Bridging from Pore to Continuum: A Hybrid Mortar Domain Decomposition Framework for Subsurface Flow and Transport

Abstract

Flow and transport in the subsurface occurs over a wide range of spatial scales (nanometer to kilometer). Modeling at the pore scale becomes imperative where scales are not separable. Since pore-scale models are computationally limited to small domain sizes, accurate field-scale modeling requires simulating parts of the reservoir at the pore scale and other parts at the continuum. The need for modeling large pore-scale domains for ascertaining macroscopic parameters is prevalent in the literature. We develop a hybrid mortar domain decomposition framework for parallel modeling (linear and nonlinear) flow and transport across scales and in large pore-scale domains. Novel and efficient mortar methods for coupling flow and transport are adapted and developed and comparisons are presented. Mortars are developed for pore-to-pore and pore-to-continuum interfaces and shown to be more suitable than the commonly used Lagrangian mortars for these interfaces. The methods are shown to produce accurate results and demonstrated to be much more efficient than solving the problem as a single domain even in the absence of parallelism (especially for transport). The coupling algorithms are also extended to include diffusive transport. The methods are further applied and validated for coupling pore-scale to continuum-scale subdomains. Finally, the methods are shown to be computationally efficient for nonlinear flow problems. The results of this work provide a promising step forward in closing the spatial gap between the pore scale and the continuum.

Keywords

  1. mortar coupling
  2. hybrid modeling
  3. multiscale modeling
  4. domain decomposition
  5. pore-scale modeling
  6. flow and transport

MSC codes

  1. 65M55
  2. 65N
  3. 68Q22
  4. 76M25
  5. 35-04
  6. 35J15
  7. 35K10
  8. 35K57
  9. 35L65

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Published In

cover image Multiscale Modeling & Simulation
Multiscale Modeling & Simulation
Pages: 667 - 693
ISSN (online): 1540-3467

History

Submitted: 10 June 2013
Accepted: 10 February 2014
Published online: 29 May 2014

Keywords

  1. mortar coupling
  2. hybrid modeling
  3. multiscale modeling
  4. domain decomposition
  5. pore-scale modeling
  6. flow and transport

MSC codes

  1. 65M55
  2. 65N
  3. 68Q22
  4. 76M25
  5. 35-04
  6. 35J15
  7. 35K10
  8. 35K57
  9. 35L65

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