共查询到20条相似文献，搜索用时 31 毫秒
1.
In this article, an approach for the efficient numerical solution of multi-species reactive transport problems in porous media
is described. The objective of this approach is to reformulate the given system of partial and ordinary differential equations
(PDEs, ODEs) and algebraic equations (AEs), describing local equilibrium, in such a way that the couplings and nonlinearities
are concentrated in a rather small number of equations, leading to the decoupling of some linear partial differential equations
from the nonlinear system. Thus, the system is handled in the spirit of a global implicit approach (one step method) avoiding
operator splitting techniques, solved by Newton’s method as the basic algorithmic ingredient. The reduction of the problem
size helps to limit the large computational costs of numerical simulations of such problems. If the model contains equilibrium
precipitation-dissolution reactions of minerals, then these are considered as complementarity conditions and rewritten as
semismooth equations, and the whole nonlinear system is solved by the semismooth Newton method. 相似文献
2.
Modeling reactive transport in porous media, using a local chemical equilibrium assumption, leads to a system of advection–diffusion
PDEs coupled with algebraic equations. When solving this coupled system, the algebraic equations have to be solved at each
grid point for each chemical species and at each time step. This leads to a coupled non-linear system. In this paper, a global
solution approach that enables to keep the software codes for transport and chemistry distinct is proposed. The method applies
the Newton–Krylov framework to the formulation for reactive transport used in operator splitting. The method is formulated
in terms of total mobile and total fixed concentrations and uses the chemical solver as a black box, as it only requires that
one be able to solve chemical equilibrium problems (and compute derivatives) without having to know the solution method. An
additional advantage of the Newton–Krylov method is that the Jacobian is only needed as an operator in a Jacobian matrix times
vector product. The proposed method is tested on the MoMaS reactive transport benchmark. 相似文献
3.
Katerina Georgiou John Harte Ali Mesbah William J. Riley 《Computational Geosciences》2018,22(3):851-865
We present a numerical method for solving a class of systems of partial differential equations (PDEs) that arises in modeling environmental processes undergoing advection and biogeochemical reactions. The salient feature of these PDEs is that all partial derivatives appear in linear expressions. As a result, the system can be viewed as a set of ordinary differential equations (ODEs), albeit each one along a different characteristic. The method then consists of alternating between equations and integrating each one step-wise along its own characteristic, thus creating a customized grid on which solutions are computed. Since the solutions of such PDEs are generally smoother along their characteristics, the method offers the potential of using larger time steps while maintaining accuracy and reducing numerical dispersion. The advantages in efficiency and accuracy of the proposed method are demonstrated in two illustrative examples that simulate depth-resolved reactive transport and soil carbon cycling. 相似文献
4.
We develop an ELLAM-MFEM approximation to the strongly coupled systems of time-dependent nonlinear partial differential equations (PDEs) and constraining equations, which describe fully miscible, highly compressible, multicomponent flows through heterogeneous and compressible porous media with singular sources and sinks. An Eulerian–Lagrangian localized adjoint method (ELLAM) is presented to solve the transport equations for concentrations. A mixed finite element method (MFEM) is used to solve the pressure PDE for the pressure and Darcy velocity simultaneously, which generates accurate fluid velocities and minimizes the numerical difficulties occurring in standard methods caused by differentiation of the pressure and then multiplication by rough coefficients. The ELLAM-MFEM solution technique symmetrizes and stabilizes the governing transport PDEs and greatly reduces nonphysical oscillation and/or excessive numerical dispersion present in many large-scale simulators. Computational experiments show that the ELLAM-MFEM solution technique can generate stable and physically reasonable numerical simulations even if coarse spatial grids and very large time steps are used. 相似文献
5.
H. Hajinezhad Ali R. Soheili Mohammad R. Rasaei F. Toutounian 《Computational Geosciences》2018,22(6):1433-1444
In this paper, the numerical methods for solving the problem of steam injection in the heavy oil reservoirs are presented. We consider a 3-dimensional model of 3-phase flow, oil, water, and steam, with the effect of 3-phase relative permeability. Interphase mass transfer of water and steam is considered; oil is assumed nonvolatile. We apply the simultaneous solution approach to solve the corresponding nonlinear discretized partial differential equation in the fully implicit form. The convergence of finite difference scheme is proved by the Rosinger theorem. The heuristic Jacobian-Free-Newton-Krylov (HJFNK) method is proposed for solving the system of algebraic equations. The result of this proposed numerical method is well compared with some experimental results. Our numerical results show that the first iteration of the full approximation scheme (FAS) provides a good initial guess for the Newton method. Therefore, we propose a new hybrid-FAS-HJFNK method while there is no steam in the reservoir. The numerical results show that the hybrid-FAS-HJFNK method converges faster than the HJFNK method. 相似文献
6.
第二类非线性Fredholm型积分方程数值解 总被引：1，自引：0，他引：1
配置法研究了地球物理中常见的第二类非线性 Fredholm 型积分方程的数值解法,将第二类非线性 Fredholm 型积分方程转化为非线性代数方程组进行求解,采用高斯数值积分公式,给出了数值计算的具体实例.利用Matlab软件的符号运算功能编程计算,克服了非线性方程难于变成求解的困难,数值例子表明该方法编程简便有效.对非线性积分方程和非线性代数方程组的求解都有重要价值. 相似文献
7.
We present a method to transform the governing equations of multispecies reactive transport in porous media. The reformulation leads to a smaller problem size by decoupling of equations and by elimination of unknowns, which increases the efficiency of numerical simulations. The reformulation presented here is a generalization of earlier works. In fact, a whole class of transformations is now presented. This class is parametrized by the choice of certain transformation matrices. For specific choices, some known formulations of reactive transport can be retrieved. Hence, the software based on the presented transformation can be used to obtain efficiency comparisons of different solution approaches. For our efficiency tests, we use the MoMaS benchmark problem on reactive transport. 相似文献
8.
Grégoire Allaire Robert Brizzi Jean-François Dufrêche Andro Mikelić Andrey Piatnitski 《Computational Geosciences》2013,17(3):479-495
In this work, we undertake a numerical study of the effective coefficients arising in the upscaling of a system of partial differential equations describing transport of a dilute N-component electrolyte in a Newtonian solvent through a rigid porous medium. The motion is governed by a small static electric field and a small hydrodynamic force, around a nonlinear Poisson–Boltzmann equilibrium with given surface charges of arbitrary size. This approach allows us to calculate the linear response regime in a way initially proposed by O’Brien. The O’Brien linearization requires a fast and accurate solution of the underlying Poisson–Boltzmann equation. We present an analysis of it, with the discussion of the boundary layer appearing as the Debye–Hückel parameter becomes large. Next, we briefly discuss the corresponding two-scale asymptotic expansion and reduce the obtained two-scale equations to a coarse scale model. Our previous rigorous study proves that the homogenized coefficients satisfy Onsager properties, namely they are symmetric positive definite tensors. We illustrate with numerical simulations several characteristic situations and discuss the behavior of the effective coefficients when the Debye–Hückel parameter is large. Simulated qualitative behavior differs significantly from the situation when the surface potential is given (instead of the surface charges). In particular, we observe the Donnan effect (exclusion of co-ions for small pores). 相似文献
9.
Numerical identification of diffusion parameters in a nonlinear convection–diffusion equation is studied. This partial differential
equation arises as the saturation equation in the fractional flow formulation of the two-phase porous media flow equations.
The forward problem is discretized with the finite difference method, and the identification problem is formulated as a constrained
minimization problem. We utilize the augmented Lagrangian method and transform the minimization problem into a coupled system
of nonlinear algebraic equations, which is solved efficiently with the nonlinear conjugate gradient method. Numerical experiments
are presented and discussed.
This work was partially supported by the Research Council of Norway (NFR), under grant 128224/431. 相似文献
10.
Rigoberto G. Sanabria Castro Sandra M. C. Malta Abimael F. D. Loula Luiz Landau 《Computational Geosciences》2001,5(4):301-330
A finite element formulation is proposed to approximate a nonlinear system of partial differential equations, composed by an elliptic subsystem for the pressure–velocity and a transport equation (convection–diffusion) for the concentration, which models the incompressible miscible displacement of one fluid by another in a rigid porous media. The pressure is approximated by the classical Galerkin method and the velocity is calculated by a post-processing technique. Then, the concentration is obtained by a Galerkin/least-squares space–time (GLS/ST) finite element method. A numerical analysis is developed for the concentration approximation. Then, stability, convergence and numerical results are presented confirming the a priori error estimates. 相似文献
11.
The upper bound method of limit analysis of perfect plasticity is applied to stability problems of slopes with a general nonlinear failure criterion. Based on the upper bound method, a numerical procedure is suggested, which converts the complex system of differential equations to an initial value problem. Using this numerical procedure, an effective numerical method, called the inverse method, suitable for the solution of slope stability problems in soil mechanics with a general nonlinear failure criterion, is presented. A general nonlinear failure criterion for soils is also suggested, from which the effects of nonlinear failure parameters on the stability of slopes are discussed. 相似文献
12.
13.
Rigoberto G. Sanabria Castro Sandra M. C. Malta Abimael F. D. Loula Luiz Landau 《Computational Geosciences》2002,5(4):301-330
A finite element formulation is proposed to approximate a nonlinear system of partial differential equations, composed by an elliptic subsystem for the pressure–velocity and a transport equation (convection–diffusion) for the concentration, which models the incompressible miscible displacement of one fluid by another in a rigid porous media. The pressure is approximated by the classical Galerkin method and the velocity is calculated by a post-processing technique. Then, the concentration is obtained by a Galerkin/least-squares space–time (GLS/ST) finite element method. A numerical analysis is developed for the concentration approximation. Then, stability, convergence and numerical results are presented confirming the a priori error estimates. 相似文献
14.
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
15.
A. M. Tartakovsky N. Trask K. Pan B. Jones W. Pan J. R. Williams 《Computational Geosciences》2016,20(4):807-834
Smoothed particle hydrodynamics (SPH) is a Lagrangian method based on a meshless discretization of partial differential equations. In this review, we present SPH discretization of the Navier-Stokes and advection-diffusion-reaction equations, implementation of various boundary conditions, and time integration of the SPH equations, and we discuss applications of the SPH method for modeling pore-scale multiphase flows and reactive transport in porous and fractured media. 相似文献
16.
17.
Ettore Vidotto Rainer Helmig Martin Schneider Barbara Wohlmuth 《Computational Geosciences》2018,22(6):1487-1502
In this paper, we present a fast streamline-based numerical method for the two-phase flow equations in high-rate flooding scenarios for incompressible fluids in heterogeneous and anisotropic porous media. A fractional flow formulation is adopted and a discontinuous Galerkin method (DG) is employed to solve the pressure equation. Capillary effects can be neglected in high-rate flooding scenarios. This allows us to present an improved streamline approach in combination with the one-dimensional front tracking method to solve the transport equation. To handle the high computational costs of the DG approximation, domain decomposition is applied combined with an algebraic multigrid preconditioner to solve the linear system. Special care at the interior interfaces is required and the streamline tracer has to include a dynamic communication strategy. The method is validated in various two- and three-dimensional tests, where comparisons of the solutions in terms of approximation of flow front propagation with standard fully implicit finite-volume methods are provided. 相似文献
18.
19.
CORE2D V4 is a finite element code for modeling partly or fully saturated water flow, heat transport, and multicomponent reactive
solute transport under both local chemical equilibrium and kinetic conditions. It can handle coupled microbial processes and
geochemical reactions such as acid–base, aqueous complexation, redox, mineral dissolution/precipitation, gas dissolution/exsolution,
ion exchange, sorption via linear and nonlinear isotherms, and sorption via surface complexation. Hydraulic parameters may
change due to mineral precipitation/dissolution reactions. Coupled transport and chemical equations are solved by using sequential
iterative approaches. A sequential partly iterative approach (SPIA) is presented which improves the accuracy of the traditional
sequential non-iterative approach (SNIA) and is more efficient than the general sequential iterative approach (SIA). While
SNIA leads to a substantial saving of computing time, it introduces numerical errors which are especially large for cation
exchange reactions. SPIA improves the efficiency of SIA because the iteration between transport and chemical equations is
only performed in nodes with a large mass transfer between solid and liquid phases. The efficiency and accuracy of SPIA are
compared to those of SIA and SNIA using synthetic examples and a case study of reactive transport through the Llobregat Delta
aquitard in Spain. SPIA is found to be as accurate as SIA while requiring significantly less CPU time. In addition, SPIA is
much more accurate than SNIA with only a minor increase in computing time. A further enhancement of the efficiency of SPIA
is achieved by improving the efficiency of the Newton–Raphson method used for solving chemical equations. Such an improvement
is obtained by working with increments of log concentrations and ignoring the terms of the Jacobian matrix containing derivatives
of activity coefficients. A proof is given for the symmetry and non-singularity of the Jacobian matrix. Numerical analyses
performed with synthetic examples confirm that these modifications improve the efficiency and convergence of the iterative
algorithm.
Changbing Yang is now at The University of Texas at Austin, USA. 相似文献
20.
由于非饱和土的渗透系数是基质吸力的函数,使得控制方程带有强非线性的特征,进而使得控制方程的解析求解变得十分困难。同伦分析法对级数基函数和辅助线性算子的选择具有更大的自由性、灵活性,且收敛性的控制和调节更加容易实现,求解强非线性微分方程时在选择线性算子以及辅助参数上具有明显的优势。因此,针对非饱和土固结方程的非线性特征,对于处于地表浅层的非饱和土层,假设孔隙气压力为大气压力,在Richard经验公式与非饱和土一维固结理论的基础上,推导了非饱和一维固结无量纲控制方程;应用同伦分析法,通过选取适当的初始猜测解与辅助参数,将该非线性方程转换为线性的微分方程组并求解得到固结问题的级数解。此外,以压实高岭土为研究对象,在收集相关试验参数基础之上,将由同伦分析法求得的固结问题的近似解析解与有限差分法数值结果相对比,分析结果验证了解析解的正确性。 相似文献