Adaptive numerical homogenization for upscaling single phase flow and transport

Yerlan Amanbek (Corresponding author), Gurpreet Singh, Mary F. Wheeler, Hans van Duijn

Research output: Contribution to journalArticleAcademicpeer-review

6 Citations (Scopus)

Abstract

We propose an adaptive multiscale method to improve the efficiency and the accuracy of numerical computations by combining numerical homogenization and domain decomposition for modeling flow and transport. Our approach focuses on minimizing the use of fine scale properties associated with advection and diffusion/dispersion. Here a fine scale flow and transport problem is solved in subdomains defined by a transient region where spatial changes in transported species concentrations are large while a coarse scale problem is solved in the remaining subdomains. Away from the transient region, effective macroscopic properties are obtained using local numerical homogenization. An Enhanced Velocity Mixed Finite Element Method (EVMFEM) as a domain decomposition scheme is used to couple these coarse and fine subdomains [1]. Specifically, homogenization is employed here only when coarse and fine scale problems can be decoupled to extract temporal invariants in the form of effective parameters. In this paper, a number of numerical tests are presented for demonstrating the capabilities of this adaptive numerical homogenization approach in upscaling flow and transport in heterogeneous porous medium.

LanguageEnglish
Pages117-133
Number of pages17
JournalJournal of Computational Physics
Volume387
DOIs
StatePublished - 15 Jun 2019

Fingerprint

single-phase flow
Upscaling
homogenizing
Homogenization
Decomposition
Advection
Domain Decomposition
Porous materials
Heterogeneous Porous Media
decomposition
Finite element method
Effective Properties
Multiscale Methods
Mixed Finite Element Method
Adaptive Method
advection
Numerical Computation
finite element method
Invariant
Modeling

Keywords

  • Adaptive mesh refinement
  • Enhanced velocity
  • Multiscale methods
  • Numerical homogenization

Cite this

Amanbek, Yerlan ; Singh, Gurpreet ; Wheeler, Mary F. ; van Duijn, Hans. / Adaptive numerical homogenization for upscaling single phase flow and transport. In: Journal of Computational Physics. 2019 ; Vol. 387. pp. 117-133
@article{e4e8cb7e73464c1bbd166e155b9a7401,
title = "Adaptive numerical homogenization for upscaling single phase flow and transport",
abstract = "We propose an adaptive multiscale method to improve the efficiency and the accuracy of numerical computations by combining numerical homogenization and domain decomposition for modeling flow and transport. Our approach focuses on minimizing the use of fine scale properties associated with advection and diffusion/dispersion. Here a fine scale flow and transport problem is solved in subdomains defined by a transient region where spatial changes in transported species concentrations are large while a coarse scale problem is solved in the remaining subdomains. Away from the transient region, effective macroscopic properties are obtained using local numerical homogenization. An Enhanced Velocity Mixed Finite Element Method (EVMFEM) as a domain decomposition scheme is used to couple these coarse and fine subdomains [1]. Specifically, homogenization is employed here only when coarse and fine scale problems can be decoupled to extract temporal invariants in the form of effective parameters. In this paper, a number of numerical tests are presented for demonstrating the capabilities of this adaptive numerical homogenization approach in upscaling flow and transport in heterogeneous porous medium.",
keywords = "Adaptive mesh refinement, Enhanced velocity, Multiscale methods, Numerical homogenization",
author = "Yerlan Amanbek and Gurpreet Singh and Wheeler, {Mary F.} and {van Duijn}, Hans",
year = "2019",
month = "6",
day = "15",
doi = "10.1016/j.jcp.2019.02.014",
language = "English",
volume = "387",
pages = "117--133",
journal = "Journal of Computational Physics",
issn = "0021-9991",
publisher = "Academic Press Inc.",

}

Adaptive numerical homogenization for upscaling single phase flow and transport. / Amanbek, Yerlan (Corresponding author); Singh, Gurpreet; Wheeler, Mary F.; van Duijn, Hans.

In: Journal of Computational Physics, Vol. 387, 15.06.2019, p. 117-133.

Research output: Contribution to journalArticleAcademicpeer-review

TY - JOUR

T1 - Adaptive numerical homogenization for upscaling single phase flow and transport

AU - Amanbek,Yerlan

AU - Singh,Gurpreet

AU - Wheeler,Mary F.

AU - van Duijn,Hans

PY - 2019/6/15

Y1 - 2019/6/15

N2 - We propose an adaptive multiscale method to improve the efficiency and the accuracy of numerical computations by combining numerical homogenization and domain decomposition for modeling flow and transport. Our approach focuses on minimizing the use of fine scale properties associated with advection and diffusion/dispersion. Here a fine scale flow and transport problem is solved in subdomains defined by a transient region where spatial changes in transported species concentrations are large while a coarse scale problem is solved in the remaining subdomains. Away from the transient region, effective macroscopic properties are obtained using local numerical homogenization. An Enhanced Velocity Mixed Finite Element Method (EVMFEM) as a domain decomposition scheme is used to couple these coarse and fine subdomains [1]. Specifically, homogenization is employed here only when coarse and fine scale problems can be decoupled to extract temporal invariants in the form of effective parameters. In this paper, a number of numerical tests are presented for demonstrating the capabilities of this adaptive numerical homogenization approach in upscaling flow and transport in heterogeneous porous medium.

AB - We propose an adaptive multiscale method to improve the efficiency and the accuracy of numerical computations by combining numerical homogenization and domain decomposition for modeling flow and transport. Our approach focuses on minimizing the use of fine scale properties associated with advection and diffusion/dispersion. Here a fine scale flow and transport problem is solved in subdomains defined by a transient region where spatial changes in transported species concentrations are large while a coarse scale problem is solved in the remaining subdomains. Away from the transient region, effective macroscopic properties are obtained using local numerical homogenization. An Enhanced Velocity Mixed Finite Element Method (EVMFEM) as a domain decomposition scheme is used to couple these coarse and fine subdomains [1]. Specifically, homogenization is employed here only when coarse and fine scale problems can be decoupled to extract temporal invariants in the form of effective parameters. In this paper, a number of numerical tests are presented for demonstrating the capabilities of this adaptive numerical homogenization approach in upscaling flow and transport in heterogeneous porous medium.

KW - Adaptive mesh refinement

KW - Enhanced velocity

KW - Multiscale methods

KW - Numerical homogenization

UR - http://www.scopus.com/inward/record.url?scp=85062886216&partnerID=8YFLogxK

U2 - 10.1016/j.jcp.2019.02.014

DO - 10.1016/j.jcp.2019.02.014

M3 - Article

VL - 387

SP - 117

EP - 133

JO - Journal of Computational Physics

T2 - Journal of Computational Physics

JF - Journal of Computational Physics

SN - 0021-9991

ER -