Enhanced multiscale restriction-smoothed basis (MsRSB) preconditioning with applications to porous media flow and geomechanics

Bosma, Sebastian B. M.; Klevtsov, Sergey; Møyner, Olav; Castelletto, Nicola

doi:10.1016/j.jcp.2020.109934

Cited by 7 publications

(1 citation statement)

References 51 publications

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“…As we can see from Figure 4.18, the multiscale solutions exhibit significant grid-orientation errors, but these are less if we choose the coarse mesh to be less skewed than the underlying fine mesh. Bosma et al [7] discuss how to formulate MsRSB with a consistent fine-scale discretization.…”

Section: Grid-orientation Errorsmentioning

confidence: 99%

Multiscale Pressure Solvers for Stratigraphic and Polytopal Grids

Lie,

Møyner

2021

Advanced Modeling With the MATLAB Reservoir Simulation Toolbox

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Section: Grid-orientation Errorsmentioning

confidence: 99%

Multiscale Pressure Solvers for Stratigraphic and Polytopal Grids

Lie,

Møyner

2021

Advanced Modeling With the MATLAB Reservoir Simulation Toolbox

Self Cite

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Parallel Non-Conforming Finite Element Technique for Mathematical Simulation of Fluid Flow in Multiscale Porous Media

Markov

Kutishcheva

Иткина

2023

Communications in Computer and Information Science

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Linear Solvers for Reservoir Simulation Problems: An Overview and Recent Developments

Nardean

Ferronato

Abushaikha

2022

Arch Computat Methods Eng

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Linear solvers for reservoir simulation applications are the objective of this review. Specifically, we focus on techniques for Fully Implicit (FI) solution methods, in which the set of governing Partial Differential Equations (PDEs) is properly discretized in time (usually by the Backward Euler scheme), and space, and tackled by assembling and linearizing a single system of equations to solve all the model unknowns simultaneously. Due to the usually large size of these systems arising from real-world models, iterative methods, specifically Krylov subspace solvers, have become conventional choices; nonetheless, their success largely revolves around the quality of the preconditioner that is supplied to accelerate their convergence. These two intertwined elements, i.e., the solver and the preconditioner, are the focus of our analysis, especially the latter, which is still the subject of extensive research. The progressive increase in reservoir model size and complexity, along with the introduction of additional physics to the classical flow problem, display the limits of existing solvers. Intensive usage of computational and memory resources are frequent drawbacks in practice, resulting in unpleasantly slow convergence rates. Developing efficient, robust, and scalable preconditioners, often relying on physics-based assumptions, is the way to avoid potential bottlenecks in the solving phase. In this work, we proceed in reviewing principles and state-of-the-art of such linear solution tools to summarize and discuss the main advances and research directions for reservoir simulation problems. We compare the available preconditioning options, showing the connections existing among the different approaches, and try to develop a general algebraic framework.

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Enhanced multiscale restriction-smoothed basis (MsRSB) preconditioning with applications to porous media flow and geomechanics

Cited by 7 publications

References 51 publications

Multiscale Pressure Solvers for Stratigraphic and Polytopal Grids

Multiscale Pressure Solvers for Stratigraphic and Polytopal Grids

Parallel Non-Conforming Finite Element Technique for Mathematical Simulation of Fluid Flow in Multiscale Porous Media

Linear Solvers for Reservoir Simulation Problems: An Overview and Recent Developments

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