好改善。因此,文章提出Chebyshev空间网格改进方法,结合有限差分方法对Richards方程进行数值离散以获得线性方程组,并通过经典的Picard迭代方法进行迭代求解线性方程组以得到Richards方程的数值解。通过均质土和分层土2个不利情况下的非饱和渗流算例,又结合模型解析解和软件Hydrus-1D,对比研究了改进网格方法与均匀网格方法获得数值解的精度。结果表明,提出的Chebyshev网格方法相较于传统的均匀网格,可以在较少的节点数下获得较高的数值精度,又具有较小的计算开销,有较好的应用前景。     

Laplace方程Cauchy问题的一种数值解法

研究了Laplace方程Cauchy问题的数值求解，该问题是一个典型的病态问题。利用格林（Green）公式将Laplace方程的Cauchy问题转化为Hausdorff矩问题。本文利用一种新方法，即矩问题的积分方程方法，求解矩问题，设计了二维Laplace方程Cauchy问题稳定的算法，给出了近似解的误差估计，并对二维Cauchy问题进行了数值模拟。     

一维泥石流的静动力阻力特征研究及数值模拟

泥石流是山区多发的一种地质灾害,它的发生和发展威胁着人们的生命和财产安全,影响着人们的正常生活,因而需要加强对其发生和发展过程的研究。结合泥石流的动力模型方程采用数值模拟方法再现泥石流发生和发展的过程,是研究和预测模拟泥石流灾害的有效手段。目前的动力模型方程大多只关注动力过程,却忽视了静动力过程的统一,这将导致在一些情况下产生错误的结果。本文研究了一维泥石流的静动力阻力特征,通过修正泥石流动力学方程的阻力项,得到了具有静动力统一特征的模型方程。并以Roe格式的近似Riemann解为基础,采用MUSCL线性重构方法建立了具有较高精度和分辨率的有限体积数值求解。具体算例的数值验证表明,方程阻力项的修正是合理的,所建立的数值求解也是稳定和有效的。     

声波方程隐式高阶有限差分数值模拟

推导了声波方程空间二阶导数的隐式求解公式及差分系数的求解方法,讨论了该方法的数值频散特征。利用该方法分别对均匀介质及Marmousi模型进行了数值模拟,将其结果与传统的显式差分格式的模拟结果进行了对比分析。结果表明:该方法较传统的显式求解方法具有更低的数值频散、更高的计算精度。      

标量拟解析近似方法模拟立方体的异常电场

拟解析近似方法是一种求解积分方程的一种近似方法,它可以处理强散射或者大扰动的电磁散射问题,在计算过程中避免了传统微分数值方法解决问题时所遇到的大型矩阵或大型代数方程组的求解。孙建国[5]将其引入直流电场的积分方程中,并给出了求解异常电场积分方程的标量拟解析近似公式。在以前的研究中,已经验证了均匀场中异常球体的拟解析近似解的精度,这里对均匀场中的立方体异常体进行数值模拟,得到了直流电场中异常立方体模型的标量拟解析近似解。由于复杂地电模型可以用立方体的组合进行模拟,因此对立方体异常电场拟解析近似解的研究,为三维直流电场中复杂地电模型的快速正反演模拟打下了基础。     

利用时间分裂的错格伪谱法模拟地震波在基于改进BISQ模型的双相介质中的传播

改进的BISQ(Biot-Squirt)模型中各参数具有明确的物理意义和可实现性,在不引入特征喷流长度的情况下可将Biot流动和喷射流动两种力学机制有机地结合起来;而高精度的地震波场数值模拟技术是研究双相介质地震波传播规律的重要手段。本文从本构方程、动力学方程和动力学达西定律出发,推导了基于改进BISQ模型的双相各向同性介质的一阶速度--应力方程组;采用时间分裂错格伪谱法求该方程组的数值解,模拟半空间及层状双相介质中的地震波场。数值模拟结果表明:①与传统方法相比,时间分裂错格伪谱法波场数值模拟的精度更高,压制网格频散效果更好;②在非黏滞相界情况下,慢纵波呈传播性,而在黏滞相界情况下,慢纵波呈扩散性,以静态模式出现在震源位置;③双相介质分界面处,各类波型复杂的反射透射规律可由数值模拟结果清晰展现。     

佳木斯市地下水水量水质模型

佳木斯市是一个以开采地下水为主要供水水源的城市.本文根据当地的水文地质条件,建立了佳木斯市的地下水的水量水质模型.用有限元法求解水量模型进行地下水资源评价.用特征有限元法求解水质模型进行地下水污染预测,该方法在求解对流一弥散方程时能有效地消除数值弥散和数值振荡,精度较高.为使该方法付诸实施,文中也提出了当利用特征有限元法求解时确定运动水质点所属单元的方法.     

基于非结构混合网格求解二维浅水方程的一种数值方法

复杂边界下的流场数值模拟常基于非结构化网格进行求解,建立一种在非结构混合网格上求解水深平均的二维浅水方程的模型,以便精确模拟复杂边界、提高计算效率。该模型时间项离散采用隐格式使得模型具有较好的稳定性,对流项和扩散项分别采用总变差减小(Total Variation Diminishing,TVD)格式和构造辅助点的方法来离散,同时采用水深平均的标准k-ε模型来封闭湍流模型。选用两个经典验证算例检验模型,计算结果表明,基于非结构混合网格开发的模型具有较高的精度,且收敛性能较好。     

用格子波耳兹曼方法模拟双重孔隙介质中的流体迁移

作者在本文中介绍了基于格子波耳兹曼模型的双重孔隙介质中流体运移的数值模拟计算方法。我们从格子波耳兹曼碰撞模型出发，利用格子波耳兹曼方程、Chapman-Enskog展开，以及多尺度技术，得到了描述双重孔隙介质中流体迁移的二维扩散方程。利用格子气自动机方法计算该扩散方程，实现了对双重孔隙介质中流体运移过程的数值模拟仿真。数值实验表明，我们所使用的方法正确、有效。     

A pore-scale numerical model for non-Darcy fluid flow through rough-walled fractures

This paper aims at developing a pore-scale numerical model for non-Darcy fluid flow through rough-walled fractures. A simple general relationship between the local hydraulic conductivity and the flow velocity is proposed. A new governing equation for non-Darcy fluid flow through rough-walled fractures is then derived by introducing this relationship into the Reynolds equation. Based on the non-linear finite element method, a self-developed code is used to simulate the non-Darcy fluid flow through fractures. It is found that the macroscopic results obtained by the numerical simulation agree well with the experimental results. Furthermore, some interesting experimental observations can be reproduced.     

Finite element modelling of three-phase flow in deforming saturated oil reservoirs

A numerical simulation is presented for three-dimensional three-phase fluid flow in a deforming saturated oil reservoir. The mathematical formulation describes a fully coupled governing equation systen which consists of the equilibrium and continuity equations for three immiscible fluids flowing in a porous medium. An elastoplastic soil model, based on a Mohr–Coulomb yield surface, is used. The finite element method is applied to obtain simultaneous solutions to the governing equations where displacement and fluid pressures are the primary unknowns. The final discretized equations are solved by a direct solver using fully implicit procedures. The developed model is used to investigate the problems of three-phase fluid flow in a deforming saturated oil reservoir.     

Hydro-micromechanical modeling of wave propagation in saturated granular crystals

Biot theory predicts wave velocities in a saturated granular medium using the pore geometry, viscosity, densities, and elastic moduli of the solid skeleton and pore fluid, neglecting the interaction between constituent particles and local flow, which becomes essential as the wavelength decreases. Here, a hydro-micromechanical model, for direct numerical simulations of wave propagation in saturated granular media, is implemented by two-way coupling the lattice Boltzmann method (LBM) and the discrete element method (DEM), which resolve the pore-scale hydrodynamics and intergranular behavior, respectively. The coupling scheme is benchmarked with the terminal velocity of a single sphere settling in a fluid. In order to mimic a small amplitude pressure wave entering a saturated granular medium, an oscillating pressure boundary on the fluid is implemented and benchmarked with the one-dimensional wave equation. The effects of input waveforms and frequencies on the dispersion relations in 3D saturated poroelastic media are investigated with granular face-centered-cubic crystals. Finally, the pressure and shear wave velocities predicted by the numerical model at various effective confining pressures are found to be in excellent agreement with Biot analytical solutions, including his prediction for slow compressional waves.     

裂隙含流体、气体各向异性介质波场数值模拟

由目前普遍被勘探地震工作者承认的Ｈｕｄｓｏｎ本构方程出发，首先讨论了裂隙含流体、气体各向异性介质一维二、三分量波动方程，然后用有限元方法进行了波场数值模拟。该研究有益于加深对地震波在裂隙含流体、气体各向异性介质中传播规律的认识。     

Laboratory validation of lattice Boltzmann method for modeling pore-scale flow in granular materials

Characteristics of fluid flow through various engineering structures, such as granular filters and asphalt pavements, influence their design life. Numerical simulation of fluid flow is useful for evaluating the hydraulic characteristics of these materials. Among various techniques, the lattice Boltzmann (LB) method is widely accepted due to the ease of implementing boundary conditions and the numerical stability in a wide variety of flow conditions. It has proven to be extremely efficient in the simulation of fluid flow through the complex geometries of granular materials. In this study, two-dimensional and three-dimensional LB models were developed to represent pore-scale monophasic Newtonian incompressible fluid flow in granular materials. Three-dimensional geometries of compacted aggregates and asphalt specimens were generated from X-ray Computed Tomography technique and used as input for the LB model. The accuracy of the models was verified by comparing the results with analytical solutions of simple geometries and hydraulic conductivity measurements on the compacted aggregates and hot mix asphalt specimens. The results of LB simulations were in excellent agreement with those obtained from analytical calculations and laboratory measurements.     

LBM–DEM modeling of fluid–solid interaction in porous media

Three porous media flow problems, in which the fluid mechanical interactions are critical, are studied in a mesoscopic–microscopic coupling system. In this system, fluid flow in the pore space is explicitly modeled at mesoscopic level by the lattice Boltzmann method, the geometrical representation and the mechanical behavior of the solid skeleton are modeled at microscopic level by the particulate distinct element method (DEM), and the interfacial interaction between the fluid and the solids is resolved by an immersed boundary scheme. In the first benchmark problem, the well‐known and frequently utilized Ergun equation is validated in periodic particle and periodic pore models. In the second problem, the upward seepage problem is simulated over three stages: The settlement of the column of sphere under gravity loading is measured to illustrate the accuracy of the DEM scheme; the system is solved to hydrostatic state with pore space filled with fluid, showing that the buoyancy effect is captured correctly in the mesoscopic–microscopic coupling system; then, the flow with constant rate is supplied at the bottom of the column; the swelling of the ground surface and pore pressure development from the numerical simulation are compared with the predictions of the macroscopic consolidation theory. In the third problem, the fluid‐flow‐induced collapse of a sand arch inside a perforation cavity is tested to illustrate a more practical application of the developed system. Through comparing simulation results with analytical solutions, empirical law and physical laboratory observations, it is demonstrated that the developed lattice Boltzmann–distinct element coupling system is a powerful fundamental research tool for investigating hydromechanical physics in porous media flow. Copyright © 2012 John Wiley & Sons, Ltd.     

Limitations of Lattice Boltzmann Modeling of Micro‐Flows in Complex Nanopores

The multiscale transport mechanism of methane in unconventional reservoirs is dominated by slip and transition flows resulting from the ultra-low permeability of micro/nano-scale pores, which requires consideration of the microscale and rarefaction effects. Traditional continuum-based computational fluid dynamics (CFD) becomes problematic when modeling micro-gaseous flow in these multiscale pore networks because of its disadvantages in the treatment of cases with a complicated boundary. As an alternative, the lattice Boltzmann method (LBM), a special discrete form of the Boltzmann equation, has been widely applied to model the multi-scale and multi-mechanism flows in unconventional reservoirs, considering its mesoscopic nature and advantages in simulating gas flows in complex porous media. Consequently, numerous LBM models and slip boundary schemes have been proposed and reported in the literature. This study investigates the predominately reported LBM models and kinetic boundary schemes. The results of these LBM models systematically compare to existing experimental results, analytical solutions of Navier-Stokes, solutions of the Boltzmann equation, direct simulation of Monte Carlo (DSMC) and information-preservation DSMC (IP_DSMC) results, as well as the numerical results of the linearized Boltzmann equation by the discrete velocity method (DVM). The results point out the challenges and limitations of existing multiple-relaxation-times LBM models in predicting micro-gaseous flow in unconventional reservoirs.     

基于等效介质理论的碳酸盐岩储层地震数值模拟

综合考虑碳酸盐岩储层孔隙度、孔隙类型对储层物性参数的影响,对常规的Xu-White模型等效介质理论进行了改进,采用K-T理论增加多种不同类型的孔隙(如粒间孔隙、刚性孔隙、裂隙等),得到了一种新的改进的Xu-White模型等效介质理论,并提出了一套新的适用于碳酸盐岩储层的地震数值模拟方法。该方法首先采用改进的Xu-White模型等效介质理论,来计算碳酸盐岩储层的等效参数,将各向异性的储层转换为均匀介质;然后再采用声学波动方程进行地震数值模拟。模型试验的结果表明,该方法不仅计算效率高,而且可以得到高信噪比的模拟记录,其主要地层的反射波场特征与弹性波方程数值模拟完全一致,是一种简单高效的适用于碳酸盐岩储层的地震数值模拟方法。     

基于常Q模型的分数阶粘弹介质数值模拟方法

基于常Q模型的解耦分数阶拉普拉斯算子粘滞波动方程,可以分开模拟振幅衰减和相位错动。但该方程拉普拉斯算子的阶数是随空间变化的,因此数值求解存在一定困难。这里基于截断的泰勒展开,经过一系列近似,推导出拉普拉斯算子的阶数与空间无关的解耦分数阶粘滞弹性波动方程。采用中心差分计算时间导数,使用交错网格伪谱法计算空间导数。数值算例表明,新的方程在处理非均匀介质时具有精度高,计算简便的优点。