An adaptive time stepping algorithm for IMPES with high order polynomial extrapolation

Paz, Stevens; Jaramillo, Alfredo; Guiraldello, Rafael T.; Ausas, Roberto F.; Sousa, Fabrício S.; Pereira, Felipe; Buscaglia, Gustavo C.

doi:10.1016/j.apm.2020.10.045

Cited by 8 publications

(2 citation statements)

References 31 publications

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“…Special attention is given to the weak and strong scalability and the gain factor obtained in solving problems by a multiscale method. To assess the precision of the multiscale solution two-phase flow simulations are also performed within an IMPES [22,23,24,25] approximation and the results for each one of the solvers are compared. Finally, some concluding remarks are drawn in Section 4.…”

Section: Introductionmentioning

confidence: 99%

Towards HPC simulations of Billion-cell Reservoirs by Multiscale Mixed Methods

Jaramillo¹,

Guiraldello²,

Paz³

et al. 2021

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A three dimensional parallel implementation of Multiscale Mixed Methods based on non-overlapping domain decomposition techniques is proposed for multi-core computers and its computational performance is assessed by means of numerical experimentation. As a prototypical method, from which many others can be derived, the Multiscale Robin Coupled Method is chosen and its implementation explained in detail. Numerical results for problems ranging from millions up to more than 2 billion computational cells in highly heterogeneous anisotropic rock formations based on the SPE10 benchmark are shown. The proposed implementation relies on direct solvers for both local problems and the interface coupling system. We find good weak and strong scalalability as compared against a state-of-the-art global fine grid solver based on Algebric Multigrid preconditioning in single and two-phase flow problems.

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Section: Introductionmentioning

confidence: 99%

Towards HPC simulations of Billion-cell Reservoirs by Multiscale Mixed Methods

Jaramillo¹,

Guiraldello²,

Paz³

et al. 2021

Preprint

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“…Our focus in this work is the solution of nonlinear two-phase flow models. In the literature the coupling of multiscale flow and transport problems has been treated by explicit operator splitting techniques [18,19] and implicit formulations [20,21]. We have considered operator splitting techniques with explicit approximations for the transport problem in previous works [15,17].…”

Section: Introductionmentioning

confidence: 99%

A multiscale Robin-coupled implicit method for two-phase flows in high-contrast formations

Rocha¹,

Sousa²,

Ausas³

et al. 2021

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In the presence of strong heterogeneities, it is well known that the use of explicit schemes for the transport of species in a porous medium suffers from severe restrictions on the time step. This has led to the development of implicit schemes that are increasingly favoured by practitioners for their computational efficiency. The transport equation requires knowledge of the velocity field, which results from an elliptic problem (Darcy problem) that is the most expensive part of the computation. When considering large reservoirs, a cost-effective way of approximating the Darcy problems is using multiscale domain decomposition (MDD) methods. They allow for the pressure and velocity fields to be computed on coarse meshes (large scale), while detailed basis functions are defined locally, usually in parallel, in a much finer grid (small scale). In this work we adopt the Multiscale Robin Coupled Method (MRCM, [Guiraldello, et al., J. Comput. Phys., 355 (2018) pp. 1-21], [Rocha, et al., J. Comput. Phys., (2020) 109316]), which is a generalization of previous MDD methods that allows for great flexibility in the choice of interface spaces. In this article we investigate the combination of the MRCM with implicit transport schemes. A sequentially implicit strategy is proposed, with different trust-region algorithms ensuring the convergence of the transport solver. The method is assessed on several very stringent 2D two-phase problems, demonstrating its stability even for large time steps. It is also shown that the best accuracy is achieved by considering recently introduced non-polynomial interface spaces, since polynomial spaces are not optimal for high-contrast channelized permeability fields.

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