Finite element seepage flow nets

Aalto, Jukka

doi:10.1002/nag.1610080307

Cited by 18 publications

(11 citation statements)

References 4 publications

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“…Admittedly, result (34) is only an approximation to the complete solution; in principle, however, the series representation can be extended to higher orders of m to provide an improved result. In connection with the computational modelling of the potential problem related to the penny-shaped crack, special singularity elements can be incorporated to capture the singular velocity field at the boundary of the crack [21]. Similar comments apply to the problem related to contamination migration from the needle-shaped source.…”

Section: Contaminant Transport From Spheroidal Cavitiesmentioning

confidence: 98%

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Advective transport from a penny‐shaped crack in a porous medium and an associated uniqueness theorem

Selvadurai

2003

Num Anal Meth Geomechanics

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SUMMARYThis paper examines the problem of the advective transport of a contaminant from sources in the shape of either a penny-shaped crack or an elongated needle-shaped cavity located in a porous medium of infinite extent. The advective transport is induced by Darcy flow in the porous medium, where the internal boundary is maintained at a constant potential. The paper presents an approximate analytical solution to this problem, which is deduced from a formulation that models a cavity in the shape of either an oblate or a prolate spheroid. The results also represent one of the few spatially three-dimensional exact analytical solutions for the, albeit linear, hyperbolic problem governing the contaminant transport problem. The paper also presents a canonical proof of uniqueness for advective contaminant transport problems associated with media of infinite extent.

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Section: Contaminant Transport From Spheroidal Cavitiesmentioning

confidence: 98%

“…The solution to the potential problem is now formally complete, in the sense that the velocity vector vða; b; gÞ can be obtained in explicit closed form by using (21) in (2); in view of the axial symmetry we obtain…”

Section: Contaminant Transport From Spheroidal Cavitiesmentioning

confidence: 99%

Advective transport from a penny‐shaped crack in a porous medium and an associated uniqueness theorem

Selvadurai

2003

Num Anal Meth Geomechanics

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“…The disadvantage is that it does not work for problems with internal holes or internal sources and sinks. Aalto [6] dealt with the internal source/sink problem by modifying the computational mesh after computing the #ow solution and before solving the stream function. The mesh was modi"ed by cutting a slice in the mesh from the outer boundary to the interior hole or source/sink, thus making the hole or source/sink a part of the outer boundary.…”

Section: Previous Workmentioning

confidence: 99%

A hybrid approach to flow net generation

Jones

Lemon

Tracy

2001

Num Anal Meth Geomechanics

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SUMMARYBy following a simple set of rules, a #ow net can be manually constructed to obtain a graphical solution to the Laplace equation for simple two-dimensional (2-D) #ow problems. With the advent of numerical solutions such as the "nite di!erence and "nite element methods, it is more common to generate a #ow net automatically using the nodal head and #ow values output by the computer program. Two methods have been published for automatically generating #ow nets from "nite element solutions: the stream-function method and the particle-tracking method. The stream-function method works well for many cases, but it does not work for problems with holes in the mesh or internal sources or sinks. The particle-tracking method works for all cases, but previously published algorithms that utilize this method do not result in the properly sized #ow channels. A new approach is presented in this paper that is a hybrid of the stream-function and particle-tracking approaches. This method works for all cases and generates the properly sized #ow channels.

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“…t i + 1 (7) Equations (7) are simple formulae for calculating the nodal co-ordinates of a quadrilateral parametric element in the vicinity of the singularity point. a and b are the lengths of the 'constant potential side' and the 'impervious side' of the element, respectively.…”

Section: Imentioning

confidence: 99%

“…This is done by locating each node i of the element at the intersection point of the stream line where c,, c2, c3 are constants and k the permeability (isotropic case). Using the notation of 7I t i + 1 (7) Equations (7) are simple formulae for calculating the nodal co-ordinates of a quadrilateral parametric element in the vicinity of the singularity point. a and b are the lengths of the 'constant potential side' and the 'impervious side' of the element, respectively.…”

Section: A Rule For Locating the Nodesmentioning

confidence: 99%