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1.
This paper presents a new approach to a local time-space grid refinement for a staggered-grid finite-difference simulation
of waves. The approach is based on approximation of a wave equation at the interface where two grids are coupled. As no interpolation
or projection techniques are used, the finite-difference scheme preserves second order of convergence. We have proved that
this approach is low-reflecting, the artificial reflections are about 10 − 4 of an incident wave. We have also shown that if a successive refinement is applied, i.e. temporal and spatial steps are refined
at different interfaces, this approach is stable. 相似文献
2.
殷文 《吉林大学学报(地球科学版)》2008,38(1):144-151
在弹性波频率空间域有限差分数值模拟方面,差分网格及边界条件是影响弹性波模拟成功与否的关键,为了压制数值模拟中的网格频散,采用25点有限差分算子,建立了有限差分矩阵方程,且借鉴匹配层衰减边界条件思想,设计了弹性波频率空间域有限差分数值模拟算法。由于采用高阶有限差分法来提高差分格式的精度,将会导致计算量显著增加,为此,对频率空间域有限差分弹性波数值模拟方法,采用流水线技术与分治策略进行了并行算法研究,提高了计算效率,使得在合理的计算时间内更精确地模拟弹性波在弹性介质中的传播过程。 相似文献
3.
为了解决长时间正演模拟的不稳定性问题, 实现天然地震波场长时间数值模拟.在高阶有限差分数值模拟的基础上, 给出了多轴向完全匹配吸收边界(M-PML)二维划分方式, 讨论了M-PML吸收边界转换系数P的取值对其吸收能力与截断误差对数值模拟有效信号的影响.实现了二维弹性波高阶有限差分的长时间数值模拟.采用2013年12月16日湖北省巴东县地震及余震信息, 对该地震数据进行了数值模拟, 并与武汉、秭归两台站数据进行了分析和讨论, 验证该正演模拟方法的正确性和有效性.为天然地震波场传播规律、成像和震相识别及震源定位等研究提供了基础. 相似文献
4.
Yudi Liu 《Computational Geosciences》2008,12(2):245-253
Starting from nonhydrostatic Boussinesq approximation equations, a general method is introduced to deduce the dispersion relationships.
A comparative investigation is performed on inertia-gravity wave with horizontal lengths of 100, 10 and 1 km. These are examined
using the second-order central difference scheme and the fourth-order compact difference scheme on vertical grids that are
currently available from the perspectives of frequency, horizontal and vertical component of group velocity. These findings
are compared to analytical solutions. The obtained results suggest that whether for the second-order central difference scheme
or for the fourth-order compact difference scheme, Charny–Phillips and Lorenz (L) grids are suitable for studying waves at
the above-mentioned horizontal scales; the Lorenz time-staggered and Charny–Phillips time staggered (CPTS) grids are applicable
only to the horizontal scales of less than 10 km, and N grid (unstaggered grid) is unsuitable for simulating waves at any
horizontal scale. Furthermore, by using fourth-order compact difference scheme with higher difference precision, the errors
of frequency and group velocity in horizontal and vertical directions produced on all vertical grids in describing the waves
with horizontal lengths of 1, 10 and 100 km cannot inevitably be decreased. So in developing a numerical model, the higher-order
finite difference scheme, like fourth-order compact difference scheme, should be avoided as much as possible, typically on
L and CPTS grids, since it will not only take many efforts to design program but also make the calculated group velocity in
horizontal and vertical directions even worse in accuracy. 相似文献
5.
This paper presents a finite-volume method for hexahedral multiblock grids to calculate multiphase flow in geologically complex reservoirs. Accommodating complex geologic and geometric features in a reservoir model (e.g., faults) entails non-orthogonal and/or unstructured grids in place of conventional (globally structured) Cartesian grids. To obtain flexibility in gridding as well as efficient flow computation, we use hexahedral multiblock grids. These grids are locally structured, but globally unstructured. One major advantage of these grids over fully unstructured tetrahedral grids is that most numerical methods developed for structured grids can be directly used for dealing with the local problems. We present several challenging examples, generated via a commercially available tool, that demonstrate the capabilities of hexahedral multiblock gridding. Grid quality is discussed in terms of uniformity and orthogonality. The presence of non-orthogonal grid and full permeability tensors requires the use of multi-point discretization methods. A flux-continuous finite-difference (FCFD) scheme, previously developed for stratigraphic hexahedral grid with full-tensor permeability, is employed for numerical flow computation. We extend the FCFD scheme to handle exceptional configurations (i.e. three- or five-cell connections as opposed to the regular four), which result from employing multiblock gridding of certain complex objects. In order to perform flow simulation efficiently, we employ a two-level preconditioner for solving the linear equations that results from the wide stencil of the FCFD scheme. The individual block, composed of cells that form a structured grid, serves as the local level; the higher level operates on the global block configuration (i.e. unstructured component). The implementation uses an efficient data structure where each block is wrapped with a layer of neighboring cells. We also examine splitting techniques [14] for the linear systems associated with the wide stencils of our FCFD operator. We present three numerical examples that demonstrate the method: (1) a pinchout, (2) a faulted reservoir model with internal surfaces and (3) a real reservoir model with multiple faults and internal surfaces. 相似文献
6.
采用高精度交错网格有限差分法,建立了在起伏地表条件下瑞雷面波数值模拟的自由边界条件,通过对倾斜二层模型模拟的结果与解析解对比,二者完全一致,由此证明了起伏地表下瑞雷面波数值模拟的正确性。在此基础之上,模拟并分析了小凸起与小凹陷模型条件下,瑞雷面波的波场传播特征。通过分析得出瑞雷面波在这二种地形传播时,都存在反射、波型转换,以及能量再分配。因此,在起伏地表条件下,利用瑞雷面波进行勘探时要考虑起伏地表对瑞雷面波波场的影响。 相似文献
7.
We simulate direct current (DC) borehole resistivity measurements acquired in steel-cased deviated wells for the assessment
of rock formation properties. The assumed data acquisition configuration considers one current (emitter) and three voltage
(collector) electrodes that are utilized to measure the second difference of the electric potential along the well trajectory.
We assume a homogeneous, 1.27-cm-thick steel casing with resistivity equal to 10 − 5 Ω· m. Simulations are performed with two different numerical methodologies. The first one is based on transferring two-dimensional
(2D) axisymmetric optimal grids to a three-dimensional (3D) simulation software. The second one automatically produces optimal
3D grids yielded by a 3D self-adaptive goal-oriented algorithm. Both methodologies utilize high-order finite elements (FE)
that are specially well-suited for problems with high-contrast coefficients and rapid spatial variations of the electric field,
as it occurs in simulations that involve steel-cased wells. The method based on transferring 2D-optimal grids is efficient
in terms of CPU time (few seconds per logging position). Unfortunately, it may produce inaccurate 3D simulations in deviated
wells, even though the error remains below 1% for the axisymmetric (vertical) well. The method based on optimal 3D grids,
although less efficient in terms of CPU time (few hours per logging position), produces more accurate results that are validated
by a built-in a posteriori error estimator. This paper provides the first existing simulations of through-casing resistivity
measurements in deviated wells. Simulated resistivity measurements indicate that, for a 30° deviated well, measurements in
conductive layers 0.01 Ω· m) are similar to those obtained in vertical wells. However, in resistive layers (10,000 Ω· m),
we observe 100% larger readings in the 30° deviated well. This difference becomes 3,000% for the case of a 60° deviated well.
For this highly-deviated well, readings corresponding to the conductive formation layer are about 30% smaller in magnitude
than those in a vertical well. Shoulder effects significantly vary in deviated wells. 相似文献
8.
近年来,瑞利波波形反演技术因其避开了常规频散曲线计算,直接进行波场计算和反演不再受水平层状介质理论假设的限制,得到广大学者的高度重视。但瑞利波波形反演过程中需要不断进行波场正演和逆推计算。另外,由于浅地表速度较小,模拟计算时需要较小的网格间距才能避免数值频散,这无疑大大增加了正演模拟的计算量。对于这一问题,通常采用并行化设计来提高正演模拟的计算效率。本文基于消息传递接口（MPI）并行有限差分算法,以区域分解思路将模型区间分解成若干子区域,各区域互相通信,共同完成对模型的正演计算。并详细给出了区域分解、坐标转换、区域通信、波场合并等并行方案中的具体实现方法和实现步骤。通过对弹性模型、Kelvin黏弹性模型和标准线弹性固体（SLS）黏弹性模型不同并行方案的计算结果进行分析,验证了本文并行方案的可行性和有效性。并行计算结果表明,与单处理器计算时间相比,增加处理器数目可以明显减少计算时间,但随着处理器数目的增加,不同处理器之间的通信时间也增大;因此,并行时需要选择合适的处理器数目。对于黏弹性介质模型,SLS黏弹性模型的并行计算效率优于Kelvin黏弹性模型。 相似文献
9.
为了更好地研究近岸海域波生沿岸流,建立了基于高阶Boussinesq水波方程的波生沿岸流时域数值模型。控制方程在中等水深范围内具有较好的色散性和变浅作用性能,同时具有二阶完全非线性特征,适合描述近岸区域波浪强非线性运动。通过采用松弛造波方法实现了非线性波浪的无反射入射,采用周期性侧边界条件模拟开敞边界。通过数值试验,讨论了模型中主要参数对数值结果的影响。利用率定后的参数模拟了均匀坡度海岸上产生的沿岸流,通过和实验数据的对比验证了模型的准确性和适用性。利用模型数值模拟了不同波浪入射条件(包括周期、波高和波浪入射角度)对波生沿岸流的影响。 相似文献
10.
11.
2.5维起伏地表条件下坐标变换法直流电场数值模拟 总被引：3，自引：1，他引：2
研究起伏地表对视电阻率分布的影响是进行地形校正的基础。由于很难处理不规则边界,计算简洁且效率高的有限差分方法很少用于解决起伏地表问题。为了解决该问题,引入曲化平思想,实现了一种基于坐标变换法的起伏地表条件下的直流电场数值模拟方法。方法从传统的2.5维基本方程及边界条件出发,通过坐标变换将起伏地表问题转化为水平地表问题,并利用有限差分法求解水平地表问题,最后再通过坐标映射得到起伏地表条件下的电位和视电阻率分布。精度分析及计算实例表明：本方法实现简洁,计算误差主要集中在震源附近,整个计算区域内的平均相对误差为1.39%,计算结果满足起伏地表条件下的电位和视电阻率的分布规律。 相似文献
12.
完全匹配层吸收边界（PML）已经被证明是非常有效的边界吸收技术,对体波和面波的吸收都具有非常好的效果,已经被广泛应用于弹性波的数值模拟中。但是在某些情况下传统的PML技术还是存在一定的问题,比如对掠射情况下的体波和窄区域自由表面条件下的面波的吸收等等。在坐标变换中采用复频移拉伸函数的复频移PML可以有效地改善PML边界条件的吸收性能。基于弹性波一阶速度-应力方程,推导了复频移PML的递推卷积实现方法,并采用交错网格高阶有限差分法对其进行了数值模拟,与传统的PML进行了对比。结果表明：传统的PML对掠射情况下的体波和窄区域自由表面条件下的面波吸收不足,会产生虚假反射,影响真实波场;而基于递推卷积的复频移PML算法能够有效地改善困难情况下的吸收效果,并且在实现过程中不用分裂变量,应用更加方便简单。计算卷积时采用递推的形式,推导过程直观易懂,易于编程,而且不会增加计算量,存储量也没有太大的变化。 相似文献
13.
在煤层气排采分析及数值模拟研究中,煤储层结构的三维建模是数值模拟和结果分析的起点,具有关键作用。三维长方体等传统网格,难以表达地层的起伏变化,角点网格具有表达起伏变化地层的优势。从煤层气动态可视化的角度出发,基于角点网格建立了煤储层三维地质模型。研究了角点网格模型的数据特点及生成角点网格的方法,采用C#编程语言并结合OpenGL图形接口,开发了煤储层三维可视化软件模型,利用该模型表达了山西省沁水盆地潘庄区块的煤储层地质构造。结果表明,角点网格适用于煤储层三维模型的构建,能较好的表达煤层的结构特征。 相似文献
14.
Improved and enhanced oil recovery methods require sophisticated simulation tools to predict the injected flow pass together with the chemical reactions inside it. One approach is application of higher-order numerical schemes to avoid excessive numerical diffusion that is very typical for transport processes. In this work, we provide a first step towards higher-order schemes applicable on general polyhedral and corner-point grids typically used in reservoir simulation. We compare three possible approaches of linear reconstruction and slope limiting techniques on a variety of different meshes in two and three spatial dimensions and discuss advantages and disadvantages. 相似文献
15.
采用易于模拟复杂地形起伏和倾斜界面的非结构三角单元剖分网格,并利用对偶加权后验误差估计指导网格自动细化过程,实现了2.5维直流电阻率法自适应有限元数值模拟。在实例模型分析中,分别计算了层状模型和垂直岩脉模型的直流电阻率响应,并与其解析解进行了比较。对比结果表明,该算法所得数值解精度很高,解的相对误差小于0.5%。最后,计算了起伏地形2.5维地电模型视电阻率异常,并利用比较法进行了地形改正。地形改正结果与水平地形时的结果对比表明,比较法可以较好地消除地形影响,突出局部地质体异常。 相似文献
16.
建立了基于高阶Boussinesq水波方程的一维波浪破碎数值模型。基于一组具有二阶完全非线性特征的Boussinesq水波方程,建立了交错网格下的高精度差分格式,推导了适用于该组方程的永形波解析解,其和松弛造波技术相结合实现了数值波浪水槽中(强)非线性波浪的无反射入射。通过模拟封闭容器内水体晃动问题对数值格式进行了验证,通过模拟孤立波在斜坡海岸上的浅化过程说明了将方程从弱非线性发展到完全非线性的必要性。采用涡粘方法处理波浪破碎,利用物理模型实验数据,分析了模型中各波浪破碎参数对数值结果的影响并对参数进行了率定。应用该模型对规则波在斜坡海岸上的传播、变浅以及破碎过程进行了数值模拟研究,数值结果同实验数据吻合良好,验证了模型的有效性。 相似文献
17.
假定各物理量沿径向不变化,建立了低应变瞬态集中荷载作用下现浇大直径管桩振动响应的计算模型和波动方程。采用Laplace变换法,求得了波动方程的频域解析解,采用Fourier逆变换求得了时域响应。将文中解计算结果与三维频域解析解进行了对比分析,文中解的入射峰-反射峰时间差与三维频域解差别很小,说明对于PCC桩这种大直径薄壁管桩,采用径向不变假定对计算结果几乎没有影响。因此,在PCC桩低应变检测波形分析时,采用基于径向不变假定的二维解是完全合理的。将文中二维频域解的计算结果与二维时域解的结果进行了对比分析,结果表明,2种解在入射波、第一个桩底反射波、第二个桩底反射波峰值大小和到达时间非常吻合,这说明考虑环向位移与否对计算结果没有太大的影响,研究PCC桩低应变动力响应的问题时忽略水平方向的位移是完全可以的。 相似文献
18.
Duan W. Y. Zheng K. Zhao B. B. Demirbilek Z. Ertekin R. C. Webster W. C. 《Natural Hazards》2016,84(2):567-583
This work is on the use of the Green–Naghdi (GN) nonlinear wave equations for simulating wave–current interaction in shallow water. The stream-function wave theory is used at the wave-maker boundary to generate nonlinear incident waves to consider the wave–current interaction. The nonlinear GN equations are solved in the time domain by use of the finite-difference method. The model is evaluated with data from three experimental studies. A strong opposing current over a submerged bar is investigated in the first test case. In the second test case, the interaction of waves with a uniform current over flat bottom is considered. In the third case, wave–current interaction over a variable bathymetry with the following and opposing currents is studied. The numerical results obtained by the GN equations are compared with the experimental data and results based on the Boussinesq equations. A good agreement is obtained for the three experimental studies considered for a wide range of wave and current conditions. 相似文献
19.
定量研究污染物在地下水中的运移过程通常采用数值模拟方法。MT3D是一套基于有限差分方法的污染物运移模拟软件，近年来在国外水文地质和水环境模拟等领域的研究中已经得到较为广泛的认可。MT3D比较全面地考虑了污染物在地下水中的对流、弥散和化学反应等过程，可以灵活处理各种复杂的源汇项和边界条件，能够准确模拟承压、无压和越流含水层中的污染物运移过程。MT3D具有模块化的程序结构、灵活的求解方法以及全面的模拟功能，非常适合实际问题的研究，值得在国内推广使用。 相似文献