537 research outputs found

    Nonlinear Acceleration of Sequential Fully Implicit (SFI) Method for Coupled Flow and Transport in Porous Media

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    The sequential fully implicit (SFI) method was introduced along with the development of the multiscale finite volume (MSFV) framework, and has received considerable attention in recent years. Each time step for SFI consists of an outer loop to solve the coupled system, in which there is one inner Newton loop to implicitly solve the pressure equation and another loop to implicitly solve the transport equations. Limited research has been conducted that deals with the outer coupling level to investigate the convergence performance. In this paper we extend the basic SFI method with several nonlinear acceleration techniques for improving the outer-loop convergence. Specifically, we consider numerical relaxation, quasi-Newton (QN) and Anderson acceleration (AA) methods. The acceleration techniques are adapted and studied for the first time within the context of SFI for coupled flow and transport in porous media. We reveal that the iterative form of SFI is equivalent to a nonlinear block Gauss-Seidel (BGS) process. The effectiveness of the acceleration techniques is demonstrated using several challenging examples. The results show that the basic SFI method is quite inefficient, suffering from slow convergence or even convergence failure. In order to better understand the behaviors of SFI, we carry out detailed analysis on the coupling mechanisms between the sub-problems. Compared with the basic SFI method, superior convergence performance is achieved by the acceleration techniques, which can resolve the convergence difficulties associated with various types of coupling effects. We show across a wide range of flow conditions that the acceleration techniques can stabilize the iterative process, and largely reduce the outer iteration count

    Parallel numerical modeling of hybrid-dimensional compositional non-isothermal Darcy flows in fractured porous media

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    This paper introduces a new discrete fracture model accounting for non-isothermal compositional multiphase Darcy flows and complex networks of fractures with intersecting, immersed and non immersed fractures. The so called hybrid-dimensional model using a 2D model in the fractures coupled with a 3D model in the matrix is first derived rigorously starting from the equi-dimensional matrix fracture model. Then, it is dis-cretized using a fully implicit time integration combined with the Vertex Approximate Gradient (VAG) finite volume scheme which is adapted to polyhedral meshes and anisotropic heterogeneous media. The fully coupled systems are assembled and solved in parallel using the Single Program Multiple Data (SPMD) paradigm with one layer of ghost cells. This strategy allows for a local assembly of the discrete systems. An efficient preconditioner is implemented to solve the linear systems at each time step and each Newton type iteration of the simulation. The numerical efficiency of our approach is assessed on different meshes, fracture networks, and physical settings in terms of parallel scalability, nonlinear convergence and linear convergence

    Une méthode mixte multi-échelles pour un simulateur de réservoir biphasé

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    A multiscale hybrid mixed finite element method is presented in this paper to solve two-phase flow equations on heterogeneous media under the effect of gravitational segregation. It is designed to cope with the complex geometry and inherent multiscale nature of the rocks, leading to stable and accurate multi-physics reservoir simulations. This multiscale approach makes use of coarse scale fluxes between subregions (macro domains) that allow to reduce substantially the dominant computational costs associated with the flux/pressure kernel embedded in the numerical model. As such, larger scale problems can be approximated in a reasonable computational time. Dividing the problems into macro domains leads to a hierarchy of meshes and approximation spaces, allowing the efficient use of static condensation and parallel computation strategies. The method documented in this work utilizes discretizations based on a general domain partition formed by poly-hedral subregions. The normal flux between these subregions is associated with a finite dimensional trace space. The global system to be solved for the fluxes and pressures is expressed only in terms of the trace variables and of a piecewise constant pressure associated with each subregion. The fine scale features are resolved by mixed finite element approximations using fine flux and pressure representations inside each subregion, and the trace variable (i.e. normal flux) as Neumann boundary conditions. This property implies that the flux approximation is globally H(div)-conforming, and, as in classical mixed formulations, local mass conservation is observed at the micro-scale elements inside the subregions, an essential property for flows in heterogeneous media

    Vanishing artifficial diffusion as a mechanism to accelerate convergence for multiphase porous media flow

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    Numerical solution of the equations governing multiphase porous media flow is challenging. A common approach to improve the performance of iterative non-linear solvers for these problems is to introduce artificial diffusion. Here, we present a mass conservative artificial diffusion that accelerates the non-linear solver but vanishes when the solution is converged. The vanishing artificial diffusion term is saturation dependent and is larger in regions of the solution domain where there are steep saturation gradients. The non-linear solver converges more slowly in these regions because of the highly non-linear nature of the solution. The new method provides accurate results while significantly reducing the number of iterations required by the non-linear solver. It is particularly valuable in reducing the computational cost of highly challenging numerical simulations, such as those where physical capillary pressure effects are dominant. Moreover, the method allows converged solutions to be obtained for Courant numbers that are at least two orders of magnitude larger than would otherwise be possible

    An HMM--ELLAM scheme on generic polygonal meshes for miscible incompressible flows in porous media

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    We design a numerical approximation of a system of partial differential equations modelling the miscible displacement of a fluid by another in a porous medium. The advective part of the system is discretised using a characteristic method, and the diffusive parts by a finite volume method. The scheme is applicable on generic (possibly non-conforming) meshes as encountered in applications. The main features of our work are the reconstruction of a Darcy velocity, from the discrete pressure fluxes, that enjoys a local consistency property, an analysis of implementation issues faced when tracking, via the characteristic method, distorted cells, and a new treatment of cells near the injection well that accounts better for the conservativity of the injected fluid
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