共查询到20条相似文献，搜索用时 828 毫秒
1.
A preliminary problem to solve in the set-up of a mathematical model simulating a geophysical process is the choice of a suitable discrete scheme to approximate the governing differential equations. This paper presents a simple technique to test finite difference schemes used in the modeling of geophysical processes occurring in a geological structure. This technique consists in generating analytical solutions similar to the ones characterizing a geophysical process, given general information on some relevant parameters. Useful information for the choice of the discrete scheme to employ in the mathematical model simulating the original geophysical process can be obtained from the comparison between the analytical solution and the approximated numerical solutions generated by means of different discrete schemes. Two classes of numerical examples approximating the differential equation that governs the steady state earth's heat flow have been treated using three different finite differences schemes. The first class of examples deals with media whose phenomenological parameters vary as continuous space functions; the second class, instead, deals with media whose phenomenological parameters vary as discontinuous space functions. The finite difference schemes that have been utilized are: Centered Finite Difference Scheme (CDS), Arithmetic Mean Scheme (AMS), and Harmonic Mean Scheme (HMS).The numerical simulations showed that: the CDS may yield physically inconsistent solutions if the lattice internodal distance is too large, but in case of phenomenological parameters varying as a continuous function, this pitfall can be avoided increasing the lattice node refinement. In case of phenomenological parameters varying as a discontinuous function, instead, the CDS may yield physically inconsistent solutions for any lattice-node refinement. The HMS produced good results for both classes of examples showing to be a scheme suitable to model situations like these. 相似文献
2.
Vasiliy Kramarenko Kirill Nikitin Yuri Vassilevski 《Computational Geosciences》2017,21(5-6):1023-1033
We present the latest enhancement of the nonlinear monotone finite volume method for the near-well regions. The original nonlinear method is applicable for diffusion, advection-diffusion, and multiphase flow model equations with full anisotropic discontinuous permeability tensors on conformal polyhedral meshes. The approximation of the diffusive flux uses the nonlinear two-point stencil which reduces to the conventional two-point flux approximation (TPFA) on cubic meshes but has much better accuracy for the general case of non-orthogonal grids and anisotropic media. The latest modification of the nonlinear method takes into account the nonlinear (e.g., logarithmic) singularity of the pressure in the near-well region and introduces a correction to improve accuracy of the pressure and the flux calculation. In this paper, we consider a linear version of the nonlinear method waiving its monotonicity for sake of better accuracy. The new method is generalized for anisotropic media, polyhedral grids and nontrivial cases such as slanted, partially perforated wells or wells shifted from the cell center. Numerical experiments show noticeable reduction of numerical errors compared to the original monotone nonlinear FV scheme with the conventional Peaceman well model or with the given analytical well rate. 相似文献
3.
建立了基于无结构三角网格下采用有限体积法求解的二维水动力学模型,用于模拟溃坝洪水在复杂边界及实际地形上的流动过程。该模型采用Roe格式的近似Riemann解计算界面水流通量,结合空间方向的TVD-MUSCL格式及时间方向的预测-校正格式,可使模型在时空方向具有二阶计算精度。模型中引入最小水深概念,提出了有效的干湿界面处理方法。模拟了理想条件下溃坝水流过程,研究不同最小水深取值对干河床上洪水演进的影响,并用两组简单溃坝水流的水槽试验资料对模型进行验证。采用该模型模拟了实际溃坝洪水的流动过程,所得计算结果与实测资料及已有模型计算结果较为符合。 相似文献
4.
We present a new nonlinear monotone finite volume method for diffusion equation and its application to two-phase flow model. We consider full anisotropic discontinuous diffusion or permeability tensors on conformal polyhedral meshes. The approximation of the diffusive flux uses the nonlinear two-point stencil which provides the conventional seven-point stencil for the discrete diffusion operator on cubic meshes. We show that the quality of the discrete flux in a reservoir simulator has great effect on the front behavior and the water breakthrough time. We compare two two-point flux approximations (TPFA), the proposed nonlinear TPFA and the conventional linear TPFA, and multipoint flux approximation (MPFA). The new nonlinear scheme has a number of important advantages over the traditional linear discretizations. Compared to the linear TPFA, the nonlinear TPFA demonstrates low sensitivity to grid distortions and provides appropriate approximation in case of full anisotropic permeability tensor. For nonorthogonal grids or full anisotropic permeability tensors, the conventional linear TPFA provides no approximation, while the nonlinear flux is still first-order accurate. The computational work for the new method is higher than the one for the conventional TPFA, yet it is rather competitive. Compared to MPFA, the new scheme provides sparser algebraic systems and thus is less computational expensive. Moreover, it is monotone which means that the discrete solution preserves the nonnegativity of the differential solution. 相似文献
5.
M. Schneider B. Flemisch R. Helmig K. Terekhov H. Tchelepi 《Computational Geosciences》2018,22(2):565-586
This article presents a new positivity-preserving finite-volume scheme with a nonlinear two-point flux approximation, which uses optimization techniques for the face stencil calculation. The gradient is reconstructed using harmonic averaging points with the constraint that the sum of the coefficients included in the face stencils must be positive. We compare the proposed scheme to a nonlinear two-point scheme available in literature and a few linear schemes. Using two test cases, taken from the FVCA6 benchmarks, the accuracy of the scheme is investigated. Furthermore, it is shown that the scheme is linearity-preserving on highly complex corner-point grids. Moreover, a two-phase flow problem on the Norne formation, a geological formation in the Norwegian Sea, is simulated. It is demonstrated that the proposed scheme is consistent in contrast to the linear Two-Point Flux Approximation scheme, which is industry standard for simulating subsurface flow on corner-point grids. 相似文献
6.
Piyang Liu Gary Douglas Couples Jun Yao Zhaoqin Huang Wenhui Song Jingsheng Ma 《Computational Geosciences》2018,22(5):1187-1201
The two-scale continuum model is widely used in simulating the reactive dissolution process and predicting the optimum injection rate for carbonate reservoir acidizing treatment. The numerical methods of this model are currently based on structured grids, which are not applicable for complicated geometries. In this study, a general numerical scheme for simulating a reactive flow problem on both structured and unstructured grids is presented based on the finite volume method (FVM). The convection and diffusion terms involved in the reactive flow model are discretized by using the upwind scheme and two-point flux approximation (TPFA), respectively. The location of the centroid node inside each control volume is moved by using an optimization algorithm to make the connections with the surrounding elements as orthogonal as possible, which systematically improves the accuracy of the TPFA scheme. Additionally, in order to avoid the computational complexity resulting from the discretization of the non-linear term, the mass balance equation is only discretized in the spatial domain to get a set of ordinary differential equations (ODEs). These ODEs are coupled with the reaction equations and then solved using the numerical algorithm on ODEs. The accuracy and efficiency of the proposed method are studied by comparing the results obtained from the proposed numerical method with previous experimental and numerical results. This comparison indicates that, compared with the previous methods, the proposed method predicts the wormhole structure more accurately. Finally, the presented method is used to check the effect of the domain geometry, and it is found that the geometry of the flow domain has no effect on the optimum injection velocity, but the radial domain requires a larger breakthrough volume than the linear domain when other parameters are fixed. 相似文献
7.
This work deals with sequential implicit schemes for incompressible and immiscible two-phase Darcy flows which are commonly used and well understood in the case of spatially homogeneous capillary pressure functions. To our knowledge, the stability of this type of splitting schemes solving sequentially a pressure equation followed by the saturation equation has not been investigated so far in the case of discontinuous capillary pressure curves at different rock type interfaces. It will be shown here to raise severe stability issues for which stabilization strategies are investigated in this work. To fix ideas, the spatial discretization is based on the Vertex Approximate Gradient (VAG) scheme accounting for unstructured polyhedral meshes combined with an Hybrid Upwinding (HU) of the transport term and an upwind positive approximation of the capillary and gravity fluxes. The sequential implicit schemes are built from the total velocity formulation of the two-phase flow model and only differ in the way the conservative VAG total velocity fluxes are approximated. The stability, accuracy and computational cost of the sequential implicit schemes studied in this work are tested on oil migration test cases in 1D, 2D and 3D basins with a large range of capillary pressure parameters for the drain and barrier rock types. It will be shown that usual splitting strategies fail to capture the right solutions for highly contrasted rock types and that it can be fixed by maintaining locally the pressure saturation coupling at different rock type interfaces in the definition of the conservative total velocity fluxes. The numerical investigation of the sequential schemes is also extended to the widely used finite volume Two-Point Flux Approximation spatial discretization.
相似文献8.
A systematic analysis shows how results from the finite difference code SEAWAT are sensitive to choice of grid dimension, time step, and numerical scheme for unstable flow problems. Guidelines to assist in selecting appropriate combinations of these factors are suggested. While the SEAWAT code has been tested for a wide range of problems, the sensitivity of results to spatial and temporal discretization levels and numerical schemes has not been studied in detail for unstable flow problems. Here, the Elder-Voss-Souza benchmark problem has been used to systematically explore the sensitivity of SEAWAT output to spatio-temporal resolution and numerical solver choice. A grid size of 0.38 and 0.60% of the total domain length and depth respectively is found to be fine enough to deliver results with acceptable accuracy for most of the numerical schemes when Courant number (Cr) is 0.1. All numerical solvers produced similar results for extremely fine meshes; however, some schemes converged faster than others. For instance, the 3rd-order total variation-diminishing method (TVD3) scheme converged at a much coarser mesh than the standard finite difference methods (SFDM) upstream weighting (UW) scheme. The sensitivity of the results to Cr number depends on the numerical scheme as expected. 相似文献
9.
10.
GJP-1 Program is used for three –dimensional elasto-static finite element analysis related to joints, which is the first stage result of three-dimensional nonlinear finite element analysis aimed at subject of rock and soil mechanics. Intact media and discontinuities are modeled by a twenty-node isoparametric finite elements and a sixteen-node isoparametric joint elements respectively, which can be subjected to nodal forces, gravity loads, uniformly or nonuniformly distributed loads acting perpendicularly or obliquely on any faces of elements properties for different elements. GJP-1 has an ability to generate and adjust meshes and to check input data autpmatically, and provides user with frotal solution and subblock triangular resolution in order to solve larger problems with medium or small computer. Several simple problems are solved with GJP-1 for illustrating and testing purposes. Comparison is made between the computational results and the theoretical solutions. 相似文献
11.
GJP-1程序是针对岩土力学课题而进行的空间非线性有限元分析的第一阶段成果,可用于含节理的三维弹性静力有限元分析。 GJP-1程序采用20节点等参元划分连续介质,而用18节点等参节理单元来模拟非连续面。本程序考虑了集中荷载、重力荷载、均布或不均布的作用方向为任意的面荷载、温度荷载,以及它们的各种组合作用。本程序允许各个单元有不同的材料性质。GJP-1程序具有自动划分网格,自动调整网格,和自动校核数据的功能,并提供波前法和分块三角分解解法供用户灵活选用,以便能在中小型计算机上求解比较大型的工程问题。本文列举了几个有理论解的算例,计算结果表明,本程序的计算精度是令人满意的 相似文献
12.
锚索与锚杆联合锚固支护岩坡的有限元分析 总被引：1，自引：0，他引：1
针对广东某高速公路74 m高的7级挖方边坡,采用三维弹塑性有限元数值计算方法分析山区路堑开挖岩质边坡的锚固支护的受力情况。分别计算了坡体无锚和3种不同的锚固方案。通过坡体无锚方案的计算确定坡体的滑动面并为锚固方案的设计提供依据。3种锚固方案中的预应力锚索和锚杆按不同方式进行了组合。所建立的锚固坡体三维有限元分析模型对锚固坡体进行了合理简化并节约了计算量。计算中锚索的预应力采用预先施加应变的方式施加。计算分析表明,边坡加锚后可显著减少边坡塑性区。实际工程中采用预应力锚索和锚杆交错布设方案进行边坡锚固支护可较好地达到安全与经济并重的边坡处治原则。现场监测结果表明,锚固边坡有限元分析合理可行。 相似文献
13.
The present paper proposes a new family of multiscale finite volume methods. These methods usually deal with a dual mesh resolution, where the pressure field is solved on a coarse mesh, while the saturation fields, which may have discontinuities, are solved on a finer reservoir grid, on which petrophysical heterogeneities are defined. Unfortunately, the efficiency of dual mesh methods is strongly related to the definition of up-gridding and down-gridding steps, allowing defining accurately pressure and saturation fields on both fine and coarse meshes and the ability of the approach to be parallelized. In the new dual mesh formulation we developed, the pressure is solved on a coarse grid using a new hybrid formulation of the parabolic problem. This type of multiscale method for pressure equation called multiscale hybrid-mixed method (MHMM) has been recently proposed for finite elements and mixed-finite element approach (Harder et al. 2013). We extend here the MH-mixed method to a finite volume discretization, in order to deal with large multiphase reservoir models. The pressure solution is obtained by solving a hybrid form of the pressure problem on the coarse mesh, for which unknowns are fluxes defined on the coarse mesh faces. Basis flux functions are defined through the resolution of a local finite volume problem, which accounts for local heterogeneity, whereas pressure continuity between cells is weakly imposed through flux basis functions, regarded as Lagrange multipliers. Such an approach is conservative both on the coarse and local scales and can be easily parallelized, which is an advantage compared to other existing finite volume multiscale approaches. It has also a high flexibility to refine the coarse discretization just by refinement of the lagrange multiplier space defined on the coarse faces without changing nor the coarse nor the fine meshes. This refinement can also be done adaptively w.r.t. a posteriori error estimators. The method is applied to single phase (well-testing) and multiphase flow in heterogeneous porous media. 相似文献
14.
二维扩散输移问题的一种新的有限体积算法 总被引：1，自引：0，他引：1
从空间离散格式上比较了有限元格式与有限体积格式的异同处,证明有限体积格式是有限元格式的一种特例,有限元格式也是一种守恒型格式。并根据有限元格式与有限体积格式的比较,提出了一种新的高精度、稳定性好的有限体积格式。通过模拟非定常的纯对流方程和二维对流扩散方程,证明了有限体积格式的优点。 相似文献
15.
An approximate step-by-step procedure is presented for the finite element analysis of transient unconfined flow problems. At each step the free surface is modelled by means of segments coinciding with sides of the elements. This leads to an approximate but extremely simple solution scheme which can be readily incorporated into standard codes for confined analysis. The solutions of some significant problems are presented and compared with other non-approximate solutions. They show that the technique, in spite of its approximation, is capable of giving meaningful results from an engineering viewpoint. 相似文献
16.
Ilya D. Mishev 《Computational Geosciences》2002,6(3-4):253-268
We extend and generalize recently proposed finite volume methods using the framework of mixed finite element methods. Proposed discretizations are defined for tensor permeabilities and naturally produce a generalization of harmonic averaging, and are therefore well suited for heterogeneous and anisotropic media. They are locally mass conservative and work on extremely flexible distorted meshes. Flux variables can be excluded locally and the resulting discretizations for the pressures has the same stencils for Voronoi/PEBI grids as 2-point finite volume discretizations currently used in many simulators. 相似文献
17.
在利用有限差分等基于网格的数值分析方法解地震波走时所满足的程函方程时,由于速度模型的网格化离散等原因,会使走时在各网格节点之间不具有计算射线路径所要求的光滑性,即走时在邻近网格节点之间不具有连续的一阶导数。因此,直接利用网格节点走时计算射线路径会使最终的射线路径不光滑。为解决这个问题,已有研究者提出了基于B样条插值的逆向梯度方案（法）。然而,在速度发生突变时,B样条逆向梯度法所计算出的射线路径会具有较大的误差。针对这个问题,首先采用适合于解最小零偏差逼近及最佳平方逼近问题的Chebyshev多项式取代B样条对来自于分区多级计算方案的网格节点走时进行最佳逼近,得到在最小平方意义下的最优走时公式;然后采用与B样条逆向梯度法类似的计算过程得到光滑的射线路径。数值实验表明,利用Chebyshev多项式逼近走时可以得到具有很高精度的多次反射射线路径,在多次波偏移成像研究中具有潜在的价值。 相似文献
18.
三维流形单元的生成是进行三维数值流形分析的首要问题之一。详细研究了三维流形单元的生成过程,并采用C++语言编写了相应的程序。借鉴二维流形单元的形成技术,基于拓扑学的“有向性”原理,将点、有向边、有向环、有向面和有向壳等作为三维块体的基本数据结构。将材料体和数学网格进行布尔交运算,并对形成的流形块体进行有效性检测,满足要求后即形成新的三维流形单元。每个数学网格的顶点作为新流形单元的数学覆盖,再对数学覆盖进行细分,形成流形单元的物理覆盖。分别选取凹形体、空心体和包含有限结构面的材料体与数学网格进行布尔交运算,并选取一个典型工程来检查该方法和程序的可行性。计算结果表明,该方法可以对复杂块体（凹形体、空心体和包含有限结构面的体）进行处理,为今后进行复杂结构计算和分析奠定基础,具有较强的适应性和可靠性。 相似文献
19.
Robert Eymard Cindy Guichard Raphaele Herbin Roland Masson 《Computational Geosciences》2012,16(4):987-1005
This paper concerns the discretisation on general 3D meshes of multiphase compositional Darcy flows in heterogeneous anisotropic porous media. Extending Coats’ formulation [15] to an arbitrary number of phases, the model accounts for the coupling of the mass balance of each component with the pore volume conservation and the thermodynamical equilibrium and dynamically manages phase appearance and disappearance. The spatial discretisation of the multiphase compositional Darcy flows is based on a generalisation of the Vertex Approximate Gradient scheme, already introduced for single-phase diffusive problems in [24]. It leads to an unconditionally coercive scheme for arbitrary meshes and permeability tensors. The stencil of this vertex-centred scheme typically comprises 27 points on topologically Cartesian meshes, and the number of unknowns on tetrahedral meshes is considerably reduced, compared with the usual cell-centred approaches. The efficiency of our approach is exhibited on several examples, including the nearwell injection of miscible CO2 in a saline aquifer taking into account the vaporisation of H2O in the gas phase as well as the precipitation of salt. 相似文献
20.
《Journal of Structural Geology》1988,10(7):755-763
Fabric elements in naturally deformed rocks are usually of a highly variable nature, and measurements contain a high degree of uncertainty. Calculation of general deformation parameters such as finite strain, volume change or the vorticity number of the flow can be difficult with such data. We present an application of the Mohr diagram for stretch which can be used with poorly constrained data on stretch and rotation of lines to construct the best fit to the position gradient tensor; this tensor describes all deformation parameters. The method has been tested on a slate specimen, yielding a kinematic vorticity number of 0.8 ± 0.1. 相似文献