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1.
Multiscale solution methods are currently under active investigation for the simulation of subsurface flow in heterogeneous formations. These procedures capture the effects of fine scale permeability variations through the calculation of specialized coarse scale basis functions. Most of the multiscale techniques presented to date employ localization approximations in the calculation of these basis functions. For some highly correlated (e.g., channelized) formations, however, global effects are important and these may need to be incorporated into the multiscale basis functions. This can be accomplished using global fine scale simulations, but this may be computationally expensive. In this paper an adaptive local–global technique, originally developed within the context of upscaling, is applied for the computation of multiscale basis functions. The procedure enables the efficient incorporation of approximate global information, determined via coarse scale simulations, into the multiscale basis functions. The resulting procedure is formulated as a finite volume element method and is applied for a number of single- and two-phase flow simulations of channelized two-dimensional systems. Both conforming and nonconforming procedures are considered. The level of accuracy of the resulting method is shown to be consistently higher than that of the standard finite volume element multiscale technique based on localized basis functions determined using linear pressure boundary conditions.  相似文献   

2.
Subsurface formations are characterized by heterogeneity over multiple length scales, which can have a strong impact on flow and transport. In this paper, we present a new upscaling approach, based on time-of-flight (TOF), to generate upscaled two-phase flow functions. The method focuses on more accurate representations of local saturation boundary conditions, which are found to have a dominant impact (in comparison to the pressure boundary conditions) on the upscaled two-phase flow models. The TOF-based upscaling approach effectively incorporates single-phase flow and transport information into local upscaling calculations, accounting for the global flow effects on saturation, as well as the local variations due to subgrid heterogeneity. The method can be categorized into quasi-global upscaling techniques, as the global single-phase flow and transport information is incorporated in the local boundary conditions. The TOF-based two-phase upscaling can be readily integrated into any existing local two-phase upscaling framework, thus more flexible than local–global two-phase upscaling approaches developed recently. The method was applied to permeability fields with different correlation lengths and various fluid-mobility ratios. It was shown that the new method consistently outperforms existing local two-phase upscaling techniques, including recently developed methods with improved local boundary conditions (such as effective flux boundary conditions), and provides accurate coarse-scale models for both flow and transport.  相似文献   

3.
Boundary conditions are required to close the mathematical formulation of unstable density‐dependent flow systems. Proper implementation of boundary conditions, for both flow and transport equations, in numerical simulation are critical. In this paper, numerical simulations using the FEFLOW model are employed to study the influence of the different boundary conditions for unstable density‐dependent flow systems. A similar set up to the Elder problem is studied. It is well known that the numerical simulation results of the standard Elder problem are strongly dependent on spatial discretization. This work shows that for the cases where a solute mass flux boundary condition is employed instead of a specified concentration boundary condition at the solute source, the numerical simulation results do not vary between different convective solution modes (i.e., plume configurations) due to the spatial discretization. Also, the influence of various boundary condition types for nonsource boundaries was studied. It is shown that in addition to other factors such as spatial and temporal discretization, the forms of the solute transport equation such as divergent and convective forms as well as the type of boundary condition employed in the nonsource boundary conditions influence the convective solution mode in coarser meshes. On basis of the numerical experiments performed here, higher sensitivities regarding the numerical solution stability are observed for the Adams‐Bashford/Backward Trapezoidal time integration approach in comparison to the Euler‐Backward/Euler‐Forward time marching approach. The results of this study emphasize the significant consequences of boundary condition choice in the numerical modeling of unstable density‐dependent flow.  相似文献   

4.
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   

5.
In this paper, we describe an efficient approach for quantifying uncertainty in two-phase flow applications due to perturbations of the permeability in a multiscale heterogeneous porous medium. The method is based on the application of the multiscale finite element method within the framework of Monte Carlo simulation and an efficient preprocessing construction of the multiscale basis functions. The quantities of interest for our applications are the Darcy velocity and breakthrough time and we quantify their uncertainty by constructing the respective cumulative distribution functions. For the Darcy velocity we use the multiscale finite element method, but due to lack of conservation, we apply the multiscale finite volume element method as an alternative for use with the two-phase flow problem. We provide a number of numerical examples to illustrate the performance of the method.  相似文献   

6.
The development of various volume penalization techniques for use in modeling topographical features in the ocean is the focus of this paper. Due to the complicated geometry inherent in ocean boundaries, the stair-step representation used in the majority of current global ocean circulation models causes accuracy and numerical stability problems. Brinkman penalization is the basis for the methods developed here and is a numerical technique used to enforce no-slip boundary conditions through the addition of a term to the governing equations. The second aspect to this proposed approach is that all governing equations are solved on a nonuniform, adaptive grid through the use of the adaptive wavelet collocation method. This method solves the governing equations on temporally and spatially varying meshes, which allows higher effective resolution to be obtained with less computational cost. When penalization methods are coupled with the adaptive wavelet collocation method, the flow near the boundary can be well-resolved. It is especially useful for simulations of boundary currents and tsunamis, where flow near the boundary is important. This paper will give a thorough analysis of these methods applied to the shallow water equations, as well as some preliminary work applying these methods to volume penalization for bathymetry representation for use in either the nonhydrostatic or hydrostatic primitive equations.  相似文献   

7.
刘财  兰慧田  郭智奇  冯晅  鹿琪 《地球物理学报》2013,56(10):3461-3473
改进BISQ(Biot-Squirt)机制在不引入特征喷流长度的情况下,将含流体孔隙介质中Biot流动和喷射流动两种重要的力学机制有机地结合起来,且各相关参数具有明确物理意义和可实现性.本文将改进BISQ机制一维孔隙流体压力公式推广到三维具有水平对称轴横向各向同性介质(HTI介质)情况,结合裂缝各向异性理论,给出了基于改进BISQ机制的双相HTI介质模型及其二维三分量波传播方程,采用伪谱法求解该方程,进行了不同相界、不同频率以及双层地质结构情况下该类介质中波场的数值模拟与特征分析.数值模拟结果表明:伪谱法模拟精度高,压制网格频散效果好,可以得到高精度的波场快照和合成记录;基于改进BISQ机制的双相HTI介质模型兼具裂缝各向异性特征和孔隙弹性特征,其为从双相各向异性理论角度深入研究裂缝性储层的地震响应奠定了理论基础.  相似文献   

8.
This paper presents analytical solutions for steady-state, compressible two-phase flow through a wellbore under isothermal conditions using the drift flux conceptual model. Although only applicable to highly idealized systems, the analytical solutions are useful for verifying numerical simulation capabilities that can handle much more complicated systems, and can be used in their own right for gaining insight about two-phase flow processes in wells. The analytical solutions are obtained by solving the mixture momentum equation of steady-state, two-phase flow with an assumption that the two phases are immiscible. These analytical solutions describe the steady-state behavior of two-phase flow in the wellbore, including profiles of phase saturation, phase velocities, and pressure gradients, as affected by the total mass flow rate, phase mass fraction, and drift velocity (i.e., the slip between two phases). Close matching between the analytical solutions and numerical solutions for a hypothetical CO2 leakage problem as well as to field data from a CO2 production well indicates that the analytical solution is capable of capturing the major features of steady-state two-phase flow through an open wellbore, and that the related assumptions and simplifications are justified for many actual systems. In addition, we demonstrate the utility of the analytical solution to evaluate how the bottomhole pressure in a well in which CO2 is leaking upward responds to the mass flow rate of CO2-water mixture.  相似文献   

9.
Hybrid simulation is a powerful and cost‐effective simulation technique to evaluate structural dynamic performance. However, it is sometimes rather difficult to guarantee all the boundaries on the physical substructures, especially when the boundary conditions are very complex, due to limited laboratory resources. Lacking of boundary conditions is bound to change the stress state of the structure and eventually result in an inaccurate evaluation of structural performance. A model updating‐based online numerical simulation method is proposed in this paper to tackle the problem of incomplete boundary conditions. In the proposed method, 2 sets of finite element models with the same constitutive model are set up for the overall analysis of the whole structure and the constitutive model parameter estimation of the physical substructure, respectively. The boundary conditions are naturally satisfied because the response is calculated from the overall structural model, and the accuracy is improved as the material constitutive parameters are updated. The effectiveness of the proposed method is validated via numerical simulations and actual hybrid tests on a RC frame structure, and the results show that the negative effect of incomplete boundary conditions is almost eliminated and the accuracy of hybrid simulation is very much improved.  相似文献   

10.
A periodic vertical movement of the groundwater table results in a subsequent cyclic response of the water content and pressure profiles in the vadose zone. The sequence of periodic wetting and drying processes can be affected by hysteresis effects in this zone. A one-dimensional saturated/unsaturated flow model based on Richards’ equation and the Mualem (Soil Sci. 137 (1984) 283) hysteresis model is formulated which can take into account multi-cycle hysteresis effects in the relation between capillary pressure and water content. The numerical integration of the unsaturated flow equation is based on a Galerkin-type finite element method. The flow domain is discretised by finite elements with linear shape functions. Simulations start with static water content and pressure profiles, which correspond to either a boundary drying or wetting retention curve. To facilitate the numerical solution of the hysteretic case an implicit non-iterative procedure was chosen for the solution of the nonlinear differential equation. Laboratory experiments were performed with a vertical sand column by imposing a high frequency periodic pressure head at the lower end of the column. The total water volume in the column, and the periodic water content profile averaged over time were measured. The boundary drying and wetting curves of the relation between water content and capillary pressure were determined by independent experiments. The simulations of the experimental conditions show a clear effect of the hysteresis phenomenon on the water content profile. The simulations with hysteresis agree well with the measurements. Computed dimensionless water content profiles are presented for different oscillation frequencies with and without consideration of hysteresis.  相似文献   

11.
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   

12.
In this work, a hybrid boundary integral equation method (BIEM) is developed, based on both displacement and hypersingular traction formulations, for the analysis of time-harmonic seismic waves propagating through cracked, multi-layered geological regions with surface topography and under plane strain conditions. Specifically, the displacement-based BIEM is used for a multi-layered deposit with interface cracks, while the regularized, traction-based BIEM is used when internal cracks are present within the layers. The standard uni-dimensional boundary element with parabolic shape functions is employed for discretizing the free surface and the layer interfaces, while special discontinuous boundary elements are placed near the crack tips to model the asymptotic behaviour of both displacements and tractions. This formulation yields displacement amplitudes and phase angles on the free surface of a geological deposit, as well as stress intensity factors near the tips of the cracks. Finally, in the companion paper, numerical results are presented which show that both scattered wave and stress concentration fields are sensitive to the incidence seismic wave parameters and to specific site conditions such as surface topography, layering, the presence of cracks and crack interaction.  相似文献   

13.
In the realm of the numerical simulation, finite difference method and finite element method are more intuitive and effective than other simulation methods. In the process of simulating seismic wave propagation, the finite differences method is widely used because of its high computational efficiency and the advantage of the algorithm is more efficient. With the demand of precision, more and more researchers have proposed more effective methods of finite differences, such as the high-order staggered-grid finite differences method, which can restore the actual process of wave propagation on the premise of ensuring accuracy and improving the efficiency of operation. In the past numerical simulation of seismic wave field, different models of isotropic medium are mostly used, but it is difficult to reflect the true layer situation. With the research demand of natural seismology and seismic exploration, the research on anisotropic media is more and more extensive. Transversely isotropic(TI)media can well simulate the seismic wave propagation in the formation medium, such as gas-bearing sandstone, mudstone, shale et al., the character of TI media is reflected by introducing the Thomsen parameters to reflect its weak anisotropy of vertical direction by using Thomson parameter. Therefore, studying the process of seismic wave propagation in TI media can restore the true information of the formation to the greatest extent, and provide a more reliable simulation basis for the numerical simulation of seismic wave propagation. In the geodynamic simulation and the numerical simulation of the seismic wave field, under the limited influence of the calculation area, if no boundary conditions are added, a strong artificial boundary reflection will be generated, which greatly reduces the validity of the simulation. In order to minimize the influence of model boundaries on the reflection of seismic waves, it is often necessary to introduce absorbing boundary conditions. At present, there are three types of absorption boundary conditions: one-way wave absorption boundary, attenuation absorption boundary, and perfectly matched layer(PML)absorption boundary. In terms of numerical simulation of seismic waves, the boundary absorption effect of PML is stronger than the first two, which is currently the most commonly used method, and it also represents the cutting-edge development direction of absorption boundary technology. The perfectly matched layer absorbing boundary is effectively applied to eliminating the reflective waves from model boundaries, but for transversely isotropic medium, the effect of the absorbing is not very well. For this reason, the elastic dynamic wave equations in transversely isotropic media are derived, and we describe a second-order accurate time, tenth-order accurate space, formulation of the Madariaga-Virieux staggered-grid finite difference methods with the perfectly matched layer(PML)are given. In addition, we have established vertical transversely isotropic(VTI)media and arbitrary inclined tilted transversely isotropic(TTI)media models, using a uniform half-space velocity model and a two-layer velocity model, respectively. By combining the actual geoscience background, we set the corresponding parameters and simulation conditions in order to make our model more research-oriented. When setting model parameters, different PML thickness, incident angle, source frequency and velocity layer models were transformed to verify the inhibition of boundary reflection effect by PML absorption boundary layer. The implementations of this simulation show that the formula is correct and for the transversely isotropic(TI)media of any angular symmetry axis, when the thickness of the PML layer reaches a certain value, the seismic wave reflection effect generated by the artificial boundary can be well suppressed, and the absorption effect of PML is not subject to changes in incident angle and wave frequency. Therefore, the results of our study indicate that our research method can be used to simulate the propagation process of seismic waves in the transversely isotropic(TI)media without being affected by the reflected waves at the model boundary to restore the actual formation information and more valuable geological research.  相似文献   

14.
本文以饱水两相介质的土力学模型为研究对象,在假定两相介质为弹性介质条件下,采用了显式有限元法和透射边界进行了饱和弹性半空间动力响应问题的研究。为避免谐波输入初始间断的影响,文中提出了一个处理函数,并以弹性半空间为算例,对饱水介质和单相介质分别进行了在底边界P波垂直入射时的动力响应分析,验证了该处理函数的有效性和实用性。  相似文献   

15.
A two-phase model for fast geomorphic shallow flows   总被引：1，自引：0，他引：1  
The paper introduces a 2D shallow water model based on a two-phase formulation for the analysis of fast geomorphic transients occurring in the context of river morphodynamics.Mass and momentum conservation principles are separately imposed for both phases.The model naturally accounts for non-equilibrium solid transport,since neither instantaneous adaptation hypothesis nor any lag equation is employed to represent sediment dynamics.The hyperbolic character of the proposed model is shown to be preserved independently on the flow conditions.Results from numerical simulations of both 1D and 2D test-cases are compared with literature experimental data and with available numerical solutions.  相似文献   

16.
A semi-analytical method has been developed for calculating oil recovery in two and three dimensions, and for calculating effective relative permeabilities for coarse grids. The calculations are based on the assumption that the effects of a changing mobility field can be accounted for by using fixed streamtube geometries with flowrates updated to account for the changing mobility distribution. The single-phase pressure distribution from a numerical solution of Laplace's equation is used to calculate the pressure distribution for a two-phase flow based on a mapping of the solution of the Buckley-Leverett equation onto the streamtubes derived from the single-phase solution. The displacement calculations for oil recovery are based on theory previously developed by Dykstra and Parsons, extended to include the effects of spatially varying permeability and continuously changing mobilities, as occurs in solutions of the Buckley-Leverett equation for typical values of the mobility ratio. This idea has also been extended to the calculation of effective relative permeabilities for coarse-grid simulation and finally establishes the proper rules for averaging the results of fine-grid numerical simulations of two-phase flow for the definition of effective two-phase flow properties on coarse grids. These calculations have been generalized to three-dimensional flows by the simple device of conceptually inserting a gridded plane across the flow and defining each streamtube at that location as those streamlines which pass through any one of the grid cells. When combined with time-of-flight calculations from the gridded plane to both the producer and injector, the distribution of pore volume along each streamtube can be calculated. This information, combined with a tabulation of the single-phase, steady-state pressure distribution along each streamtube, provides all of the information needed for the semi-analytical calculation of oil recovery and effective flow properties in three-dimensional flows. © 1997 Elsevier Science Ltd. All rights reserved  相似文献   

17.
The paper presents numerical simulations of water infiltration in unsaturated porous media containing coarse-textured inclusions embedded in fine-textured background material. The calculations are performed using the two-phase model for water and air flow and a simplified model known as the Richards equation. It is shown that the Richards equation cannot correctly describe flow in the presence of heterogeneities. However, its performance can be improved by introducing appropriately defined effective capillary and permeability functions, representing largescale behaviour of the heterogeneous medium.  相似文献   

18.
如何选取非岩性地基的处理方案对于不满足抗震适应性要求的核岛厂房地基而言具有重要的工程实用价值。结合国内某内陆核电不符合抗震适应性要求的实际厂址条件,给出地基处理方案评价的数值计算模型及分析过程。首先针对该核电工程实际项目,提出嵌岩桩、CFG桩及水泥土搅拌桩三种地基预处理方案,并以规范法验证处理后地基的承载力要求;进而通过建立非岩性地基条件下的桩-土-结构动力相互作用计算模型来综合考虑各方案对核岛厂房的地震响应影响,其中通过引入黏性人工边界和能量传递边界模拟无限地基辐射阻尼效应,采用等效线性法描述近场地基非线性特征,并基于上述有限元模型以全耦合方式考虑群桩效应的影响;最后从满足厂址地基适应性和经济效益两方面进行综合评价,给出针对本工程的最佳设计方案。该分析方法及研究成果可为类似条件下的核岛厂房非岩性地基处理方案的比选问题提供借鉴与参考。  相似文献   

19.
The problem of quantifying the effects of flexible plants on flow resistance and eddy viscosity by vegetated floodplains is first addressed with a one‐dimensional (1D) approximation based upon the so‐called lateral distribution method. The estimates so obtained are then tested with two‐dimensional (2D) numerical simulations based on the full shallow water equations through the use of the computational code Telemac‐2D. Data obtained on a physical model of the Besòs River (Spain), whose floodplains were covered with plastic ornamental plants to mimic the effect of flexible vegetation, is used for the validation of the numerical results. Additionally, the values of flow resistance estimated numerically with the 1D and 2D simulations are compared with values obtained in a rectangular flume under flow conditions (slope, water depth and artificial lining) similar to those used on the reduced model. It is then established that as more physical mechanisms are included in the mathematical model used to study the problem, the ratio between the floodplain and the main channel flow resistance coefficient increases. The approach demonstrates that whenever enough flow data is available, the lateral distribution method delivers values of flow resistance and eddy viscosity which are highly consistent with 2D numerical modelling. This finding could mean considerable savings in the burdensome task of specifying flow resistance and turbulence dissipation values for 2D modelling of large compound channel systems. Copyright © 2004 John Wiley & Sons, Ltd.  相似文献   

20.
The discontinuous spectral Galerkin method uses a finite-element discretization of the groundwater flow domain with basis functions of arbitrary order in each element. The independent choice of the basis functions in each element permits discontinuities in transmissivity in the flow domain. This formulation is shown to be of high order accuracy and particularly suitable for accurately calculating the flow field in porous media. Simulations are presented in terms of streamlines in a bidimensional aquifer, and compared with the solution calculated with a standard finite-element method and a mixed finite-element method. Numerical simulations show that the discontinuous spectral Galerkin approximation is more efficient than the standard finite-element method (in computing fluxes and streamlines/pathlines) for a given accuracy, and it is more accurate on a given grid. On the other hand the mixed finite-element method ensures the continuity of the fluxes at the cell boundaries and it is particular efficient in representing complicated flow fields with few mesh points. Simulations show that the mixed finite-element method is superior to the discontinuous spectral Galerkin method producing accurate streamlines even if few computational nodes are used. The application of the discontinuous Galerkin method is thus of interest in groundwater problems only when high order and extremely accurate solutions are needed.  相似文献   

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