Доступ предоставлен для: Guest
Портал Begell Электронная Бибилиотека e-Книги Журналы Справочники и Сборники статей Коллекции
International Journal for Multiscale Computational Engineering
Импакт фактор: 1.016 5-летний Импакт фактор: 1.194 SJR: 0.554 SNIP: 0.68 CiteScore™: 1.18

ISSN Печать: 1543-1649
ISSN Онлайн: 1940-4352

Выпуски:
Том 17, 2019 Том 16, 2018 Том 15, 2017 Том 14, 2016 Том 13, 2015 Том 12, 2014 Том 11, 2013 Том 10, 2012 Том 9, 2011 Том 8, 2010 Том 7, 2009 Том 6, 2008 Том 5, 2007 Том 4, 2006 Том 3, 2005 Том 2, 2004 Том 1, 2003

International Journal for Multiscale Computational Engineering

DOI: 10.1615/IntJMultCompEng.2018027832
pages 487-507

NONLINEAR NONLOCAL MULTICONTINUA UPSCALING FRAMEWORK AND ITS APPLICATIONS

Eric T. Chung
Department of Mathematics, The Chinese University of Hong Kong, Shatin, New Territories, Hong Kong SAR, China
Yalchin Efendiev
Department of Mathematics and Institute for Scientific Computation (ISC), Texas A&M University, College Station, TX 77840, USA; Multiscale Model Reduction Laboratory, North-Eastern Federal University, Yakutsk, Russia, 677980
Wing T. Leung
Center for Subsurface Modeling, Institute for Computational Engineering and Sciences, The University of Texas, Austin, TX 78712, USA
Mary Wheeler
Center for Subsurface Modeling, Institute for Computational Engineering and Sciences, The University of Texas, Austin, TX 78712, USA

Краткое описание

We discuss multiscale methods for nonlinear problems by extending recently developed multiscale concepts for linear problems. The main idea of these approaches is to use local constraints and solve problems in oversampled regions for constructing macroscopic equations. These techniques are intended for problems without scale separation and high contrast, which often occur in applications. For linear problems, the local solutions with constraints are used as basis functions. This technique is called Constraint Energy Minimizing Generalized Multiscale Finite Element Method (CEM-GMsFEM). GMsFEM identifies macroscopic quantities based on rigorous analysis. In corresponding upscaling methods, the multiscale basis functions are selected such that the degrees of freedom have physical meanings, such as averages of the solution on each continuum. This paper extends the linear concepts to local nonlinear problems. The main concept consists of: (1) identifying macroscopic quantities; (2) constructing appropriate oversampled local problems with coarse-grid constraints; (3) formulating macroscopic equations. We consider two types of approaches. In the first approach, the solutions of local problems are used as basis functions (in a linear fashion) to solve nonlinear problems. This approach is simple to implement; however, it lacks the nonlinear interpolation, which we present in our second approach. In this approach, the local solutions are used as a nonlinear forward map from local averages (constraints) of the solution in oversampling region. This local fine-grid solution is further used to formulate the coarse-grid problem. Both approaches are discussed on several examples and applied to single-phase and two-phase flow problems, which are challenging because of convection-dominated nature of the concentration equation. The numerical results show that we can achieve good accuracy using our new concepts for these complex problems.

Ключевые слова: multiscale, nonlinear, multicontinua, upscaling, porous media

Articles with similar content:

MULTIPLE SCENARIOS INTEGRATED UPSCALING WITH FULL TENSOR EFFECTS OF FRACTURED RESERVOIRS
Special Topics & Reviews in Porous Media: An International Journal, Vol.8, 2017, issue 4
Junchao Li, Zhengdong Lei, Shuhong Wu
BAYESIAN MULTISCALE FINITE ELEMENT METHODS. MODELING MISSING SUBGRID INFORMATION PROBABILISTICALLY
International Journal for Multiscale Computational Engineering, Vol.15, 2017, issue 2
Wing Tat Leung, B. Mallick, Yalchin Efendiev, N. Guha, V. H. Hoang, S. W. Cheung
SPARSE GENERALIZED MULTISCALE FINITE ELEMENT METHODS AND THEIR APPLICATIONS
International Journal for Multiscale Computational Engineering, Vol.14, 2016, issue 1
Wing Tat Leung, Eric T. Chung, Yalchin Efendiev, Guanglian Li
REITERATED MULTISCALE MODEL REDUCTION USING THE GENERALIZED MULTISCALE FINITE ELEMENT METHOD
International Journal for Multiscale Computational Engineering, Vol.14, 2016, issue 6
Wing Tat Leung, Maria Vasilyeva, Eric T. Chung, Yalchin Efendiev
A MULTI-INDEX MARKOV CHAIN MONTE CARLO METHOD
International Journal for Uncertainty Quantification, Vol.8, 2018, issue 1
Ajay Jasra, Yan Zhou, Kengo Kamatani, Kody J. H. Law