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1.
A convection-diffusion equation arises from the conservation equations in miscible and immiscible flooding, thermal recovery, and water movement through desiccated soil. When the convection term dominates the diffusion term, the equations are very difficult to solve numerically. Owing to the hyperbolic character assumed for dominating convection, inaccurate, oscillating solutions result. A new solution technique minimizes the oscillations. The differential equation is transformed into a moving coordinate system which eliminates the convection term but makes the boundary location change in time. We illustrate the new method on two one-dimensional problems: the linear convection-diffusion equation and a non-linear diffusion type equation governing water movement through desiccated soil. Transforming the linear convection diffusion equation into a moving coordinate system gives a diffusion equation with time dependent boundary conditions. We apply orthogonal collocation on finite elements with a Crank-Nicholson time discretization. Comparisons are made to schemes using fixed coordinate systems. The equation describing movement of water in dry soil is a highly non-linear diffusion-type equation with coefficients varying over six orders of magnitude. We solve the equation in a coordinate system moving with a time-dependent velocity, which is determined by the location of the largest gradient of the solution. The finite difference technique with a variable grid size is applied, and a modified Crank-Nicholson technique is used for the temporal discretization. Comparisons are made to an exact solution obtained by similarity transformation, and with an ordinary finite difference scheme on a fixed coordinate system. 相似文献
2.
针对利用波函数展开法进行三维地震响应研究中的坐标变换问题,提出了在两斜交柱坐标系间谐波函数空间坐标变换的辅助平面方法．通过建立与空间点对应的一系列辅助平面,将地震波三维散射研究中的谐波函数表达式从柱坐标系变换至辅助平面内的极坐标系,然后在辅助平面内运用Graf加法公式,将柱坐标系下的波函数表达式变换至与该柱坐标系斜交的另一柱坐标系下,从而将三维问题转换成二维问题进行处理,最终得到了斜交柱坐标系下内域问题和外域问题的坐标变换公式． 相似文献
3.
随着国内石油公司在海外石油勘探步伐的加快,海外钻井数量日益增长,所面临的坐标转换问题突出。本文以探索研究适用于在海外油气勘探钻井设计过程的实用方法为目标,阐述坐标转换在储层横向变化快的地区进行钻探的重要意义,深入研究坐标系统的组成与特点,提出利用已有的地震解释软件、自编软件等两种快捷简便且准确的坐标转换方式,所得结果经过已知数据对比验证,误差在0．3m范围内。将上述两种转换方法应用在西非深水区X研究区的边界成像模糊浊积水道储层的井位设计中,经钻井证实,井点位置准确,钻探结果符合预期。 相似文献
4.
In this paper we describe the transport of pollution in groundwater in the neighbourhood of a well in a uniform background flow. We compute the rate at which contaminated particles reach the well as a function of the place of the source of pollution. The motion of a particle in a dispersive flow is seen as a random walk process. The Fokker-Planck equation for the random motion of a particle is transformed using the complex potential for the advective flow field. The resulting equation is solved asymptotically after a stretching transformation. Finally, the analytical solution is compared with results from Monte Carlo simulations with the random walk model. The method can be extended to arbitrary flow fields. Then by a numerical coordinate transformation the analytical results can still be employed. 相似文献
5.
以旋转椭球体面上某点为原点建立一个大地坐标单位活动坐标架. 通过平移, 使活动坐标架的原点与以椭球中心为原点的笛卡尔单位标架的原点相重合. 然后再通过两次标架旋转, 使活动坐标架与笛卡尔单位标架完全重合. 本文给出了使两个单位标架相重合的转换关系式, 以及该点位移在两个单位标架中的坐标转换式； 在此基础上, 考虑该点的位移及活动坐标架皆为该点大地坐标的函数, 经复杂推导, 分别给出了该点位移向量的微分在大地坐标系中的分量以及该点分别沿坐标曲线的弧微分表达式, 继而导出了该点的位移梯度矩阵; 最后推导出了椭球坐标系的应变张量与转动张量表达式, 并对转动张量的几何含义进行了较详细的解释, 且采用曲面理论对球面与椭球面的应变张量间的内在关系进行了讨论. 相似文献
6.
Expression of strain and rotation tensor in geodetic coordinates 总被引：1，自引：0，他引：1
In this paper, unit moving trihedron is first constructed for a point on the surface of a revolution ellipsoid. Via translation, the origin of the trihedron coincides with that of Cartesian coordinates established at the center of the ellipsoid, and then through two coordinate rotations, the trihedron completely coincides with the Cartesian coordi-nates. Transformation formulae between the moving trihedron and unit Cartesian coordinate frameworks as well as transformation of point displacement between two unit coordinate frameworks are presented. Based on the above transformation formulae between two different coordinate frameworks, due to the fact that the displacement and moving trihedron of the point are both functions of the geodetic coordinates, components in the corresponding axis for differential of displacement vector and geodetic curves arc differential at the point in geodetic system can be obtained through complicated derivation. Displacement gradient matrix at the point in geodetic system is also given. Finally, expressions of strain and rotation tensor in geodetic coordinates are presented. Geometric meanings of the rotation tensor are explained in detail. The intrinsic relationship between strain tensors of sphere and ellip-soid are also discussed. 相似文献
7.
Fitts CR 《Ground water》2006,44(1):99-101
Although most current applications of the analytic element method are formulated for isotropic hydraulic conductivity, anisotropic domains can be modeled with analytic elements using the well-known coordinate transformation where one coordinate axis is scaled by the square root of the anisotropy ratio. If the standard analytic solution for steady radial flow to a well is used with this coordinate transformation, the resulting solution correctly models the far field but it does not meet the constant head boundary condition at the well radius. This could be a significant shortcoming if you are interested in the flow field close to the well or want to estimate the head at the pumping well. A new solution for two-dimensional steady flow to a well in an anisotropic domain is presented. This solution satisfies the governing equations exactly and meets the constant head boundary condition at the well radius exactly. It was derived using a conformal mapping. 相似文献
8.
Sergey Fomel 《Geophysical Prospecting》2015,63(5):1246-1255
In certain seismic data processing and interpretation tasks such as spiking deconvolution, tuning analysis, impedance inversion, and spectral decomposition, it is commonly assumed that the vertical direction is normal to reflectors. This assumption is false in the case of dipping layers and may therefore lead to inaccurate results. To overcome this limitation, we propose a coordinate system in which geometry follows the shape of each reflector and the vertical direction corresponds to normal reflectivity. We call this coordinate system stratigraphic coordinates. We develop a constructive algorithm that transfers seismic images into the stratigraphic coordinate system. The algorithm consists of two steps. First, local slopes of seismic events are estimated by plane‐wave destruction; then structural information is spread along the estimated local slopes, and horizons are picked everywhere in the seismic volume by the predictive‐painting algorithm. These picked horizons represent level sets of the first axis of the stratigraphic coordinate system. Next, an upwind finite‐difference scheme is used to find the two other axes, which are perpendicular to the first axis, by solving the appropriate gradient equations. After seismic data are transformed into stratigraphic coordinates, seismic horizons should appear flat, and seismic traces should represent the direction normal to the reflectors. Immediate applications of the stratigraphic coordinate system are in seismic image flattening and spectral decomposition. Synthetic and real data examples demonstrate the effectiveness of stratigraphic coordinates. 相似文献
9.
Giuseppe Muscolino 《地震工程与结构动力学》1990,19(2):205-216
A method to evaluate the dynamic response of composite multiply connected primary-secondary systems is presented. For this purpose the nodal equations of motion of the composite system are given in ‘total’ and ‘relative’ coordinates. In the framework of the component-mode synthesis method a coordinate transformation, here defined as an admissible one, is used to reduce the nodal equations of motion. This coordinate transformation is theoretically and numerically compared with the coordinate transformation usually used in the literature, which generally gives larger errors with respect to the former when a reduced number of nodes is considered. 相似文献
10.
11.
Effect of common point selection on coordinate transformation parameter determination 总被引：2，自引：0，他引：2
The use of satellite positioning techniques commonly requires a transformation from a Conventional Terrestrial coordinate
system to a Geodetic coordinate system, or vice versa. For such a transformation, the main problem is the determination of
transformation parameters between these coordinate systems. The transformation parameters are estimated by a least-squares
process using “common” points, i.e., those points whose coordinates are known in both systems. Therefore, the precision of
so estimated transformation parameters is closely related to certain characteristics of the common points. In this contribution,
we have formulated some theoretical relations between the transformation parameters and the number and the distribution of
common points, and corroborated the theoretical results numerically, using a simulated geodetic network. 相似文献
12.
Scattering of SH waves induced by a symmetrical V-shaped canyon: a unified analytical solution 总被引：2，自引：1，他引：1
This paper reports a series solution of wave functions for two-dimensional scattering and diffraction of plane SH waves induced by a symmetrical V-shaped canyon with different shape ratios. A half-space with a symmetrical V-shaped canyon is divided into two sub-regions by using a circular-arc auxiliary boundary. The two sub-regions are represented by global and local cylindrical coordinate systems, respectively. In each coordinate system, the wave field satisfying the Helmholtz equation is represented by the separation of variables method, in terms of the series of both Bessel functions and Hankel functions with unknown complex coefficients. Then, the two wave fields are described in the local coordinate system using the Graf addition theorem. Finally, the unknown coefficients are sought by satisfying the continuity conditions of the auxiliary boundary. To consider the phase characteristics of the wave scattering, a parametric analysis is carried out in the time domain by assuming an incident signal of the Ricker type. Surface and subsurface transient responses demonstrate the characteristics and mechanisms of wave propagating and scattering. 相似文献
13.
14.
Oblique wave scattering by undulating porous bottom in a two-layer fluid: Fourier transform approach
Srikumar Panda 《地球物理与天体物理流体动力学》2014,108(6):587-614
The problem involving scattering of oblique waves by small undulation on the porous ocean bed in a two-layer fluid is investigated within the framework of linearised theory of water waves where the upper layer is free to the atmosphere. In such a two-layer fluid, there exist waves with two different wave numbers (modes): wave with lower wave number propagates along the free surface whilst that with higher wave number propagates along the interface. When an oblique incident wave of a particular mode encounters the undulating bottom, it gets reflected and transmitted into waves of both modes so that some of the wave energy transferred from one mode to another mode. Perturbation analysis in conjunction with Fourier transform technique is used to derive the first-order corrections of velocity potentials, reflection and transmission coefficients at both modes due to oblique incident waves of both modes. One special type of undulating bottom topography is considered as an example to evaluate the related coefficients in detail. These coefficients are shown in graphical forms to demonstrate the transformation of water wave energy between the two modes. Comparisons between the present results with those in the literature are made for particular cases and the agreements are found to be satisfactory. In addition, energy identity, an important relation in the study of water wave theory, is derived with the help of the Green’s integral theorem. 相似文献
15.
The delay coordinate technique is examined as an indicator of the regime of particle dynamics for the system of single charged particle motion in magnetic reversals. Examples of numerically integrated trajectories in both static (zero electric field) and time dependent (corresponding nonzero induction electric field) simple models for magnetic reversals are considered. In the static case, the dynamics can in principle be directly classified by constructing Poincaré surfaces of section; here we demonstrate that whilst the Poincaré surface contains the relevant information to classify the dynamics, the corresponding delay coordinate plot can provide a far more sensitive indication of the onset of nonregular behaviour. In the case of nonperiodic time dependence considered here Poincaré plots cannot in general be constructed directly. Nevertheless, delay coordinate plots can still reveal details of the phase space portrait of the system, and here are shown to indicate whether segments of stochastic motion exist in a given trajectory. It is anticipated that the delay coordinate plot technique as realized here will be a valuable tool in characterizing the behaviour in large numbers of trajectories that are evolved in time-dependent systems, thereby giving us insight into the evolution of the distribution function as a whole, either in prescribed fields or in self-consistent numerical simulations. 相似文献
16.
Many popular groundwater modeling codes are based on the finite differences or finite volume method for orthogonal grids. In cases of complex subsurface geometries this type of grid either leads to coarse geometric representations or to extremely fine meshes. We use a coordinate transformation method (CTM) to circumvent this shortcoming. In computational fluid dynamics (CFD), this method has been applied successfully to the general Navier–Stokes equation. The method is based on tensor analysis and performs a transformation of a curvilinear into a rectangular unit grid, on which a modified formulation of the differential equations is applied. Therefore, it is not necessary to reformulate the code in total. We applied the CTM to an existing three-dimensional code (SHEMAT), a simulator for heat conduction and advection in porous media. The finite volume discretization scheme for the non-orthogonal, structured, hexahedral grid leads to a 19-point stencil and a correspondingly banded system matrix. The implementation is straightforward and it is possible to use some existing routines without modification. The accuracy of the modified code is demonstrated for single phase flow on a two-dimensional analytical solution for flow and heat transport. Additionally, a simple case of potential flow is shown for a two-dimensional grid which is increasingly deformed. The result reveals that the corresponding error increases only slightly. Finally, a thermal free-convection benchmark is discussed. The result shows, that the solution obtained with the new code is in good agreement with the ones obtained by other codes. 相似文献
17.
George D. Manolis Richard P. Shaw Stavros Pavlou 《Soil Dynamics and Earthquake Engineering》1999,18(1):952
The purpose of this work is to present three methods of analysis for elastic waves propagating in two dimensional, elastic nonhomogeneous media. The first step, common to all methods, is a transformation of the governing equations of motion so that derivatives with respect to the material parameters no longer appear in the differential operator. This procedure, however, restricts analysis to a very specific class of nonhomogeneous media, namely those for which Poisson's ratio is equal to 0.25 and the elastic parameters are quadratic functions of position. Subsequently, fundamental solutions are evaluated by: (i) conformal mapping in conjunction with wave decomposition, which in principle allows for both vertical and lateral heterogeneities; (ii) wave decomposition into pseudo-dilatational and pseudo-rotational components, which results in an Euler-type equation for the transformed solution if medium heterogeneity is a function of one coordinate only; and (iii) Fourier transformation followed by a first order differential equation system solution, where the final step involving inverse transformation from the wavenumber domain is accomplished numerically. Finally, in the companion paper numerical examples serve to illustrate the above methodologies and to delineate their range of applicability. 相似文献
18.
Increasing numerical efficiency of iterative solution for total least-squares in datum transformations 总被引：1，自引：0，他引：1
Cartesian coordinate transformation between two erroneous coordinate systems is considered within the Errors-In-Variables (EIV) model. The adjustment of this model is usually called the total Least-Squares (LS). There are many iterative algorithms given in geodetic literature for this adjustment. They give equivalent results for the same example and for the same user-defined convergence error tolerance. However, their convergence speed and stability are affected adversely if the coefficient matrix of the normal equations in the iterative solution is ill-conditioned. The well-known numerical techniques, such as regularization, shifting-scaling of the variables in the model, etc., for fixing this problem are not applied easily to the complicated equations of these algorithms. The EIV model for coordinate transformations can be considered as the nonlinear Gauss-Helmert (GH) model. The (weighted) standard LS adjustment of the iteratively linearized GH model yields the (weighted) total LS solution. It is uncomplicated to use the above-mentioned numerical techniques in this LS adjustment procedure. In this contribution, it is shown how properly diminished coordinate systems can be used in the iterative solution of this adjustment. Although its equations are mainly studied herein for 3D similarity transformation with differential rotations, they can be derived for other kinds of coordinate transformations as shown in the study. The convergence properties of the algorithms established based on the LS adjustment of the GH model are studied considering numerical examples. These examples show that using the diminished coordinates for both systems increases the numerical efficiency of the iterative solution for total LS in geodetic datum transformation: the corresponding algorithm working with the diminished coordinates converges much faster with an error of at least 10-5 times smaller than the one working with the original coordinates. 相似文献
19.
A three-dimensional non-hydrostatic numerical model for simulation of the free-surface stratified flows is presented. The model is a non-hydrostatic extension of free-surface primitive equation model with a general vertical coordinate and horizontal orthogonal curvilinear coordinates. The model equations are integrated with mode-splitting technique and decomposition of pressure and velocity fields on hydrostatic and non-hydrostatic components. The model was tested against laboratory experiments on the steep wave transformation over the longshore bar, solitary wave impact on the vertical wall, the collapse of the mixed region in the thin pycnocline, mixing in the lock-exchange flows and water exchange through the sea strait. The agreement is generally fair.Responsible Editor: Hans Burchard 相似文献
20.
Miloš Cimbálník 《Studia Geophysica et Geodaetica》1991,35(3):133-144
Summary Short history of the National Geodetic Reference System (NGRS), Common Network of the Socialist Countries (CNSC/42/58, Czech S-42), CNSC/42/83 (S-42/83) — result of the second adjustment of the CNSC in Moscow 1983; the state and accuracy of the existing horizontal control.Low accuracy of national coordinate systems, especially the scale. Conform transformation of the global system into the national and calculation of corrections (dx,dy) by quadratic, cubic or biquadratic transformation under condition of minimum differences between the national and new system. Adjustment of length and direction corrections, numerical example.The proposed method indicates the possibility of improving national coordinate systems on a permanent basis with the aid of improved and, therefore, changing global systems. 相似文献