A boundary element‐finite element procedure for porous and fractured media flow

Research output: Contribution to journalArticle

11 Citations (Scopus)

Abstract

A coupled boundary element‐finite element procedure is presented for linear and nonlinear fluid flow simulation in porous and fractured aquifers. Quadratic variation of both element geometry and fundamental singularity is used in the constitutively linear direct boundary element formulation. Compatible 3‐to 9‐noded Lagrangian finite elements are used to represent the plane flow domain for mixed linear and nonlinear flows, alike. Nodes on the external contour of the boundary element domain are only retained if flux boundary conditions are not prescribed, thus resulting in reduced matrix dimension. The geometric conductance of the linear boundary element region is evaluated only once. The resulting system matrices remain sparse, positive definite, and may be arranged for symmetry. Nonlinearity, in this context, is restricted to turbulent flow at high Reynolds numbers, although other nonlinearities may be easily accommodated using a similar procedure. A Missbach relationship is implemented to represent turbulent flow in rock fractures. Turbulent effects are confined to the finite element domain, and the resulting nonlinear equations are solved by direct iteration. Validation studies are completed against analytical solutions to linear and nonlinear flow problems. Excellent agreement is obtained with relatively sparing nodal coverage.

Original languageEnglish (US)
Pages (from-to)551-560
Number of pages10
JournalWater Resources Research
Volume23
Issue number4
DOIs
StatePublished - Jan 1 1987

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Insulator Elements
fractured medium
porous medium
turbulent flow
nonlinearity
Turbulent flow
matrix
Flow simulation
Aquifers
Nonlinear equations
Reynolds number
aquifers
fluid flow
symmetry
Flow of fluids
boundary condition
rocks
Rocks
Boundary conditions
aquifer

All Science Journal Classification (ASJC) codes

  • Water Science and Technology

Cite this

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abstract = "A coupled boundary element‐finite element procedure is presented for linear and nonlinear fluid flow simulation in porous and fractured aquifers. Quadratic variation of both element geometry and fundamental singularity is used in the constitutively linear direct boundary element formulation. Compatible 3‐to 9‐noded Lagrangian finite elements are used to represent the plane flow domain for mixed linear and nonlinear flows, alike. Nodes on the external contour of the boundary element domain are only retained if flux boundary conditions are not prescribed, thus resulting in reduced matrix dimension. The geometric conductance of the linear boundary element region is evaluated only once. The resulting system matrices remain sparse, positive definite, and may be arranged for symmetry. Nonlinearity, in this context, is restricted to turbulent flow at high Reynolds numbers, although other nonlinearities may be easily accommodated using a similar procedure. A Missbach relationship is implemented to represent turbulent flow in rock fractures. Turbulent effects are confined to the finite element domain, and the resulting nonlinear equations are solved by direct iteration. Validation studies are completed against analytical solutions to linear and nonlinear flow problems. Excellent agreement is obtained with relatively sparing nodal coverage.",
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A boundary element‐finite element procedure for porous and fractured media flow. / Elsworth, Derek.

In: Water Resources Research, Vol. 23, No. 4, 01.01.1987, p. 551-560.

Research output: Contribution to journalArticle

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