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1.
The coupling upscaling finite element method is developed for solving the coupling problems of deformation and consolidation of heterogeneous saturated porous media under external loading conditions. The method couples two kinds of fully developed methodologies together, i.e., the numerical techniques developed for calculating the apparent and effective physical properties of the heterogeneous media and the upscaling techniques developed for simulating the fluid flow and mass transport properties in heterogeneous porous media. Equivalent permeability tensors and equivalent elastic modulus tensors are calculated for every coarse grid block in the coarse-scale model of the heterogeneous saturated porous media. Moreover, an oversampling technique is introduced to improve the calculation accuracy of the equivalent elastic modulus tensors. A numerical integration process is performed over the fine mesh within every coarse grid element to capture the small scale information induced by non-uniform scalar field properties such as density, compressibility, etc. Numerical experiments are carried out to examine the accuracy of the developed method. It shows that the numerical results obtained by the coupling upscaling finite element method on the coarse-scale models fit fairly well with the reference solutions obtained by traditional finite element method on the fine-scale models. Moreover, this method gets more accurate coarse-scale results than the previously developed coupling multiscale finite element method for solving this kind of coupling problems though it cannot recover the fine-scale solutions. At the same time, the method developed reduces dramatically the computing effort in both CPU time and memory for solving the transient problems, and therefore more large and computational-demanding coupling problems can be solved by computers. 相似文献
2.
A three‐dimensional (3D) electrical resistivity modelling code is developed to interpret surface and subsurface data. Based on the integral equation, it calculates the charge density caused by conductivity gradients at each interface of the mesh, allowing the estimation of the potential everywhere without the need to interpolate between nodes. Modelling generates a huge matrix, made up of Green's functions, which is stored by using the method of pyramidal compression. The potential is compared with the analytical and the numerical solutions obtained by finite‐difference codes for two models: the two‐layer case and the vertical contact case. The integral method is more accurate around the source point and at the limits of the domain for the potential calculation using a pole‐pole array. A technique is proposed to calculate the sensitivity (Jacobian) and Hessian matrices in 3D. The sensitivity is based on the derivative with respect to the block conductivity of the potential computed using the integral equation; it is only necessary to compute the electrical field at the source location. A direct extension of this technique allows the determination of the second derivatives. The technique is compared with the analytical solutions and with the calculation of the sensitivity according to the method using the inner product of the current densities calculated at the source and receiver points. Results are very accurate when the Green's function that includes the source image is used. The calculation of the three components of the electric field on the interfaces of the mesh is carried out simultaneously and quickly, using matrix compression. 相似文献
3.
本文提出了一种基于非结构化网格的海洋电磁有限单元正演算法.为了回避场源奇异性,文中选用二次场算法,将背景电阻率设置为水平层状且各向异性,场源在水平层状各向异性介质中所激发的一次场通过汉克尔积分得到.基于Coulomb规范得到二次矢量位和标量位所满足的Maxwell方程组,通过Galerkin加权余量法形成大型稀疏有限元方程,采用不完全LU分解(ILU)预条件因子的quasi-minimum residual(QMR)迭代解法对有限元方程进行求解得到二次矢量位和标量位;进而,利用滑动平均方法得到二次矢量位和标量位在空间的导数,由此得到二次电磁场;通过一维模型对算法的可靠性进行验证,与此同时,针对实际复杂海洋电磁模型,比较有限元模拟结果与积分方程模拟结果,进一步验证算法精度.若干计算结果均表明,文中算法具有良好的通用性,适用于井中电磁、航空电磁,环境地球物理等非均匀且各向异性介质中的电磁感应基础研究. 相似文献
4.
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
5.
In the analytic element method, strings of line-sinks may be used to model streams and strings of line-doublets may be used to model impermeable walls or boundaries of inhomogeneities. The resulting solutions are analytic, but the boundary conditions are met approximately. Equations for line elements may be derived in two ways: through integration of point elements (the integral solution) and through application of separation of variables in elliptical coordinates (the elliptical solution). Using both approaches, two sets of line elements are presented for four flow problems: line-sinks and line-doublets in (un)confined flow, and line-sinks and line-doublets in semi-confined flow. Elliptical line elements have the advantage that they do not need a far-field expansion for accurate evaluation far away from the element. The derivation of elliptical line elements is new and applicable to both (un)confined flow and semi-confined flow; only the resulting expressions for elliptical line elements for semi-confined flow have not been found in the current groundwater literature. Existing solutions for elliptical line elements for (un)confined flow were intended for the modeling of isolated features. Four examples are presented, one for each flow problem, to demonstrate that strings of elliptical line elements may be used to obtain accurate solutions; elliptical line-doublets for semi-confined flow can only be strung together in combination with two integral line-doublets. For a zigzag canal in (un)confined flow, a string of elliptical line-sinks performed better than a string of integral line-sinks of the same order when the smallest angle between two adjacent segments is less than 130°. Elliptical line-doublets performed better than integral line-doublets for a square inhomogeneity in a uniform, confined flow field; the difference was smaller for an octagonal inhomogeneity. For semi-confined flow, the difference between the integral and elliptical line-sinks was small when modeling a zigzag canal. 相似文献
6.
《Advances in water resources》1998,21(5):351-362
Flow and displacement of non-Newtonian fluids in porous media occurs in many subsurface systems, related to underground natural resource recovery and storage projects, as well as environmental remediation schemes. A thorough understanding of non-Newtonian fluid flow through porous media is of fundamental importance in these engineering applications. Considerable progress has been made in our understanding of single-phase porous flow behavior of non-Newtonian fluids through many quantitative and experimental studies over the past few decades. However, very little research can be found in the literature regarding multi-phase non-Newtonian fluid flow or numerical modeling approaches for such analyses.For non-Newtonian fluid flow through porous media, the governing equations become nonlinear, even under single-phase flow conditions, because effective viscosity for the non-Newtonian fluid is a highly nonlinear function of the shear rate, or the pore velocity. The solution for such problems can in general only be obtained by numerical methods.We have developed a three-dimensional, fully implicit, integral finite difference simulator for single- and multi-phase flow of non-Newtonian fluids in porous/fractured media. The methodology, architecture and numerical scheme of the model are based on a general multi-phase, multi-component fluid and heat flow simulator — TOUGH2. Several rheological models for power-law and Bingham non-Newtonian fluids have been incorporated into the model. In addition, the model predictions on single- and multi-phase flow of the power-law and Bingham fluids have been verified against the analytical solutions available for these problems, and in all the cases the numerical simulations are in good agreement with the analytical solutions. In this presentation, we will discuss the numerical scheme used in the treatment of non-Newtonian properties, and several benchmark problems for model verification.In an effort to demonstrate the three-dimensional modeling capability of the model, a three-dimensional, two-phase flow example is also presented to examine the model results using laboratory and simulation results existing for the three-dimensional problem with Newtonian fluid flow. 相似文献
7.
《Advances in water resources》2001,24(8):899-911
A new computational method for the calculation of shallow water flows with moving physical boundaries is presented. The procedure can cope with shallow water problems having arbitrarily complex geometries and moving boundary elements. Although the method provides a fully boundary-fitted capability, no mesh generation is required in the conventional sense. Solid regions are simply cut out of a background Cartesian mesh with their boundaries represented by different types of cut cell. Moving boundaries are accommodated by up-dating the local cut cell information on a stationary background mesh as the boundaries move. No large-scale re-meshing is required. For the flow calculations, a multi-dimensional high resolution upwind finite volume scheme is used in conjunction with an efficient approximate Riemann solver at flow interfaces, and an exact Riemann solution for a moving piston at moving boundary elements. The method is validated for test problems that include a ship's hull moving at supercritical velocity and two hypothetical landslide events where material plunges laterally into a quiescent shallow lake and a fiord. 相似文献
8.
本文就波动问题提出一种移动边界的有限单元解法。此时模型边界的位置不是固定的,它将随着波前向前推进和退回,以保证在计算时间长度内边界反射波不到达观测点。文中给出了计算边界有效载荷的递推公式,可以简便有效地避免虚假反射波的干扰。为降低运算量和虚模型中的存贮,应适当选取移动间隔,截断误差和移动起点。对于层状模型,若采用直接积分的中心差分方法,计算过程十分简单,也可用于有限差分等方法的计算中。该方法在应用上的限制是对计算机内存量的要求较通常方法为大。 相似文献
9.
Two new approaches are presented for the accurate computation of the potential due to line elements that satisfy the modified Helmholtz equation with complex parameters. The first approach is based on fundamental solutions in elliptical coordinates and results in products of Mathieu functions. The second approach is based on the integration of modified Bessel functions. Both approaches allow evaluation of the potential at any distance from the element. The computational approaches are applied to model transient flow with the Laplace transform analytic element method. The Laplace domain solution is computed using a combination of point elements and the presented line elements. The time domain solution is obtained through a numerical inversion. Two applications are presented to transient flow fields, which could not be modeled with the Laplace transform analytic element method prior to this work. The first application concerns transient single-aquifer flow to wells near impermeable walls modeled with line-doublets. The second application concerns transient two-aquifer flow to a well near a stream modeled with line-sinks. 相似文献
10.
在复杂山地和复杂海底条件下,地表和海底的剧烈起伏对地震波数值模拟提出了更高的要求.常规有限差分法采用矩形网格对模型进行网格剖分,由于矩形网格自身的限制,起伏地表或起伏海底只能由一系列阶梯状折线代替,从而引起人为虚假绕射波.此外,在模拟液-固界面的反射波时,如果界面与网格线不一致,则需要更密的网格才能得到精确的结果.为了解决上述问题,本文将自适应网格生成技术引入到起伏海底速度模型的网格剖分中,采用高阶仿真型有限差分法(MFD)对曲线坐标下的声波方程波进行了数值模拟.利用自适应网格生成技术对速度模型进行网格剖分不仅可以准确地描述模型边界,而且可以有效消除虚假绕射波.高阶仿真型有限差分法可以有效压制频散提高计算精度.模型试算结果表明,本文方法对复杂海底模型具有很好的适应性. 相似文献
11.
We present an immersed structure approach for modeling the interaction between surface flows and vegetation. Fluid flow and rigid and flexible vegetative obstacles are coupled through a local drag relation that conserves momentum. In the presented method, separate meshes are used for the fluid domain and vegetative obstacles. Taking techniques from immersed boundary finite element methods, the effects of the fluid on the vegetative structures and vice versa are calculated using integral transforms. Using a simple elastic structure model we incorporate bending and moving vegetative obstacles. We model flexible vegetation as thin, elastic, inextensible cantilever beams. Using the immersed structure approach, a fully coupled fluid-vegetation interaction model is developed assuming dynamic fluid flow and quasi-static bending. This relatively computationally inexpensive model allows for thousands of vegetative obstacles to be included in a simulation without requiring an extremely refined fluid mesh. The method is validated with comparisons to mean velocity profiles and bent vegetation heights from experiments that are reproduced computationally. We test the method on several channel flow setups. We calculate the bulk drag coefficient in these flow scenarios and analyze their trends with changing model parameters including stem population density and flow Reynolds number. Bulk drag models are the primary method of incorporating small-scale drag from individual plants into a value that can be used in larger-scale models. Upscaled bulk drag quantities from this method may be utilized in larger-scale simulations of flow through vegetation regions. 相似文献
12.
《Advances in water resources》2004,27(6):583-599
Methods for estimating the parameter distributions necessary for modeling fluid flow and contaminant transport in the shallow subsurface are in great demand. Soil properties such as permeability, porosity, and water retention are typically estimated through the inversion of hydrological data (e.g., measurements of capillary pressure and water saturation). However, ill-posedness and non-uniqueness commonly arise in such non-linear inverse problems making their solutions elusive. Incorporating additional types of data, such as from geophysical methods, may greatly improve the success of inverse modeling. In particular, ground-penetrating radar (GPR) methods have proven sensitive to subsurface fluid flow processes and appear promising for such applications. In the present work, an inverse technique is presented which allows for the estimation of flow parameter distributions and the prediction of flow phenomena using GPR and hydrological measurements collected during a transient flow experiment. Specifically, concepts from the pilot point method were implemented in a maximum a posteriori (MAP) framework to allow for the generation of permeability distributions that are conditional to permeability point measurements, that maintain specified patterns of spatial correlation, and that are consistent with geophysical and hydrological data. The current implementation of the approach allows for additional flow parameters to be estimated concurrently if they are assumed uniform and uncorrelated with the permeability distribution. (The method itself allows for heterogeneity in these parameters to be considered, and it allows for parameters of the petrophysical and semivariogram models to be estimated as well.) Through a synthetic example, performance of the method is evaluated under various conditions, and some conclusions are made regarding the joint use of transient GPR and hydrological measurements in estimating fluid flow parameters in the vadose zone. 相似文献
13.
The finite element method is employed in the prediction of the dynamic transient response of two- and three-dimensional solids exhibiting geometric (large deformations) and material (elasto-plastic) non-linearities. Explicit time marching schemes are adopted for integration of the dynamic equilibrium equation and a diagonal ‘lumped’ mass matrix is employed with a special procedure applicable to parabolic isoparametric elements. A variety of problems are presented including a solid/fluid interaction situation, and the method is shown to be able to solve economically many problems of dynamic or catastrophic nature which can occur in such structures as nuclear reactors, containment vessels, etc. 相似文献
14.
A multiscale adjoint (MSADJ) method is developed to compute high-resolution sensitivity coefficients for subsurface flow in large-scale heterogeneous geologic formations. In this method, the original fine-scale problem is partitioned into a set of coupled subgrid problems, such that the global adjoint problem can be efficiently solved on a coarse grid. Then, the coarse-scale sensitivities are interpolated to the local fine grid by reconstructing the local variability of the model parameters with the aid of solving embedded adjoint subproblems. The approach employs the multiscale finite-volume (MSFV) formulation to accurately and efficiently solve the highly detailed flow problem. The MSFV method couples a global coarse-scale solution with local fine-scale reconstruction operators, hence yielding model responses that are quite accurate at both scales. The MSADJ method is equally efficient in computing the gradient of the objective function with respect to model parameters. Several examples demonstrate that the approach is accurate and computationally efficient. The accuracy of our multiscale method for inverse problems is twofold: the sensitivity coefficients computed by this approach are more accurate than the traditional finite-difference-based numerical method for computing derivatives, and the calibrated models after history matching honor the available dynamic data on the fine scale. In other words, the multiscale based adjoint scheme can be used to history match fine-scale models quite effectively. 相似文献
15.
LI Yitian XIE Jianheng Wuhan University of Hydraulic Electric Engineering Wuhan University of Hydraulic Electric Engineering 《国际泥沙研究》1993,(1)
I. INTRODUCTIONIt is necessary, sometimes, to predict river bed deformahon during the alanning and design stages of a hydraulic project. As the nuvial process is quite complicated, the I --Dmathematical models currently in use can not satisfy the various needs in hydraulic engineering. Particularly in engineering practice, there is a strong desire of knowing the hydraulicconditions and river bed deformation in details. Some two dimensional models as well asqusi--two--dissensional models … 相似文献
16.
A wetting and drying method for free-surface problems for the three-dimensional, non-hydrostatic Navier–Stokes equations is proposed. The key idea is to use a horizontally fixed mesh and to apply different boundary conditions on the free-surface in wet and dry zones. In wet areas a combined pressure/free-surface kinematic boundary condition is applied, while in dry areas a positive water level and a no-normal flow boundary condition are enforced. In addition, vertical mesh movement is performed to accurately represent the free-surface motion. Non-physical flow in the remaining thin layer in dry areas is naturally prevented if a Manning–Strickler bottom drag is used. The treatment of the wetting and drying processes applied through the boundary condition yields great flexibility to the discretisation used. Specifically, a fully unstructured mesh with any finite element choice and implicit time discretisation method can be applied. The resulting method is mass conservative, stable and accurate. It is implemented within Fluidity-ICOM [1] and verified against several idealized test cases and a laboratory experiment of the Okushiri tsunami. 相似文献
17.
Numerical simulation of an unsaturated flow equation 总被引：1，自引：1，他引：0
A numerical model for an unsaturated flow problem by using the finite element method is established in order to simulate liquid
moisture flow In an unsaturated zone with homogeneous soil and deep subsurface water, and with different initial and boundary
conditions. For infiltration or evaporation problems, a traditional method usually yields oscillatory non-physics profiles.
However, nonoscillatory solutions are obtained and non-physics solutions for these problems are evaded by using the mass-lumped
finite element method. Moreover, the kind of boundary condition is handled very well.
Project supported by the National Key Project of Fundamental Research ”Climate Dynamics and Climate Prediction Theory“ and
China Postdoctoral Science Foundation. 相似文献
18.
Abstract Finite difference algorithms have been developed to solve a one-dimensional non-linear parabolic equation with one or two moving boundaries and to analyse the unsteady plane flow of ice-sheets. They are designed to investigate the response of an ice-sheet to changes in climate, and to reconstruct climatic changes implied by past ice-sheet variations inferred from glacial geological data. Two algorithms are presented and compared. The first, a fixed domain method, replaces time as an independent variable with span. The grid interval in real space is kept constant, and thus the number of grid points changes with span. The second, a moving mesh method, retains time as one of the independent variables, but normalises the spatial variable relative to the span, which now enters the diffusion and advection coeficients in the parabolic equation for the surface profile. Crank-Nicholson schemes for the solution of the equations are constructed, and iterative schemes for the solution of the resulting non-linear equations are considered. Boundary (margin) motion is governed by the surface slope at the margin. Differentiation of the evolution equations results in an evolution equation for the margin slopes. It is shown that incorporation of this evolution equation, while not formally increasing the accuracy of the finite difference schemes, in practice increases accuracy of the solution. 相似文献
19.
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
20.
《Advances in water resources》2003,26(11):1189-1198
A two-dimensional finite element based overland flow model was developed and used to study the accuracy and stability of three numerical schemes and watershed parameter aggregation error. The conventional consistent finite element scheme results in oscillations for certain time step ranges. The lumped and the upwind finite element schemes are tested as alternatives to the consistent scheme. The upwind scheme did not improve on the stability or the accuracy of the solution, while the lumped scheme provided stable and accurate solutions for time steps twice the size of time steps needed for the consistent scheme. A new accuracy based dynamic time step estimate for the two-dimensional overland flow kinematic wave solution is developed for the lumped scheme. The newly developed dynamic time step estimates are functions of the mesh size, and time of concentration of the watershed hydrograph. Due to lack of analytical solutions, the time step was developed by comparing numerical solutions of various levels of discretization to a reference solution using a very fine mesh and a very small time step. The time step criteria were tested on a different set of problems and proved to be adequate for accurate and stable solutions. A sensitivity analysis for the watershed slope, Manning’s roughness coefficient and excess rainfall rate was conducted in order to test the effect of parameter aggregation on the stability and accuracy of the solution. The results of this analysis show that aggregation of the slope data resulted in the highest error. The roughness coefficient had a smaller effect on the solution while the rainfall intensity did not show any significant effect on the flow rate solution for the range of rainfall intensity used. This work pioneers the challenge of providing guidelines for accurate and stable numerical solutions of the two-dimensional kinematic wave equations for overland flow. 相似文献