Mixed Multiscale Finite Volume Methods for Elliptic Problems in Two-Phase Flow Simulations

Jiang, Lijian; Mishev, Ilya D.

doi:10.4208/cicp.170910.180311a

Cited by 10 publications

(3 citation statements)

References 29 publications

(66 reference statements)

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“…An important subclass of numerical multi-scale methods are numerical discretization schemes (e.g., finite element, finite volume or finite difference methods), which modify the finite discretization space to consider explicitly the micro-scale features of the problem. In other words, the finite discretization space is adapted by including functions with the proper micro-scale characteristics or by creating multi-scale basis functions that relate the micro-to macro-scale simulations [219][220][221][222][223]. A more in-depth understanding of numerical multi-scale methods for micro-meso-macroscopic scales coupling can be found in [143,144,224,225].…”

Section: Numerical Multi-scale Modelingmentioning

confidence: 99%

Multi-Scale Surface Texturing in Tribology—Current Knowledge and Future Perspectives

2019

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Surface texturing has been frequently used for tribological purposes in the last three decades due to its great potential to reduce friction and wear. Although biological systems advocate the use of hierarchical, multi-scale surface textures, most of the published experimental and numerical works have mainly addressed effects induced by single-scale surface textures. Therefore, it can be assumed that the potential of multi-scale surface texturing to further optimize friction and wear is underexplored. The aim of this review article is to shed some light on the current knowledge in the field of multi-scale surface textures applied to tribological systems from an experimental and numerical point of view. Initially, fabrication techniques with their respective advantages and disadvantages regarding the ability to create multi-scale surface textures are summarized. Afterwards, the existing state-of-the-art regarding experimental work performed to explore the potential, as well as the underlying effects of multi-scale textures under dry and lubricated conditions, is presented. Subsequently, numerical approaches to predict the behavior of multi-scale surface texturing under lubricated conditions are elucidated. Finally, the existing knowledge and hypotheses about the underlying driven mechanisms responsible for the improved tribological performance of multi-scale textures are summarized, and future trends in this research direction are emphasized.

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Section: Numerical Multi-scale Modelingmentioning

confidence: 99%

Multi-Scale Surface Texturing in Tribology—Current Knowledge and Future Perspectives

2019

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“…In subsurface modeling, local mass conservation is vitally important for the transportation of the solute. To this end, mixed multiscale finite element methods [1,15,2,20], mortar multiscale methods [45,3,30,4], finite volume methods [31,43,24,44] and some kinds of post-processing approaches [36,9,42] are proposed. Among these mass conservative multiscale methods, the mixed multiscale finite element method (MMsFEM) [15] has been successfully applied for various types of flow simulations.…”

Section: Introductionmentioning

confidence: 99%

A conservative multiscale method for stochastic highly heterogeneous flow

Chung¹,

Fu²

2022

Preprint

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In this paper, we propose a local model reduction approach for subsurface flow problems in stochastic and highly heterogeneous media. To guarantee the mass conservation, we consider the mixed formulation of the flow problem and aim to solve the problem in a coarse grid to reduce the complexity of a large-scale system. We decompose the entire problem into a training and a testing stage, namely the offline coarse-grid multiscale basis generation stage and online simulation stage with different parameters. In the training stage, a parameter-independent and small-dimensional multiscale basis function space is constructed, which includes the media, source and boundary information. The key part of the basis generation stage is to solve some local problems defined specially. With the parameter-independent basis space, one can efficiently solve the concerned problems corresponding to different samples of permeability field in a coarse grid without repeatedly constructing a multiscale space for each new sample. A rigorous analysis on convergence of the proposed method is proposed. In particular, we consider a generalization error, where bases constructed with one source will be used to a different source. In the numerical experiments, we apply the proposed method for both single-phase and twophase flow problems. Simulation results for both 2D and 3D representative models demonstrate the high accuracy and impressive performance of the proposed model reduction techniques.

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“…Furthermore, there are several methods that fit into the framework of the Multiscale Finite Element Method (MsFEM) proposed in [35]) or its modified version, the Mixed Multiscale Finite Element Method, proposed in [24]. Multiscale methods based on a Finite Volume or Finite Volume Element approach can be for instance found in [47,46,38,40,3,29,37]. The construction of conservative fluxes in a post-processing step for Generalized Multiscale Finite Element approximations (GMsFEM) was suggested in [17].…”

Section: Introductionmentioning

confidence: 99%

Adaptive heterogeneous multiscale methods for immiscible two-phase flow in porous media

2014

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In this contribution we present the first formulation of a heterogeneous multiscale method for an incompressible immiscible two-phase flow system with degenerate permeabilities. The method is in a general formulation which includes oversampling. We do not specify the discretization of the derived macroscopic equation, but we give two examples of possible realizations, suggesting a finite element solver for the fine scale and a vertex centered finite volume method for the effective coarse scale equations. Assuming periodicity, we show that the method is equivalent to a discretization of the homogenized equation. We provide an a-posteriori estimate for the error between the homogenized solutions of the pressure and saturation equations and the corresponding HMM approximations. The error estimate is based on the results recently achieved in [C. Cancès, I. S. Pop, and M. Vohralík. An a posteriori error estimate for vertex-centered finite volume discretizations of immiscible incompressible two-phase flow. Math. Comp., 2014].

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Mixed Multiscale Finite Volume Methods for Elliptic Problems in Two-Phase Flow Simulations

Cited by 10 publications

References 29 publications

Multi-Scale Surface Texturing in Tribology—Current Knowledge and Future Perspectives

Multi-Scale Surface Texturing in Tribology—Current Knowledge and Future Perspectives

A conservative multiscale method for stochastic highly heterogeneous flow

Adaptive heterogeneous multiscale methods for immiscible two-phase flow in porous media

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