Two-Scale Preconditioning for Two-Phase Nonlinear Flows in Porous Media

Skogestad, Jan Ole; Keilegavlen, Eirik; Nordbotten, Jan Martin

doi:10.1007/s11242-015-0587-5

Cited by 15 publications

(8 citation statements)

References 40 publications

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“…Comprehensive studies of nonlinear DD schemes in the field of fluid dynamics can be found in [36,37,38]. For articles strictly related to porous media flow models, we refer to [39,40] for an overview of different overlapping domain decomposition strategies.…”

Section: Introductionmentioning

confidence: 99%

A linear domain decomposition method for partially saturated flow in porous media

Seus

Mitra

Pop

et al. 2018

Computer Methods in Applied Mechanics and Engineering

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The Richards equation is a nonlinear parabolic equation that is commonly used for modelling saturated/unsaturated flow in porous media. We assume that the medium occupies a bounded Lipschitz domain partitioned into two disjoint subdomains separated by a fixed interface Γ. This leads to two problems defined on the subdomains which are coupled through conditions expressing flux and pressure continuity at Γ. After an Euler implicit discretisation of the resulting nonlinear subproblems a linear iterative (L-type) domain decomposition scheme is proposed. The convergence of the scheme is proved rigorously. In the last part we present numerical results that are in line with the theoretical finding, in particular the unconditional convergence of the scheme. We further compare the scheme to other approaches not making use of a domain decomposition. Namely, we compare to a Newton and a Picard scheme. We show that the proposed scheme is more stable than the Newton scheme while remaining comparable in computational time, even if no parallelisation is being adopted. Finally we present a parametric study that can be used to optimize the proposed scheme.

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Section: Introductionmentioning

confidence: 99%

A linear domain decomposition method for partially saturated flow in porous media

Seus

Mitra

Pop

et al. 2018

Computer Methods in Applied Mechanics and Engineering

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“…Employing the polynomial chaos framework admits low-cost post-processing of the output to obtain statistics of interest. Skogestad et al (2015) propose a two-scale nonlinear preconditioning technique for multiphase flow problems in porous media that allows for incorporating physical intuition directly in the preconditioner. The developed preconditioner exhibits good scalability properties for challenging problems regardless of dominant physics.…”

Section: Research Area B: Numerical Methodsmentioning

confidence: 99%

Editorial

et al. 2016

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This special issue of Transport in Porous Media contains contributions from the community of researchers within the NUPUS collaboration. Submissions are authored by the full range of NUPUS members, from senior faculty members to the young researchers whose studies have been shaped by this international training network. Many of the contributions highlight the strong inter-university, inter-disciplinary and international connections which are reviewed in the accompanying foreword . The topics of this special issue reflect those of NUPUS itself, and the contributions are grouped in the NUPUS research areas as follows.

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“…Due to different hydrogeological properties of the different rocks, domain decomposition (DD) methods appear to be a natural way to solve efficiently two-phase flow models, see [92,93,2], and also [57,85,86,83,82]. This paper complements [3], where a global-in-time domain decomposition method for this nonlinear and degenerate parabolic problem was proposed (without analysis), using the Optimized Schwarz Waveform Relaxation algorithm (OSWR) with Robin or Ventcell transmission conditions.…”

Section: Introductionmentioning

confidence: 99%

Space–time domain decomposition for two-phase flow between different rock types

Ahmed

Japhet

Kern

2020

Computer Methods in Applied Mechanics and Engineering

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In [3] a space-time domain decomposition method was proposed for two-phase flow in a porous medium composed of two different rock types, so that the capillary pressure field is discontinuous at the interface between the rocks. For this nonlinear and degenerate parabolic problem, with nonlinear and discontinuous transmission conditions on the interface, the Optimized Schwarz waveform relaxation method (OSWR) with Robin or Ventcell transmission conditions was considered. A guaranteed and fully computable a posteriori error estimate was derived, which in particular took into account the domain decomposition error. In this paper we provide a mathematical and numerical analysis of this space-time domain decomposition method in the Robin case. Complete numerical approximation is achieved by a finite volume scheme in space and the lowest order discontinuous Galerkin method in time. We prove the existence of a weak solution of the two-phase flow subdomain problem with Robin boundary conditions by analyzing the convergence of the finite volume scheme. The domain decomposition algorithm is based on the solution of space-time nonlinear subdomain problems over the whole time interval, allowing for different time steps in different parts of the domain, adapted to the physical properties of each subdomain, and we show that such an algorithm is well-defined. Numerical experiments on three-dimensional problems with different rock types illustrate the performance of the domain decomposition method.

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Two-Scale Preconditioning for Two-Phase Nonlinear Flows in Porous Media

Cited by 15 publications

References 40 publications

A linear domain decomposition method for partially saturated flow in porous media

A linear domain decomposition method for partially saturated flow in porous media

Editorial

Space–time domain decomposition for two-phase flow between different rock types

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