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1.
A new approach is presented for the numerical solution of the complete 1D Saint-Venant equations. At each time step, the governing system of partial differential equations (PDEs) is split, using a fractional time step methodology, into a convective prediction system and a diffusive correction system. Convective prediction system is further split into a convective prediction and a convective correction system, according to a specified approximated potential. If a scalar exact potential of the flow field exists, correction vanishes and the solution of the convective correction system is the same solution of the prediction system. Both convective prediction and correction systems are shown to have at each x − t point a single characteristic line, and a corresponding eigenvalue equal to the local velocity. A marching in space and time (MAST) technique is used for the solution of the two systems. MAST solves a system of two ordinary differential equations (ODEs) in each computational cell, using for the time discretization a self-adjusting fraction of the original time step. The computational cells are ordered and solved according to the decreasing value of the potential in the convective prediction step and to the increasing value of the same potential in the convective correction step. The diffusive correction system is solved using an implicit scheme, that leads to the solution of a large linear system, with the same order of the cell number, but sparse, symmetric and well conditioned. The numerical model shows unconditional stability with regard of the Courant–Friedrichs–Levi (CFL) number, requires no special treatment of the source terms and a computational effort almost proportional to the cell number. Several tests have been carried out and results of the proposed scheme are in good agreement with analytical solutions, as well as with experimental data. 相似文献
2.
A nearly analytic exponential time difference method for solving 2D seismic wave equations 
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下载免费PDF全文 In this paper, we propose a nearly analytic exponential time difference (NETD) method for solving the 2D acoustic and elastic wave equations. In this method, we use the nearly analytic discrete operator to approximate the high-order spatial differential operators and transform the seismic wave equations into semi-discrete ordinary differential equations (ODEs). Then, the converted ODE system is solved by the exponential time difference (ETD) method. We investigate the properties of NETD in detail, including the stability condition for 1-D and 2-D cases, the theoretical and relative errors, the numerical dispersion relation for the 2-D acoustic case, and the computational efficiency. In order to further validate the method, we apply it to simulating acoustic/elastic wave propagation in multilayer models which have strong contrasts and complex heterogeneous media, e.g., the SEG model and the Marmousi model. From our theoretical analyses and numerical results, the NETD can suppress numerical dispersion effectively by using the displacement and gradient to approximate the high-order spatial derivatives. In addition, because NETD is based on the structure of the Lie group method which preserves the quantitative properties of differential equations, it can achieve more accurate results than the classical methods. 相似文献
3.
自适应基质矿物体积模量提取和流体替换验证(英文) 总被引：1，自引：1，他引：0
岩石物理学研究中Gassmann方程被广泛应用于预测岩石中的地震波速度,由于输入的基质矿物体积模量参数不准确,极大的影响预测结果的可靠性,特别是复杂基质矿物组合的碳酸盐岩储层。因此本文结合Russell流体因子和Gassmann-Boit-Geertsma方程计算式,通过引入干岩石骨架泊松比,提出了一种基质矿物体积模量提取方法,能够自适应反演岩石基质矿物等效体积模量,提高流体影响预测的可靠性,通过实际资料流体替换验证,该方法的预测结果是可靠的,并且计算效率高、适应性强。 相似文献
4.
质点的轨迹计算是半拉格朗日模式的重要基础,传统的数值计算方法由于采用时间差分代替微分,只能得到质点运动轨迹终点的速度,因此质点的移动轨迹（位移）只能靠风速外推的方法计算,导致了模式计算不稳定等问题.借鉴精细积分法中使用半解析解的思路,利用正压原始方程研究了用运动方程的半解析解构建数值模式的可能性.求解了运动方程的一阶和二阶微分方程组的半解析解,通过时间积分半解析解计算质点运动轨迹.数值试验表明,一阶微分方程组的半解析解比差分解略有优势.二阶微分方程组的半解析解在时间步长增大时优势非常明显,而且在保证计算精度的前提下,节省计算时间,这对提高模式性能有重要作用. 相似文献
5.
提高计算精度和运算效率是所有波场正演方法所追求的目标,本文通过将速度 （应力）对时间的奇数阶高阶寻数转化为应力（速度）对空间的导数,运用时间和空间差分精度 均可达任意阶的高阶差分法,通过交错网格技术,对一阶速度－应力弹性波方程进行了数值求 解．波场快照以及实际模型的正演结果表明,这种求解一阶弹性波方程的高阶差分解法,和 常规的差分法相比网格频散显著减小,精度明显提高,而且可以取较大的空间步长,提高计算 效率。 相似文献
6.
《国际泥沙研究》2020,35(4):328-346
Hydraulic geometry relations comprise a classic way to understand characteristics of a river. However, environmental changes pose large uncertainties for the reliability of such relations. In the current study, on the basis of the ordinary differential equations (ODEs) formed through linear treatment of the deterministic power-law hydraulic geometry relations, a set of stochastic differential equations (SDEs) driven by Fractional white noise and Poisson noise are developed to simulate the historical dynamic probability distributions of typical hydraulic geometry variables such as slope, width, depth, and velocity with bankfull discharge variation over time in the lower Yellow River of China. One group of possible stochastic average behaviors within the next 50 years are calculated under three different design incoming water-sediment conditions (including 300, 600, and 800 million t of annual average sediment discharge). In each part of the lower reaches, after estimation of the SDE parameters using a nonparametric maximum likelihood estimation (MLE) method, the model is carefully examined using Monte Carlo simulation as compared with the deterministic control models. The results of this comparison reveal the potential responses of hydraulic geometry characteristics to environmental disturbances, and the average trends mainly agree with the measurements. Comparisons among the three different prediction results reveal the stochastic average solution generally is greater than the deterministic solution. The results also confirm the severe negative impacts that result from the condition of 300 million t of incoming sediment, thus, pointing out the need to raise the level of river evolution alert for the lower Yellow River of China in the future. Moreover, with the help of the stochastic computation, the stream power and hydraulic width/depth ratio could be representative of an effective systematic measure for river dynamics. The proposed stochastic approach is not only important to development in the field of fluvial relations, but also beneficial to the practical design and monitoring of a river system according to specified accuracy requirements. 相似文献
7.
通过融合Gassmann方程和由微分等效介质理论建立的干岩石骨架模型--DEM解析模型,本文提出根据纵波(和横波)速度反演岩石等效孔隙纵横比进行储层孔隙结构评价和横波速度预测的方法.首先,利用Gassmann方程和DEM解析模型建立岩石的纵、横波速度与密度、孔隙度、饱和度和矿物组分等各参数之间的关系;其次,将岩石孔隙等效为具有单一纵横比的理想椭球孔,应用非线性全局寻优算法来寻找最佳的等效孔隙纵横比使得理论预测与实际测量的弹性模量之间的误差最小;最后,将反演得到的等效孔隙纵横比代入到Gassmann方程和DEM解析模型中构建横波速度.实验室和井孔测量数据应用表明,反演得到的等效孔隙纵横比可准确反映储层的孔隙结构,对于裂缝型储层如花岗岩,其孔隙纵横比通常小于0.025,而对于孔隙型储层如砂岩,其孔隙纵横比通常大于0.08.只利用纵波与同时利用纵、横波反演得到的孔隙纵横比结果几乎完全一致,而且由纵波构建的横波与实测横波吻合良好,说明本文提出的等效孔隙纵横比反演及其横波速度预测方法是有效的. 相似文献
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A novel methodology for the solution of the 2D shallow water equations is proposed. The algorithm is based on a fractional step decomposition of the original system in (1) a convective prediction, (2) a convective correction, and (3) a diffusive correction step. The convective components are solved using a Marching in Space and Time (MAST) procedure, that solves a sequence of small ODEs systems, one for each computational cell, ordered according to the cell value of a scalar approximated potential. The scalar potential is sought after computing first the minimum of a functional via the solution of a large linear system and then refining locally the optimum search. Model results are compared with the experimental data of two laboratory tests and with the results of other simulations carried out for the same tests by different authors. A comparison with the analytical solution of the oblique jump test has been also considered. Numerical results of the proposed scheme are in good agreement with measured data, as well as with analytical and higher order approximation methods results. The growth of the CPU time versus the cell number is investigated successively refining the elements of an initially coarse mesh. The CPU specific time, per element and per time step, is found out to be almost constant and no evidence of Courant–Friedrichs–Levi (CFL) number limitation has been detected in all the numerical experiments. 相似文献
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A semi-analytical time integration method is proposed for the numerical simulation of transient groundwater flow in unconfined aquifers by the nonlinear Boussinesq equation. The method is based on the analytical solution of the system of ordinary differential equations with constant coefficients. While it is unconditionally stable and more accurate than the finite difference methods, the computational cost is much more expensive than (can be more than 10 times) that of the finite difference methods for a single time step. However, by partitioning the nonlinear parameters into linear and nonlinear parts, the costly computation can be performed only once. With larger and less variable time step sizes, the total computational cost can be significantly reduced. Three examples are included to illustrate the advantages and limitations of the proposed method. 相似文献
12.
页岩气储层中含有大量有机碳(TOC),其丰度与成熟度对页岩力学特性有重要影响.建立包含TOC的精细数值模型,将有助于探索页岩微结构与矿物组分含量对等效弹性模量的作用程度,是“甜点区”预测的重要理论基础.本文提出了一种离散数值建模方法,基于高精度成像技术,采用晶格弹簧-随机孔隙耦合模型(LSM-RVM)模拟包含多种矿物组分及不同成熟度干酪根的数字岩心,分析TOC成熟度及含量对弹性参数的影响.在该模型中,参数设置(数值阻尼与加载应变速率)至关重要,选取不当会对计算精度造成一定影响.研究结果表明,LSM-RVM能够生成符合TOC及多种矿物实际分布特征的数值模型,是一种精细数值建模方法. 相似文献
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汪梦甫 《地震工程与工程振动(英文版)》2007,6(1):57-64
The precise integration method proposed for linear time-invariant homogeneous dynamic systems can provide accurate numerical results that approach an exact solution at integration points. However, difficulties arise when the algorithm is used for non-homogeneous dynamic systems due to the inverse matrix calculation required. In this paper, the structural dynamic equalibrium equations are converted into a special form, the inverse matrix calculation is replaced by the Crout decomposition method to solve the dynamic equilibrium equations, and the precise integration method without the inverse matrix calculation is obtained. The new algorithm enhances the present precise integration method by improving both the computational accuracy and efficiency. Two numerical examples are given to demonstrate the validity and efficiency of the proposed algorithm. 相似文献
15.
地应力的精确预测是对页岩地层进行水平井钻井轨迹设计和压裂的基础.本文在分析页岩构造特征的基础上,提出了适用于页岩地层的岩石物理等效模型的建立流程,并以此为基础实现了最小水平地应力的有效预测.首先,通过分析页岩地层的矿物、孔隙、流体及各向异性特征,将其等效为具有垂直对称轴的横向各向同性介质,进行了页岩岩石物理等效模型的构建;然后建立了页岩地层纵横波速度经验公式,并将该经验公式与岩石物理等效模型均应用于实际页岩工区的横波速度预测中,二者对比表明,本文中建立的页岩气岩石物理等效模型具有更高的横波预测精度,验证了该模型的适用性;最后,利用该模型计算各弹性刚度张量,进而实现了页岩地层最小水平地应力的预测,与各向同性模型估测结果对比表明,该模型预测的最小水平地应力与地层瞬间闭合压力一致性更高,且储层位置更为明显,具有较高的实用性. 相似文献
16.
Pu Wang R. Kahawita Professor of Mechanics Lenzhou University Lanzhou China. Professor of Civil Ensineering Ecole Polytechnique de Montreal Canada. 《国际泥沙研究》1990,(1)
I. INTRODUCTIONNumerical models of estuaries incorporating simulation of the density induced circulation are consideredimPOrtant tools in the assessment of their dispersive characteristics. Most models to date have used finite difference approximations to the governing equations (see for example thericke and Hogan, 1977, Blumberg,1 977, Perrels and Karelse, 1978). A numeriCal model of estuarine circulation using a SADI (Spline Alternating Direction implicit) procedure together with a… 相似文献
17.
K. H. Hamed A. E. Hassan 《Stochastic Environmental Research and Risk Assessment (SERRA)》2000,14(6):428-448
An efficient numerical solution for the two-dimensional groundwater flow problem using artificial neural networks (ANNs)
is presented. Under stationary velocity conditions with unidirectional mean flow, the conductivity realizations and the head
gradients, obtained by a traditional finite difference solution to the flow equation, are given as input-output pairs to train
a neural network. The ANN is trained successfully and a certain level of recognition of the relationship between input conductivity
patterns and output head gradients is achieved. The trained network produced velocity realizations that are physically plausible
without solving the flow equation for each of the conductivity realizations. This is achieved in a small fraction of the time
necessary for solving the flow equations. The prediction accuracy of the ANN reaches 97.5% for the longitudinal head gradient
and 94.7% for the transverse gradient. Head-gradient and velocity statistics in terms of the first two moments are obtained
with a very high accuracy. The cross covariances between head gradients and the fluctuating log-conductivity (log-K) and between velocity and log-K obtained with the ANN approach match very closely those obtained by a traditional numerical solution. The same is true for
the velocity components auto-covariances. The results are also extended to transport simulations with very good accuracy.
Spatial moments (up to the fourth) of mean-concentration plumes obtained using ANNs are in very good agreement with the traditional
Monte Carlo simulations. Furthermore, the concentration second moment (concentration variance) is very close between the two
approaches. Considering the fact that higher moments of concentration need more computational effort in numerical simulations,
the advantage of the presented approach in saving long computational times is evident. Another advantage of the ANNs approach
is the ability to generalize a trained network to conductivity distributions different from those used in training. However,
the accuracy of the approach in cases with higher conductivity variances is being investigated. 相似文献
18.
MAST-2D diffusive model for flood prediction on domains with triangular Delaunay unstructured meshes
A new methodology for the solution of the 2D diffusive shallow water equations over Delaunay unstructured triangular meshes is presented. Before developing the new algorithm, the following question is addressed: it is worth developing and using a simplified shallow water model, when well established algorithms for the solution of the complete one do exist?The governing Partial Differential Equations are discretized using a procedure similar to the linear conforming Finite Element Galerkin scheme, with a different flux formulation and a special flux treatment that requires Delaunay triangulation but entire solution monotonicity. A simple mesh adjustment is suggested, that attains the Delaunay condition for all the triangle sides without changing the original nodes location and also maintains the internal boundaries. The original governing system is solved applying a fractional time step procedure, that solves consecutively a convective prediction system and a diffusive correction system. The non linear components of the problem are concentrated in the prediction step, while the correction step leads to the solution of a linear system of the order of the number of computational cells. A semi-analytical procedure is applied for the solution of the prediction step. The discretized formulation of the governing equations allows to handle also wetting and drying processes without any additional specific treatment. Local energy dissipations, mainly the effect of vertical walls and hydraulic jumps, can be easily included in the model.Several numerical experiments have been carried out in order to test (1) the stability of the proposed model with regard to the size of the Courant number and to the mesh irregularity, (2) its computational performance, (3) the convergence order by means of mesh refinement. The model results are also compared with the results obtained by a fully dynamic model. Finally, the application to a real field case with a Venturi channel is presented. 相似文献
19.
An automatically adaptive element free method is presented to analyze the seismic response of liquefiable soils.The method is based on the element free Galerkin method (EFGM) and the fission procedure that is part of h-refinement,indicated by error estimation. In the proposed method, a posteriori error estimate procedure that depends on the energy normof stress and the T-Belytschko (TB) stress recovery scheme is incorporated. The effective cyclic elasto-plastic constitutivemodel is used to describe the nonlinear behavior of the saturated soil. The governing equations are established by u-pformulation. The proposed method can effectively avoid the volumetric locking due to large deformation that usually occursin numerical computations using the finite element method (FEM). The efficiency of the proposed method is demonstratedby evaluating the seismic response of an embankment and comparing it to results obtained through FEM. It is shown that theproposed method provides an accurate seismic analysis of saturated soil that includes the effects of liquefaction 相似文献
20.
An efficient and accurate numerical model for multicomponent compressible single-phase flow in fractured media is presented. The discrete-fracture approach is used to model the fractures where the fracture entities are described explicitly in the computational domain. We use the concept of cross flow equilibrium in the fractures. This will allow large matrix elements in the neighborhood of the fractures and considerable speed up of the algorithm. We use an implicit finite volume (FV) scheme to solve the species mass balance equation in the fractures. This step avoids the use of Courant–Freidricks–Levy (CFL) condition and contributes to significant speed up of the code. The hybrid mixed finite element method (MFE) is used to solve for the velocity in both the matrix and the fractures coupled with the discontinuous Galerkin (DG) method to solve the species transport equations in the matrix. Four numerical examples are presented to demonstrate the robustness and efficiency of the proposed model. We show that the combination of the fracture cross-flow equilibrium and the implicit composition calculation in the fractures increase the computational speed 20–130 times in 2D. In 3D, one may expect even a higher computational efficiency. 相似文献