Upscaling method for problems in perforated domains with non-homogeneous boundary conditions on perforations using Non-Local Multi-Continuum method (NLMC)

Vasilyeva, Maria; Chung, Eric T.; Leung, Wing Tat; Wang, Yating; Spiridonov, Denis

doi:10.1016/j.cam.2019.02.030

Cited by 17 publications

(10 citation statements)

References 33 publications

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“…The main idea of the NLMC method is the use of multiple upscaled variables per coarse element and local multiscale basis functions to form the upscaled system [13,[49][50][51]. First of all, for each coarse element, the upscaled variables are the average values of the solution on separate fracture networks as well as the matrix part.…”

Section: Coarse-grid Nonlocal Multicontinuum Upscalingmentioning

confidence: 99%

Upscaling of the single-phase flow and heat transport in fractured geothermal reservoirs using nonlocal multicontinuum method

et al. 2019

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In this work, we consider a single-phase flow and heat transfer problem in fractured geothermal reservoirs. Mixed dimensional problems are considered, where the temperature and pressure equations are solved for porous matrix and fracture networks with transfer term between them. For the fine-grid approximation, a finite volume method with embedded fracture model is employed. To reduce size of the fine-grid system, an upscaled coarse-grid model is constructed using the nonlocal multicontinuum (NLMC) method. We present numerical results for two-dimensional problems with complex fracture distributions and investigate an accuracy of the proposed method. The simulations using upscaled model provide very accurate solutions with significant reduction in the dimension of problem.Publisher's note Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

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Section: Coarse-grid Nonlocal Multicontinuum Upscalingmentioning

confidence: 99%

Upscaling of the single-phase flow and heat transport in fractured geothermal reservoirs using nonlocal multicontinuum method

et al. 2019

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“…In recently developed Constrained Energy Minimization and Nonlocal Multicontinuum methods [10,12,33,36], multiscale basis functions are defined in the oversampled domains and constructed via solving local constrained energy minimization problems, where constraints are related to each continuum. Continuum plays a role of macroscopic parameter.…”

Section: Introductionmentioning

confidence: 99%

Learning macroscopic parameters in nonlinear multiscale simulations using nonlocal multicontinua upscaling techniques

Vasilyeva

Leung

Chung

et al. 2020

Journal of Computational Physics

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In this work, we present a novel nonlocal nonlinear coarse grid approximation using a machine learning algorithm. We consider unsaturated and two-phase flow problems in heterogeneous and fractured porous media, where mathematical models are formulated as general multicontinuum models. We construct a fine grid approximation using the finite volume method and embedded discrete fracture model. Macroscopic models for these complex nonlinear systems require nonlocal multicontinua approaches, which are developed in earlier works [8]. These rigorous techniques require complex local computations, which involve solving local problems in oversampled regions subject to constraints. The solutions of these local problems can be replaced by solving original problem on a coarse (oversampled) region for many input parameters (boundary and source terms) and computing effective properties derived by nonlinear nonlocal multicontinua approaches. The effective properties depend on many variables (oversampled region and the number of continua), thus their calculations require some type of machine learning techniques. In this paper, our contribution is two fold. First, we present macroscopic models and discuss how to effectively compute macroscopic parameters using deep learning algorithms. The proposed method can be regarded as local machine learning and complements our earlier approaches on global machine learning [39,38]. We consider a coarse grid approximation using two upscaling techniques with single phase upscaled transmissibilities and nonlocal nonlinear upscaled transmissibilities using a machine learning algorithm. We present results for two model problems in heterogeneous and fractured porous media and show that the presented method is highly accurate and provides fast coarse grid calculations.

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“…The concept of non-local upscaling has been successfully applied to problems in porous media, see, e.g., [14,11,13]. Motivated by the work given in [15], the nonlocal multicontinua (NLMC) upscaling technique was initially introduced for flows in heterogeneous fractured media in [9], and have been successfully applied to different problems under application [25,26,27,28]. The main idea of NLMC upscaling technique is to construct the multiscale basis functions over the oversampling domain via an energy minimization principle.…”

Section: Introductionmentioning

confidence: 99%

An analysis of the NLMC upscaling method for high contrast problems

Zhao

Chung

2020

Journal of Computational and Applied Mathematics

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In this paper we propose simple multiscale basis functions with constraint energy minimization to solve elliptic problems with high contrast medium. Our methodology is based on the recently developed non-local multicontinuum method (NLMC). The main ingredient of the method is the construction of suitable local basis functions with the capability of capturing multiscale features and non-local effects. In our method, each coarse block is decomposed into various regions according to the contrast ratio, and we require that the contrast ratio should be relatively small within each region. The basis functions are constructed by solving a local problem defined on the oversampling domains and they have mean value one on the chosen region and zero mean otherwise. Numerical analysis shows that the resulting basis functions can be localizable and have a decay property. The convergence of the multiscale solution is also proved. Finally, some numerical experiments are carried out to illustrate the performances of the proposed method. They show that the proposed method can solve problem with high contrast medium efficiently. In particular, if the oversampling size is large enough, then we can achieve the desired error.

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Upscaling method for problems in perforated domains with non-homogeneous boundary conditions on perforations using Non-Local Multi-Continuum method (NLMC)

Cited by 17 publications

References 33 publications

Upscaling of the single-phase flow and heat transport in fractured geothermal reservoirs using nonlocal multicontinuum method

Upscaling of the single-phase flow and heat transport in fractured geothermal reservoirs using nonlocal multicontinuum method

Learning macroscopic parameters in nonlinear multiscale simulations using nonlocal multicontinua upscaling techniques

An analysis of the NLMC upscaling method for high contrast problems

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