Multi-level adaptive solution of anisotropic porous media flow with strong discontinuous jumps in permeability

Y. C. Lee, P. H. Gaskell

Research output: Contribution to journalArticle

Abstract

A fast and robust multi-grid algorithm for the efficient solution of diffusion-like, elliptic problems which exhibit strong discontinuous jumps in diffusivity is presented. Although generally applicable to this class of problem, the focus for illustrative purposes is that of porous media flow; in particular, such flows for which accurate solutions can only be achieved if the full permeability tensor is taken into consideration. The merits of adopting one or the other of two different approaches to deriving a discrete analogue to the steady-state Darcy equation, namely a novel weighted average of permeability formulation and a continuity of flux preservation method, are explored. In addition, automatic mesh refinement is incorporated seamlessly via a multi-level adaptive technique, making full use of the local truncation error estimates available from the inclusive full approximation storage scheme. Adaptive cell- and patch-wise mesh refinement strategies are developed and investigated for this purpose and used to solve a sequence of benchmark problems of increasing complexity. The results obtained reveal: (a) the ease with which the overall approach deals with generating accurate solutions for flows involving both distributed anisotropy and strong discontinuous jumps in permeability; (b) that both discrete analogues produce equivalent results in comparable execution times; and (c) the significant reductions in computing resource, memory, and CPU, to accrue from employing automatic adaptive mesh refinement.

Original languageEnglish
Pages (from-to)853-868
Number of pages16
JournalProceedings of the Institution of Mechanical Engineers, Part C: Journal of Mechanical Engineering Science
Volume225
Issue number4
DOIs
Publication statusPublished - Apr 2011

Fingerprint

porous medium
permeability
diffusivity
anisotropy
resource
method

Keywords

  • Anisotropy
  • Automatic adaptive mesh refinement
  • Diffusion-like elliptic problems
  • Heterogeneity
  • Multi-grid
  • Porous media

Cite this

@article{eaef45469294434f82197968e279c280,
title = "Multi-level adaptive solution of anisotropic porous media flow with strong discontinuous jumps in permeability",
abstract = "A fast and robust multi-grid algorithm for the efficient solution of diffusion-like, elliptic problems which exhibit strong discontinuous jumps in diffusivity is presented. Although generally applicable to this class of problem, the focus for illustrative purposes is that of porous media flow; in particular, such flows for which accurate solutions can only be achieved if the full permeability tensor is taken into consideration. The merits of adopting one or the other of two different approaches to deriving a discrete analogue to the steady-state Darcy equation, namely a novel weighted average of permeability formulation and a continuity of flux preservation method, are explored. In addition, automatic mesh refinement is incorporated seamlessly via a multi-level adaptive technique, making full use of the local truncation error estimates available from the inclusive full approximation storage scheme. Adaptive cell- and patch-wise mesh refinement strategies are developed and investigated for this purpose and used to solve a sequence of benchmark problems of increasing complexity. The results obtained reveal: (a) the ease with which the overall approach deals with generating accurate solutions for flows involving both distributed anisotropy and strong discontinuous jumps in permeability; (b) that both discrete analogues produce equivalent results in comparable execution times; and (c) the significant reductions in computing resource, memory, and CPU, to accrue from employing automatic adaptive mesh refinement.",
keywords = "Anisotropy, Automatic adaptive mesh refinement, Diffusion-like elliptic problems, Heterogeneity, Multi-grid, Porous media",
author = "Lee, {Y. C.} and Gaskell, {P. H.}",
year = "2011",
month = "4",
doi = "10.1243/09544062JMES1921",
language = "English",
volume = "225",
pages = "853--868",
journal = "Proceedings of the Institution of Mechanical Engineers, Part C: Journal of Mechanical Engineering Science",
issn = "0954-4062",
publisher = "SAGE Publications Ltd",
number = "4",

}

TY - JOUR

T1 - Multi-level adaptive solution of anisotropic porous media flow with strong discontinuous jumps in permeability

AU - Lee, Y. C.

AU - Gaskell, P. H.

PY - 2011/4

Y1 - 2011/4

N2 - A fast and robust multi-grid algorithm for the efficient solution of diffusion-like, elliptic problems which exhibit strong discontinuous jumps in diffusivity is presented. Although generally applicable to this class of problem, the focus for illustrative purposes is that of porous media flow; in particular, such flows for which accurate solutions can only be achieved if the full permeability tensor is taken into consideration. The merits of adopting one or the other of two different approaches to deriving a discrete analogue to the steady-state Darcy equation, namely a novel weighted average of permeability formulation and a continuity of flux preservation method, are explored. In addition, automatic mesh refinement is incorporated seamlessly via a multi-level adaptive technique, making full use of the local truncation error estimates available from the inclusive full approximation storage scheme. Adaptive cell- and patch-wise mesh refinement strategies are developed and investigated for this purpose and used to solve a sequence of benchmark problems of increasing complexity. The results obtained reveal: (a) the ease with which the overall approach deals with generating accurate solutions for flows involving both distributed anisotropy and strong discontinuous jumps in permeability; (b) that both discrete analogues produce equivalent results in comparable execution times; and (c) the significant reductions in computing resource, memory, and CPU, to accrue from employing automatic adaptive mesh refinement.

AB - A fast and robust multi-grid algorithm for the efficient solution of diffusion-like, elliptic problems which exhibit strong discontinuous jumps in diffusivity is presented. Although generally applicable to this class of problem, the focus for illustrative purposes is that of porous media flow; in particular, such flows for which accurate solutions can only be achieved if the full permeability tensor is taken into consideration. The merits of adopting one or the other of two different approaches to deriving a discrete analogue to the steady-state Darcy equation, namely a novel weighted average of permeability formulation and a continuity of flux preservation method, are explored. In addition, automatic mesh refinement is incorporated seamlessly via a multi-level adaptive technique, making full use of the local truncation error estimates available from the inclusive full approximation storage scheme. Adaptive cell- and patch-wise mesh refinement strategies are developed and investigated for this purpose and used to solve a sequence of benchmark problems of increasing complexity. The results obtained reveal: (a) the ease with which the overall approach deals with generating accurate solutions for flows involving both distributed anisotropy and strong discontinuous jumps in permeability; (b) that both discrete analogues produce equivalent results in comparable execution times; and (c) the significant reductions in computing resource, memory, and CPU, to accrue from employing automatic adaptive mesh refinement.

KW - Anisotropy

KW - Automatic adaptive mesh refinement

KW - Diffusion-like elliptic problems

KW - Heterogeneity

KW - Multi-grid

KW - Porous media

U2 - 10.1243/09544062JMES1921

DO - 10.1243/09544062JMES1921

M3 - Article

VL - 225

SP - 853

EP - 868

JO - Proceedings of the Institution of Mechanical Engineers, Part C: Journal of Mechanical Engineering Science

JF - Proceedings of the Institution of Mechanical Engineers, Part C: Journal of Mechanical Engineering Science

SN - 0954-4062

IS - 4

ER -