共查询到19条相似文献,搜索用时 453 毫秒
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在有限体积法框架下应用通量向量分裂(FVS)格式进行平面二维水流 水质模拟。通过对偏微分方程进行有限体积的积分离散、利用通量的旋转不变性,把二维问题转化为一系列局部的一维问题进行求解,采用FVS格式计算各跨单元边界的水量、动量及污染物输运等通量。应用该格式计算了理想条件下的浓度输移,其结果与精确解拟合很好;模拟了长江江苏靖江段的水质及污染带,计算结果与水质监测值相当吻合,为长江江苏干流段水质评价提供了科学依据。 相似文献
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天然水体具有形状复杂的计算区域和水下地形。本文采用无结构的网格以适合这一情况,并能方便地根据工程应用的要求局部地和适应性地加密网格。相应地,对二维水流计算问题采用了有限体积法的数学表示。跨单元边界的法向数值通量通过用Osher格式求解黎曼问题得到。文中给出了适合于二维浅水方程组的有关单元界面和各种物理边界的法向数值通量公式。分析了这一格式所具有的优点,包括:普适性、守恒性、逆风性、单调保持性、高效性、对间断的高分辨率、边界处理和内部格式相容,以及不引入数值边界条件等。最后,通过长江口南支水流计算的实例,阐明其良好性能。 相似文献
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为高效求解扩展型Boussinesq水波方程,建立了基于有限差分和有限体积方法的混合数值格式。将一维控制方程写为守恒形式,方程中通量部分采用有限体积方法求解,剩余部分采用有限差分方法求解。其中,有限体积方法采用Godunov类高分辨率格式,并结合HLL(Harten-Lax and van Leer)式黎曼问题近似解求界面数值通量,黎曼问题界面左右变量通过高精度状态插值方法(MUSCL)构筑。有限差分方法则采用具有二阶精度的中心差分公式进行。采用具有TVD(Total Variation Diminishing)性质的三阶龙格-库塔多步积分法进行时间积分。对数值模式进行了验证,数值结果同解析解或实验数据吻合良好。 相似文献
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为保证计算格式的和谐性,通过特殊的底坡源项处理技术,在三角形网格上建立了求解二维浅水流动方程的具有空间二阶精度的Godunov格式。应用准确Riemann解求解法向数值通量,用改正的干底Riemann解处理动边界问题。经典型算例和钱塘江河口涌潮计算验证,表明模型健全,分辨率高,具有较大的推广应用价值。 相似文献
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This paper is concerned with numerical methods for the modeling of flow and transport of contaminant in porous media. The
numerical methods feature the mixed finite element method over triangles as a solver to the Darcy flow equation and a conservative
finite volume scheme for the concentration equation. The convective term is approximated with a Godunov scheme over the dual
finite volume mesh, whereas the diffusion–dispersion term is discretized by piecewise linear conforming triangular finite
elements. It is shown that the scheme satisfies a discrete maximum principle. Numerical examples demonstrate the effectiveness
of the methodology for a coupled system that includes an elliptic equation and a diffusion–convection–reaction equation arising
when modeling flow and transport in heterogeneous porous media. The proposed scheme is robust, conservative, efficient, and
stable, as confirmed by numerical simulations.
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In reservoir simulation, the upstream mobility scheme is widely used for calculating fluid flow in porous media and has been
shown feasible for flow when the porous medium is homogeneous. In the case of flow in heterogeneous porous media, the scheme
has earlier been shown to give erroneous solutions in approximating pure gravity segregation. Here, we show that the scheme
may exhibit larger errors when approximating flow in heterogeneous media for flux functions involving both advection and gravity
segregation components. Errors have only been found in the case of countercurrent flow. The physically correct solution is
approximated by an extension of the Godunov and Engquist–Osher flux. We also present a new finite volume scheme based on the
local Lax–Friedrichs flux and test the performance of this scheme in the numerical experiments. 相似文献
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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
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Edison Caballero Fernando A. Rochinha Marcio Borges Marcio A. Murad 《国际地质力学数值与分析法杂志》2019,43(2):482-500
In this work, we construct a new methodology for enhancing the predictive accuracy of sequential methods for coupling flow and geomechanics while preserving low computational cost. The new computational approach is developed within the framework of the fixed-stress split algorithm procedure in conjunction with data assimilation based on the ensemble Kalman filter (EnKF). In this context, we identify the high-fidelity model with the two-way formulation where additional source term appears in the flow equation containing the time derivative of total mean stress. The iterative scheme is then interlaced with data assimilation steps, which also incorporate the modeling error inherent to the EnKF framework. Such a procedure gives rise to an “enhanced one-way formulation,” exhibiting substantial improvement in accuracy compared with the classical one-way method. The governing equations are discretized by mixed finite elements, and numerical simulation of a 2D slab problem between injection and production wells illustrate the tremendous achievement of the method proposed herein. 相似文献
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研究了大孔膦酸树脂对毒砂中主、次和痕量元素的吸附行为及洗脱条件,结合巯基棉和TBP柱分离技术,建立了两个分离流程。在J-A1160型多道直读光谱仪上实现了毒砂单矿物中包括主量元素Fe和As在内的20个元素测定。主量元素As和Fe的相对标准偏差(n为5~10)分别为1.03%和0.9%,其它元素在5%~11%范围。流程经实际试样分析验证,结果与化学法相符。 相似文献
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In this paper we consider the numerical solution of a coupled geomechanics and a stress-sensitive porous media reservoir flow
model. We combine mixed finite elements for Darcy flow and Galerkin finite elements for elasticity. This work focuses on deriving
convergence results for the numerical solution of this nonlinear partial differential system. We establish convergence with
respect to the L
2-norm for the pressure and for the average fluid velocity and with respect to the H
1-norm for the deformation. Estimates with respect to the L
2-norm for mean stress, which is of special importance since it is used in the computation of permeability for poro-elasticity,
can be derived using the estimates in the H
1-norm for the deformation. We start by deriving error estimates in a continuous-in-time setting. A cut-off operator is introduced
in the numerical scheme in order to derive convergence. The spatial grids for the discrete approximations of the pressure
and deformation do not need be the same. Theoretical convergence error estimates in a discrete-in-time setting are also derived
in the scope of this investigation. A numerical example supports the convergence results. 相似文献
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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
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Faults are geological entities with thickness several orders of magnitude smaller than the grid blocks typically used to discretize geological formations. On using the extended finite element method (X-FEM), a structured mesh suffices and the faults can arbitrarily cut the elements in the mesh. Modeling branched and intersecting faults is a challenge, in particular when the faults work as internal fluid flow conduits that allow fluid flow in the faults as well as to enter/leave the faults. By appropriately selecting the enrichment function and the nodes to be enriched, we are able to capture the special characteristics of the solution in the vicinity of the fault. We compare different enrichment schemes for strong discontinuities and develop new continuous enrichment functions with discontinuous derivatives to model branched and intersecting weak discontinuities. Symmetric fluid flows within the regions embedded by branched, coplanar intersecting, and noncoplanar intersecting faults are considered to verify the effectiveness of the proposed enrichment scheme. For a complex fault consisting of branched and intersecting faults, the accuracy and efficiency of the X-FEM is compared with the FEM. We also demonstrate different slipping scenarios for branched and intersecting faults with the same friction coefficient. In addition, fault slipping triggered by an injection pressure and three-dimensional fluid flows are modeled to show the versatility of the proposed enrichment scheme for branched and intersecting weak discontinuities. 相似文献