An explicit characteristic finite volume element method for non-divergence free convection–diffusion-reaction equation

Phongthanapanich, Sutthisak; Dechaumphai, Pramote

doi:10.1007/s12572-012-0071-1

Cited by 3 publications

(7 citation statements)

References 25 publications

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“…By applying a characteristic approximation to trace advection in time as explained in Refs. [23, 25, 26] to Equation (), we obtain

\frac{\partial ϕ}{\partial t} - \nabla^{'} \cdot (ε \nabla^{'} ϕ) = 0,

where all terms are to be evaluated at

{boldx}^{'} = {boldx}^{'} false(t false)

. We then discretize the time with time steps

Δ t

and define

ϕ^{n} = ϕ false(t^{n} false)

, where

t^{n} = n Δ t, n = 0, 1, 2, \dots

.…”

Section: The Numerical Schemementioning

confidence: 99%

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An accuracy comparison of piecewise linear reconstruction techniques for the characteristic finite volume method for two‐dimensional convection‐diffusion equation

et al. 2021

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In this paper, we apply the characteristic finite volume method (CFVM) for solving a convection‐diffusion problem on two‐dimensional triangular grids. The finite volume method is used to discretize the equation while the finite element method is applied to estimate the gradient quantities at cell faces. The numerical analysis of the convergence has been implemented for the CFVM in one‐dimension. The approximate L2 norm of the error is derived to determine the errors for the approximate solution. The accuracy of four piecewise linear reconstruction techniques, namely, Frink, Holmes‐Connell, Green‐Gauss, and least‐squares methods are investigated on structured triangular grids. Numerical evidence shows that the least‐squares method is the most accurate of all methods for smooth initial condition problems. For discontinuous initial condition problems, the Frink and the Holmes‐Connell methods give a spurious oscillating solution in the vicinity of the discontinuity upstream of the discontinuity, and the Green‐Gauss and least‐squares methods give a spurious oscillating solution in the vicinity of the discontinuity downstream of the discontinuity. Moreover, the amplitude of the oscillation could be amplified on the finer grid sizes.

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“…By applying a characteristic approximation to trace advection in time as explained in Refs. [23, 25, 26] to Equation (), we obtain

\frac{\partial ϕ}{\partial t} - \nabla^{'} \cdot (ε \nabla^{'} ϕ) = 0,

where all terms are to be evaluated at

{boldx}^{'} = {boldx}^{'} false(t false)

. We then discretize the time with time steps

Δ t

and define

ϕ^{n} = ϕ false(t^{n} false)

, where

t^{n} = n Δ t, n = 0, 1, 2, \dots

.…”

Section: The Numerical Schemementioning

confidence: 99%

“…By applying a characteristic approximation to trace advection in time as explained in Refs. [23,25,26] to Equation (1), we obtain…”

Section: The Characteristic Unsteady Convection-diffusion Equationmentioning

confidence: 99%

An accuracy comparison of piecewise linear reconstruction techniques for the characteristic finite volume method for two‐dimensional convection‐diffusion equation

et al. 2021

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“…By applying a characteristic approximation to trace advection in time, as explained in Ref. [5][6][7] to Eq. ( 1) yields (5) where all terms are to be evaluated at .…”

Section: The Characteristic Convection-diffusionreaction Equationmentioning

confidence: 99%

“…The last example is the skew flow problem presented by Hauke [12,7]. This example considers the behavior of the numerical solutions under the convection-reactiondominated diffusion condition in a square domain , with the initial condition .…”

Section: Skew Flow To the Meshmentioning

confidence: 99%

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A Comparative Study of Characteristic Finite Element and Characteristic Finite Volume Methods for Convection-Diffusion-Reaction Problems on Triangular Grids

Phongthanapanich¹,

Eymard²

2019

j.asep

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The paper aims to compare the accuracy and robustness of the characteristic finite element method (CFEM) and characteristic finite volume method (CFVM) for solving convection-diffusionreaction problems on two-dimensional triangular grids. The tests are performed on a square unit domain, to which an advective field is imposed in a domain. The results show that the CFEM gives less accurate solution than CFVM for the rotation of a slotted-cylinder and rotation of Gaussian cone problems. Moreover, CFEM gives oscillate solution while the CFVM provides an oscillationfree solution for the skew flow to the mesh problem.

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A comparison of TVD limiter functions for a convection–diffusion–reaction equation and Euler equations on triangular grids

Kaewta

Khansai

Sirisubtawee

et al. 2022

J Braz. Soc. Mech. Sci. Eng.

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An explicit characteristic finite volume element method for non-divergence free convection–diffusion-reaction equation

Cited by 3 publications

References 25 publications

An accuracy comparison of piecewise linear reconstruction techniques for the characteristic finite volume method for two‐dimensional convection‐diffusion equation

An accuracy comparison of piecewise linear reconstruction techniques for the characteristic finite volume method for two‐dimensional convection‐diffusion equation

A Comparative Study of Characteristic Finite Element and Characteristic Finite Volume Methods for Convection-Diffusion-Reaction Problems on Triangular Grids

A comparison of TVD limiter functions for a convection–diffusion–reaction equation and Euler equations on triangular grids

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