Application of the control volume mixed finite element method to a triangular discretization

Naff, R. L.

doi:10.1002/nme.3265

Cited by 2 publications

(8 citation statements)

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“…Equations and place somewhat diverse requirements on the test function. In , when test functions of the form

ω_{i k} ~ ν_{i k} / ς_{i k} |_{r \in F_{i k}}

were used in , it was demonstrated that an optimal weighting resulted. With regard to , two piecewise pressure approximations associated with the test function are investigated herein.…”

Section: Solving the Darcy Problem With Control‐volume Vixed Finite‐ementioning

confidence: 99%

“…For the CVMFE method, the vector test function in reference space,

{\overset{bold-italicω}{true}}_{i}

, is obtained from the vector shape function evaluated at the primary face

{\overset{F}{true}}_{i 1} : {\overset{bold-italicω}{true}}_{i} \sim ((), {\overset{bold-italicν}{true}}_{i 1} |_{ζ = 0}) / {\overset{ς}{true}}_{i 1}

. From , this expression becomes

\frac{{\overset{bold-italicν}{true}}_{i 1} |_{ζ = 0}}{{\overset{ς}{true}}_{i 1}} = \frac{2 \sqrt{2}}{J_{i}} ([], \frac{\sqrt{6} {normalΓ}_{i}}{3} - ξ {normalΣ}_{i} - η {normalΨ}_{i}) .

To obtain an appropriate scaling factor relating

{\overset{bold-italicω}{true}}_{i}

((), {\overset{bold-italicν}{true}}_{i 1} |_{ζ = 0}) / {\overset{ς}{true}}_{i 1}

, property for test functions is used:

\int_{Q_{ik}} {bold-italicω}_{ik} \cdot \nabla p dv = \int_{{\overset{Q}{true}}_{1}} {\overset{bold-italicω}{true}}_{i} \cdot \overset{\nabla}{true} p J_{i} d \overset{v}{true} = {\overset{p}{true}}_{i} - {\overset{p}{true}}_{}

…”

Section: Solving the Darcy Problem With Control‐volume Vixed Finite‐ementioning

confidence: 99%

“…By applying Gauss's divergence theorem, this integral can be reduced to a discrete form. Similarly, a weak form for (3) can be obtained by multiplying both sides by a test function ! ik for face k and integrating over the control volume Q ik : Z…”

Section: Solving the Darcy Problem With Control-volume Mixed Finite-ementioning

confidence: 99%

“…The CVMFE formulation was originally developed by Cai et al , for modeling 2‐D Darcy flow using a quadrilateral discretization and was later extended by Naff et al , to modeling 3‐D flow using hexahedral elements. More recently, Naff has extended the CVMFE method to modeling 2‐D flow with triangular elements. To some extent, the interest in the CVMFE formulation, versus the SMFE formulation, has to do with the relative diagonal dominance of the two formulations.…”

Section: Introductionmentioning

confidence: 99%

“…To some extent, the interest in the CVMFE formulation, versus the SMFE formulation, has to do with the relative diagonal dominance of the two formulations. The CVMFE formulation has been shown to be more diagonally dominant than the SMFE formulation for certain, regular discretization geometries ; whether this diagonal dominance is beneficial to other, more random discretization geometries is investigated in this study. A more diagonally dominant formulation should be more robust, requiring for instance fewer iterations when an iterative solver is employed in its solution.…”

Section: Introductionmentioning

confidence: 99%

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A control volume mixed finite element formulation for tetrahedral elements

Naff

2015

Numerical Meth Engineering

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SummaryThe control‐volume mixed finite element method is formulated for and applied to a computational domain consisting of a tetrahedral partitioning to solve the steady groundwater flow equations. Test functions consistent with piecewise constant and piecewise linear pressure distributions are used in the formulation. Comparisons are made with a standard mixed finite element formulation using lowest‐order Raviart Thomas basis functions. Results suggest that the control‐volume based formulation is a viable alternative to the standard formulation. Copyright © 2015 John Wiley & Sons, Ltd.

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“…Equations and place somewhat diverse requirements on the test function. In , when test functions of the form

ω_{i k} ~ ν_{i k} / ς_{i k} |_{r \in F_{i k}}

were used in , it was demonstrated that an optimal weighting resulted. With regard to , two piecewise pressure approximations associated with the test function are investigated herein.…”