Iterative Solution Methods for Modeling Multiphase Flow in Porous Media Fully Implicitly

Lacroix, S.; Vassilevski, Yuri; Wheeler, John Archibald; Wheeler, Mary F.

doi:10.1137/s106482750240443x

Cited by 105 publications

(73 citation statements)

References 17 publications

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“…years instead of million years), so that the porosity φ and the effective stress σ = σ z − P f can be kept constant, thus leading to systems similar to (2.26), but in pressure and saturation only. In [3,4,5,6,7] a preconditioning strategy has been developed for these problems decoupling the treatment of pressure and saturation. We will use a similar strategy for (2.26).…”

Section: Preconditioning Strategymentioning

confidence: 99%

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Decoupling and Block Preconditioning for Sedimentary Basin Simulations

Scheichl

Masson

Wendebourg

2003

Computational Geosciences

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Abstract. The simulation of sedimentary basins aims at reconstructing its historical evolution in order to provide quantitative predictions about phenomena leading to hydrocarbon accumulations. The kernel of this simulation is the numerical solution of a complex system of partial differential equations of mixed parabolic-hyperbolic type. A discretisation and linearisation of this system leads to large ill-conditioned non-symmetric linear systems with three unknowns per mesh element. The preconditioning which we will present for these systems consists in three stages: (i) a local decoupling of the equations which (in addition) aims at concentrating the elliptic part of the system in the "pressure block"; (ii) an efficient preconditioning of the pressure block using AMG; (iii) the "recoupling" of the equations. In all our numerical tests on real case studies we observed a reduction of the CPU-time for the linear solver (up to a factor 4.3 with respect to the current preconditioner ILU(0)) and almost no degradation with respect to physical and numerical parameters.

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Section: Preconditioning Strategymentioning

confidence: 99%

“…In particular, the idea for our preconditioning strategy is based on the methods developed in [3,4,5,6,7]. It consists of three stages.…”

Section: Introductionmentioning

confidence: 99%

Decoupling and Block Preconditioning for Sedimentary Basin Simulations

Scheichl

Masson

Wendebourg

2003

Computational Geosciences

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“…Therefore, the compromise between the numerical efficiency of a preconditioner and the performance of its algorithm's implementation for each hardware configuration must be studied. In this paper, we focus on BiCGStab linear solver (used for both symmetric and non-symmetric systems) preconditioned by Neumann Polynomial, BSSOR, ILU, AMG and CPR-AMG [7]. The strong and the weak points of these preconditioners are discussed below.…”

Section: Preconditioners Overviewmentioning

confidence: 99%

Survey on Efficient Linear Solvers for Porous Media Flow Models on Recent Hardware Architectures

Anciaux–Sedrakian

Gottschling

Gratien

et al. 2014

Oil Gas Sci. Technol. – Rev. IFP Energies nouvelles

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Re´sume´-Revue des algorithmes de solveurs line´aires utilise´s en simulation de re´servoir, efficaces sur les architectures mate´rielles modernes -Depuis quelques anne´es, en calculs haute performance les constructeurs ont recours de plus en plus a`des architectures base´es sur des unite´s de calculs multicoeurs e´ventuellement acce´le´re´es avec des cartes de type GPGPU (General Purpose Processing on Graphics Processing Units). L'intereˆt de telles architectures offrant un grand nombre d'unite´s de calcul pourrait eˆtre grand pour le domaine de la simulation d'e´coulements multiphasiques en milieu poreux, utilise´e par exemple dans les applications de type se´questration ge´ologique du CO 2 ou simulateur de re´cupe´ration avance´e de pe´trole dans des re´servoirs. Il faut ne´anmoins ve´rifier si les algorithmes des logiciels actuels sont adapte´s pour eˆtre efficaces avec ces nouvelles technologies. La re´solution de grands syste`mes line´aires creux constitue souvent la partie la plus couˆteuse des simulateurs d'e´coulement en milieu poreux. En effet, ces syste`mes sont souvent mal conditionne´s duˆau caracte`re souvent tre`s he´te´roge`ne et anisotrope des donne´es ge´ologiques. Les solveurs line´aires constituent pour ces raisons un point crucial pour les performances de ces simulateurs. Dans cet article, nous proposons un panorama des diffe´rents algorithmes de solveurs line´aires et de pre´conditionneurs utilise´s dans nos applications. Nous analysons leur efficacite´nume´rique et leur performance en fonction de diffe´rentes configurations mate´rielles. Nous proposons une nouvelle approche, base´e sur la programmation hybride, performante sur des architectures he´te´roge`nes a`base de processeurs multicoeurs ou d'acce´le´rateurs de type GPGPU. Cette approche est valide´e dans l'imple´mentation d'un BiCGStab pre´conditionneá vec des algorithmes de type ILU(0), BSSOR, pre´conditionneur polynomial ou CPR-AMG. Des tests de performances ont alors e´te´effectue´s sur differents cas d'e´tudes d'e´coulement en milieu poreux, utilisant des maillages de grande taille.Abstract -Survey on Efficient Linear Solvers for Porous Media Flow Models on Recent Hardware Architectures -In the past few years, High Performance Computing (HPC) technologies led to General Purpose Processing on Graphics Processing Units (GPGPU) and many-core architectures. These emerging technologies offer massive processing units and are interesting for porous media flow simulators may used for CO 2 geological sequestration or Enhanced Oil Recovery (EOR) simulation. However the crucial point is "are current algorithms and software able to use these new technologies efficiently?" The resolution of large sparse linear systems, almost ill-conditioned, constitutes the most CPUconsuming part of such simulators. This paper proposes a survey on various solver and preconditioner

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“…In addition, particularly for multiphase groundwater flow purposes, computation of an updated version of the preconditioner may be a time consuming task or even impossible to carry out when there is not an explicit form of such preconditioner as it happens in two-stage preconditioning [6,20] multilevel [4] or in general inner-outer iterations [2]. Assuming that the preconditioner is fixed after each Krylov-secant update seems to be the simplest and most efficient strategy, even though this may introduce some extra inaccuracies in the computations [18].…”

Section: Preconditioningmentioning

confidence: 99%

Nonlinear Krylov-Secant Solvers

Klíe¹,

Wheeler²

2006

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Iterative Solution Methods for Modeling Multiphase Flow in Porous Media Fully Implicitly

Cited by 105 publications

References 17 publications

Decoupling and Block Preconditioning for Sedimentary Basin Simulations

Decoupling and Block Preconditioning for Sedimentary Basin Simulations

Survey on Efficient Linear Solvers for Porous Media Flow Models on Recent Hardware Architectures

Nonlinear Krylov-Secant Solvers

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