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1.
Oversampling techniques are often used in porous media simulations to achieve high accuracy in multiscale simulations. These methods reduce the effect of artificial boundary conditions that are imposed in computing local quantities, such as upscaled permeabilities or basis functions. In the problems without scale separation and strong non-local effects, the oversampling region is taken to be the entire domain. The basis functions are computed using single-phase flow solutions which are further used in dynamic two-phase simulations. The standard oversampling approaches employ generic global boundary conditions which are not associated with actual flow boundary conditions. In this paper, we propose a flow based oversampling method where the actual two-phase flow boundary conditions are used in constructing oversampling auxiliary functions. Our numerical results show that the flow based oversampling approach is several times more accurate than the standard oversampling method. We provide partial theoretical explanation for these numerical observations. 相似文献
2.
Vladimir Priklonsky Anvar Shukurov Dmitry Sokoloff Andrew Soward 《地球物理与天体物理流体动力学》2013,107(1-2):97-114
Abstract We reconsider thin-disc global asymptotics for kinematic, axisymmetric mean-field dynamos with vacuum boundary conditions. Non-local terms arising from a small but finite radial field component at the disc surface are consistently taken into account for quadrupole modes. As in earlier approaches, the solution splits into a local part describing the field distribution along the vertical direction and a radial part describing the radial (global) variation of the eigenfunction. However, the radial part of the eigenfunction is now governed by an integro-differential equation whose kernel has a weak (logarithmic) singularity. The integral term arises from non-local interactions of magnetic fields at different radii through vacuum outside the disc. The non-local interaction can have a stronger effect on the solution than the local radial diffusion in a thin disc, however the effect of the integral term is still qualitatively similar to magnetic diffusion. 相似文献
3.
This contribution is aimed at a comparison of two different methods of how to deal with the solid inner core in geodynamo models. The first method, based on a direct application of the non-slip boundary conditions, was frequently used in the past. The second one, developed by the authors of the present paper, is based on an advanced analytical solution within the boundary layers and consequent formulation of new boundary conditions on the flow in the volume of the outer core. As an example we have used the results obtained by Hollerbach (1997) in the study of the influence of an imposed axial magnetic field on the fluid flow in a differentially rotating spherical shell. In the case of a weak imposed magnetic field, our solutions are very similar to those of Hollerbach. This non-trivial correspondence confirms the correctness of both methods, which are different not only in the formulation of boundary conditions, but also in the numerical methods: whereas Hollerbach used spectral methods, our computer code is based on finite differences. The influence of the conductivity of the inner core on the fluid flow was also studied. 相似文献
4.
A complex response algorithm for the dynamic analysis of axisymmetric thin shells supported on an interactive foundation is developed. The substructure deletion method is employed through the utilization of a dynamic boundary system at the contact area between the superstructure and the substructure. A new mathematical formulation in conjunction with the shell behaviour is developed to deal with rigid body motions due to the negation of the fixed base assumption. Four foundation conditions, that is, a fixed base, two pile foundation cases and a flexible base, are to examine the effect of base flexibility on the seismic response of cooling towers. Also, excellent comparative results between the frequency domain solution and a time domain solution are obtained. 相似文献
5.
The various boundary-element methods, well established in the frequency domain, are developed in the time domain for a foundation embedded in a layered halfspace. They are the weighted-residual technique and the indirect boundary-element method, based on a weighted-residual equation, and the direct boundary-element method based on a reciprocity equation, both equations involving time and space. In the indirect approach, formulating the weighted-residual equation over the last time step only results in the truncated indirect boundary-element formulation which requires a reduced computational effort. In all cases, convolution integrals occur. The truncated indirect boundary-element method leads to a highly reliable algorithm, as is verified when a linear analysis in the time domain is compared to the corresponding one in the frequency domain. This boundary-element formulation, which is non-local in space and time, represents a rigorous generally applicable method taking into account a layered halfspace in a non-linear soil-structure interaction analysis. As an example, the non-linear soil-structure interaction analysis of a structure embedded in a halfspace with partial uplift of the basemat and separation of the side wall is investigated. 相似文献
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7.
The nodal domain integration method is used to develop a numerical model of the linear diffusion equation. The nodal domain integration approach is shown to represent an infinity of finite element mass matrix lumping schemes including the Galerkin and subdomain integration versions of the weighted residual method and an integrated finite difference method. Neumann, Dirichlet and mixed boundary conditions are accommodated analogous to the Galerkin finite element method. In order to reduce the overall integrated approximation relative error, a mass matrix lumping formulation is developed which is based on the Crank-Nicolson time advancement approximation. The optimum mass lumping factors are found to be strongly related to the model timestep size. 相似文献
8.
The transient analysis of dam–reservoir systems by employing perfectly matched layers has been investigated. In previous studies, boundary conditions of the PML region in the reservoir have been neglected. In this paper, they are incorporated completely in the formulation. Moreover, a technique is introduced to involve the effect of incident waves caused by vertical ground motions at the reservoir bottom in the analysis. Performing several numerical experiments indicates that applying boundary conditions of the PML domain and utilizing the proposed method for vertical excitation cases reduce the computational cost significantly and make the PML method a very efficient approach for the transient analysis of dam–reservoir systems. 相似文献
9.
An absorbing boundary for saturated porous media is developed that can be used for transient analyses in the time domain. The elastic constitutive equations for the saturated porous media follow Bowen's formulation. The method consists of applying viscous tractions along the artificial boundary. The absorbing boundary behaviour is assumed linear and isotropic. Hadamard's conditions provide the speeds of the dilatational and shear waves that propagate in saturated porous media. Since these expressions are frequency independent, the intensities of the viscous tractions are evaluated in the time domain, and the two dilatational waves are accounted for. The viscous tractions are defined from the drained characteristics, assuming an infinite permeability, at variance with the traditional ‘undrained’ method based on undrained characteristics and a null permeability. Solid media and materials with low permeability are also retrieved as subcases. The results show that, at no additional cost, this ‘drained’ method is more accurate for all permeabilities than the ‘undrained’ method, which disregards the existence of the second dilatational wave. Copyright © 2003 John Wiley & Sons, Ltd. 相似文献
10.
提出了一种用边界元法计算频率域人工源三维地形电磁场的数值模拟方法.首先用矢量积分理论和电磁场边界条件，将上半空间（空气）和下半空间（地下介质）两个区域电磁场边值问题变为仅对地形界面的两个矢量面积分方程.然后将对地形界面的积分剖分为一系列的三角单元积分.在三角单元积分中，假设单元中电磁场为无限大气空间电磁场与地形影响的叠加,并假设地形影响为常项,这样既保证了计算精度又使得计算方法简便.通过分解和计算，每一个矢量面积分方程分解为对应三个坐标方向的三个常量线性方程，这些线性方程组成了对角占优的线性方程组，可用SSOR方法求解.文中给出了垂直磁偶源的垂直磁场地形影响的例子. 相似文献
11.
A study on the seismic response of massive flexible strip-foundations embedded in layered soils and subjected to seismic excitation is presented. Emphasis is placed on the investigation of the system response with the aid of a boundary element–finite element formulation proper for the treatment of such soil–structure interaction problems. In the formulation, the boundary element method (BEM) is employed to overcome the difficulties that arise from modeling the infinite soil domain, and the finite element method (FEM) is applied to model the embedded massive flexible strip-foundation. The numerical solution for the soil–foundation system is obtained by coupling the FEM with the BEM through compatibility and equilibrium conditions at the soil–foundation and soil layer interfaces. A parametric study is conducted to investigate the effects of foundation stiffness and embedment on the seismic response. 相似文献
12.
动荷载作用下欧拉梁动响应的计算是一个初边值问题,通常很难得到解析解,传统数值方法一般是把空间和时间分别离散进行求解,计算相对复杂,效率也不高.针对分布动荷载作用下欧拉梁的振动偏微分方程,采用传统微分求积法,在空间和时间上同时进行离散;对于所有非0阶的初/边值条件,采用嵌入法在权系数计算中予以考虑.算例的数值结果与精确解的对比证明采用传统微分求积法处理此问题是可行的,而且是高效的.对于实际工程中的其他类似问题,该方法同样适用. 相似文献
13.
We present a new finite element (FE) method for magnetotelluric modelling of three-dimensional conductivity structures. Maxwell's equations are treated as a system of first-order partial differential equations for the secondary fields. Absorbing boundary conditions are introduced, minimizing undesired boundary effects and allowing the use of small computational domains. The numerical algorithm presented here is an iterative, domain decomposition procedure employing a nonconforming FE space. It does not use global matrices, therefore allowing the modellization of large and complicated structures. The algorithm is naturally parallellizable, and we show results obtained in the IBM SP2 parallel supercomputer at Purdue University. The accuracy of the numerical method is verified by checking the computed solutions with the results of COMMEMI, the international project on the comparison of modelling methods for electromagnetic induction. 相似文献
14.
Josef Brechler 《Studia Geophysica et Geodaetica》1990,34(1):65-77
Summary This article deals with some problems connected with the formulation of a non-hydrostatic mesoscale model of airflow in the atmosphere. Due to an irregular surface a terrain-following coordinate system is used and the equations of the model are transformed into this system. Sound waves are eliminated by the use of the anelastic approximation. The influence of boundaries is minimized by the use of open boundary conditions at the lateral boundaries of the computational domain and of the absorbing layer beneath the upper boundary. 相似文献
15.
The first attempt at numerical MHD simulations of the appearance of several current sheets above an active region before a
series of elementary flares is described. Energy accumulates in the field of each sheet that can be released during one of
the flares. The computations started three days before the appearance of a series of flares, i.e., before the emergence of
a new magnetic flux in the active region. The initial (potential) magnetic field was calculated by solving the Laplace equation
with an oblique derivative. The boundary conditions on the photosphere were specified from maps of the measured magnetic field
in the active region for various instants of time. The Peresvet program solving the full system of MHD equations with dissipative
terms was used in the computations. An absolutely implicit scheme conservative relative to the magnetic flux was used. The
problem of properly choosing the size of the computational domain and finding the positions of singular magnetic field lines
is discussed. 相似文献
16.
Detection of potential fields source boundaries by enhanced horizontal derivative method 总被引：1，自引：0，他引：1
A high‐resolution method to image the horizontal boundaries of gravity and magnetic sources is presented (the enhanced horizontal derivative (EHD) method). The EHD is formed by taking the horizontal derivative of a sum of vertical derivatives of increasing order. The location of EHD maxima is used to outline the source boundaries. While for gravity anomalies the method can be applied immediately, magnetic anomalies should be previously reduced to the pole. We found that working on reduced‐to‐the‐pole magnetic anomalies leads to better results than those obtainable by working on magnetic anomalies in dipolar form, even when the magnetization direction parameters are not well estimated. This is confirmed also for other popular methods used to estimate the horizontal location of potential fields source boundaries. The EHD method is highly flexible, and different conditions of signal‐to‐noise ratios and depths‐to‐source can be treated by an appropriate selection of the terms of the summation. A strategy to perform high‐order vertical derivatives is also suggested. This involves both frequency‐ and space‐domain transformations and gives more stable results than the usual Fourier method. The high resolution of the EHD method is demonstrated on a number of synthetic gravity and magnetic fields due to isolated as well as to interfering deep‐seated prismatic sources. The resolving power of this method was tested also by comparing the results with those obtained by another high‐resolution method based on the analytic signal. The success of the EHD method in the definition of the source boundary is due to the fact that it conveys efficiently all the different boundary information contained in any single term of the sum. Application to a magnetic data set of a volcanic area in southern Italy helped to define the probable boundaries of a calderic collapse, marked by a number of magmatic intrusions. Previous interpretations of gravity and magnetic fields suggested a subcircular shape for this caldera, the boundaries of which are imaged with better detail using the EHD method. 相似文献
17.
应用高精度人工边界条件可有效提升近场波动数值模拟计算效率.完美匹配层是吸收层形式高精度人工边界条件,匹配层内场方程和界面条件通常分别采用复坐标延伸技术变换强形式无限域内波动方程和界面条件得到,亦曾将无限域界面条件当作匹配层界面条件.场方程和界面条件构建过程相互独立,可能出现匹配不合理而引发数值失稳、计算精度低下等问题.本文提出采用复坐标延伸技术变换弱形式无限域波动方程以构建完美匹配层的方法.弱形式波动方程耦合了波动方程及界面条件,进而规避了变换后所得场方程与界面条件之间的匹配不合理问题.新方法可直接建立弱形式匹配层,在此基础上亦可给出强形式匹配层.弱形式便于有限元离散,强形式便于有限差分离散.基于弱形式完美匹配层,结合勒让德谱元建立了弹性介质近场波动谱元模拟方案.利用算例验证了新方案的精度及数值稳定性.本文工作可直接推广至多相耦合介质近场波动数值模拟. 相似文献
18.
《Advances in water resources》1999,22(5):461-478
Fractional flow formulations of the multi-phase flow equations exhibit several attractive attributes for numerical simulations. The governing equations are a saturation equation having an advection diffusion form, for which characteristic methods are suited, and a global pressure equation whose form is elliptic. The fractional flow approach to the governing equations is compared with other approaches and the implication of equation form for numerical methods discussed. The fractional flow equations are solved with a modified method of characteristics for the saturation equation and a finite element method for the pressure equation. An iterative algorithm for determination of the general boundary conditions is implemented. Comparisons are made with a numerical method based on the two-pressure formulation of the governing equations. While the fractional flow approach is attractive for model problems, the performance of numerical methods based on these equations is relatively poor when the method is applied to general boundary conditions. We expect similar difficulties with the fractional flow approach for more general problems involving heterogenous material properties and multiple spatial dimensions. 相似文献
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20.
地电磁场的直接求解法存在伪解现象,且电磁场分量在界面上的不连续性与节点型有限元的基本要求矛盾. 本文将Coulomb 规范下磁矢量势-电标量势与自适应有限元相结合,提出了地球物理电磁场计算的快速、高精度方法. 首先从地电磁场一般边值问题出发,给出了Coulomb 规范下磁矢量势-电标量势的公式系统,分析了求解域内势的连续性. 采用Galerkin 加权余值法推导出积分弱解形式和Delaunay非结构化四面体单元时Hierarchal 基函数的有限元方程. 基于超收敛恢复技术,提出了适用于电磁场的后验误差估计方法,阐述了地电磁场自适应计算的策略及迭代算法,分析了计算时间消耗和误差收敛性质,表明本文方法可以用最优的计算资源得到呈拟指数收敛到准确解的数值结果,从而为后续的数值计算奠定了理论基础. 相似文献