Efficient multiphysics modelling with adaptive grid refinement using a MPFA method

Faigle, Benjamin; Helmig, Rainer; Aavatsmark, Ivar; Flemisch, Bernd

doi:10.1007/s10596-014-9407-1

Cited by 28 publications

(14 citation statements)

References 22 publications

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“…We point out that the local coercivity condition on this form is an inherent feature of these types of methods and appears for both the MPSA-O method discretization [33] and all convergence proofs for the MPFA-type methods for scalar equations (e.g., [40,44]). However, as mentioned also in these references, because the coercivity condition is locally computable, it can be verified directly at the time of discretization, and corrective measures, such as local grid refinement, can be applied if necessary [45].…”

Section: Proofmentioning

confidence: 99%

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Finite volume methods for elasticity with weak symmetry

Keilegavlen

Nordbotten

2017

Numerical Meth Engineering

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We introduce a new cell-centered finite volume discretization for elasticity with weakly enforced symmetry of the stress tensor. The method is motivated by the need for robust discretization methods for deformation and flow in porous media and falls in the category of multi-point stress approximations (MPSAs). By enforcing symmetry weakly, the resulting method has flexibility beyond previous MPSA methods. This allows for a construction of a method that is applicable to simplexes, quadrilaterals, and most planar-faced polyhedral grids in both 2D and 3D, and in particular, the method amends a convergence failure in previous MPSA methods for certain simplex grids. We prove convergence of the new method for a wide range of problems, with conditions that can be verified at the time of discretization. We present the first set of comprehensive numerical tests for the MPSA methods in three dimensions, covering Cartesian and simplex grids, with both heterogeneous and nearly incompressible media. The tests show that the new method consistently is second order convergent in displacement, despite being the lowest order, with a rate that mostly is between 1 and 2 for stresses. The results further show that the new method is more robust and computationally cheaper than previous MPSA methods.

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Section: Proofmentioning

confidence: 99%

“…However, as mentioned also in these references, because the coercivity condition is locally computable, it can be verified directly at the time of discretization, and corrective measures, such as local grid refinement, can be applied if necessary [45].…”

mentioning

confidence: 99%

Finite volume methods for elasticity with weak symmetry

Keilegavlen

Nordbotten

2017

Numerical Meth Engineering

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“…In some simulators, it is possible for the grids to adapt to evolving physical processes over the course of a simulation by refining the grid dynamically and automatically in certain regions of interest (e.g. Jackson et al 2013a, b;Faigle et al 2014) (Fig. 7).…”

Section: ; Moog 2013)mentioning

confidence: 99%

Fundamental controls on fluid flow in carbonates: current workflows to emerging technologies

Agar

Geiger

2014

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The introduction reviews topics relevant to the fundamental controls on fluid flow in carbonate reservoirs and to the prediction of reservoir performance. The review provides research and industry contexts for papers in this volume only. A discussion of global context and frameworks emphasizes the value yet to be captured from compare and contrast studies. Multidisciplinary efforts highlight the importance of greater integration of sedimentology, diagenesis and structural geology. Developments in analytical and experimental methods, stimulated by advances in the materials sciences, support new insights into fundamental (pore-scale) processes in carbonate rocks. Subsurface imaging methods relevant to the delineation of heterogeneities in carbonates highlight techniques that serve to decrease the gap between seismically resolvable features and well-scale measurements. Methods to fuse geological information across scales are advancing through multiscale integration and proxies. A surge in computational power over the last two decades has been accompanied by developments in computational methods and algorithms. Developments related to visualization and data interaction support stronger geoscience-engineering collaborations. High-resolution and real-time monitoring of the subsurface are driving novel sensing capabilities and growing interest in data mining and analytics. Together, these offer an exciting opportunity to learn more about the fundamental fluid-flow processes in carbonate reservoirs at the interwell scale.

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“…Multiscale Finite-Element (MsFE) [2][3][4] and Finite-Volume (MsFV) [5][6][7][8][9][10] methods along with Dynamic Local Grid Refinement (DLGR) techniques [11][12][13][14][15][16][17][18][19] are two classes of such advanced methods that aim to achieve accurate and efficient simulations by tackling different aspects of the entire complexity map. Multiscale methods have been developed to efficiently solve the elliptic (or parabolic) pressure equation, which highly heterogeneous coefficients, by solving the system on a coarse grid while preserving the fine-scale heterogeneities.…”

Section: Introductionmentioning

confidence: 99%