Study of a finite element method for the time-dependent generalized Stokes system associated with viscoelastic flow

Araujo, J. H. Carneiro de; Gomes, P. D.; Ruas, V.

doi:10.1016/j.cam.2010.03.025

Cited by 8 publications

(10 citation statements)

References 25 publications

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“…Now we recall a result given in Lemma 3 of [10], which allows us to assert that the norm v ε h is bounded above by v ε h ,h ∀v ∈ V h . In order to prove such a result we use the barycentric…”

Section: Full Discretizationmentioning

confidence: 99%

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An explicit P1 finite element scheme for Maxwell's equations with constant permittivity in a boundary neighborhood

Beilina,

Ruas

2018

Preprint

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This paper is devoted to the complete convergence study of the approximation of Maxwell's equations in terms of the sole electric field, by means of standard linear finite elements for the space discretization, combined with a well-known explicit finite-difference scheme for the time discretization. The analysis applies to the particular case where the electric permittivity has a constant value outside a sub-domain, whose closure does not intersect the boundary of the domain where the problem is defined. Optimal convergence results are derived in natural norms under reasonable assumptions, provided a classical CFL condition holds.

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Section: Full Discretizationmentioning

confidence: 99%

“…The proof of Lemma 5.1 is based on the Bramble-Hilbert Lemma, and we refer to [10] for more details. Lemma 5.2 in turn follows from the same arguments combined with the Trace Theorem, which ensures that 3 .…”

Section: Preliminariesmentioning

confidence: 99%

An explicit P1 finite element scheme for Maxwell's equations with constant permittivity in a boundary neighborhood

Beilina,

Ruas

2018

Preprint

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“…Our analysis shows that the equations do not take into account the influence of trailing oil on the contamination length. Therefore, after the simulation and data analysis, we used MATLAB software (MATLAB 8.3, The MathWorks, Natick, MA, USA, 2014) to perform multi-nonlinear regression for the oil substitution time, the length of the dead-leg, and the flow speed to calculate the contamination length [22]. We were able to correct the existing equation to bring its solutions to better fit the actual data.…”

Section: Methodsmentioning

confidence: 99%

Formation Mechanism of Trailing Oil in Product Oil Pipeline

Liu

Hong-jun

et al. 2018

Processes

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Trailing oil is the tail section of contamination in oil pipelines. It is generated in batch transportation, for which one fluid, such as diesel oil follows another fluid, such as gasoline, and it has an effect on the quality of oil. This paper describes our analysis of the formation mechanism of trailing oil in pipelines and our study of the influence of dead-legs on the formation of trailing oil. We found that the oil replacement rate in a dead-leg is exponentially related to the flow speed, and the length of the dead-leg is exponentially related to the replacement time of the oil. To reduce the amount of mixed oil, the main flow speed should be kept at about 1.6 m/s, and the length of the dead-leg should be less than five times the diameter of the main pipe. In our work, the Reynolds time-averaged method is used to simulate turbulence. To obtain contamination-related experimental data, computational fluid dynamics (CFD) software is used to simulate different flow rates and bypass lengths. MATLAB software was used to perform multi-nonlinear regression for the oil substitution time, the length of the bypass, and the flow speed. We determined an equation for calculating the length of the trailing oil contamination produced by the dead-leg. A modified equation for calculating the length of the contamination was obtained by combining the existing equation for calculating the length of the contamination with new factors based on our work. The amounts of contamination predicted by the new equation is closer to the actual contamination amounts than predicted values from other methods suggested by previous scholars.

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“…Next we recall the classical inverse inequality (cf. [12]) together with a result in [11] according to which,…”

Section: Convergence Resultsmentioning

confidence: 99%

Numerical validation of an explicit P1 finite-element scheme for Maxwell's equations in a polygon with variable permittivity away from its boundary

Beilina,

Ruas

2019

Preprint

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This paper is devoted to the numerical validation of an explicit finite-difference scheme for the integration in time of Maxwell's equations in terms of the sole electric field, using standard linear finite elements for the space discretization. The rigorous reliability analysis of this numerical model was the object of another authors' arXiv paper. More specifically such a study applies to the particular case where the electric permittivity has a constant value outside a sub-domain, whose closure does not intersect the boundary of the domain where the problem is defined. Our numerical experiments in two-dimension space certify that the convergence results previously derived for this approach are optimal, as long as the underlying CFL condition is satisfied.

show abstract

Study of a finite element method for the time-dependent generalized Stokes system associated with viscoelastic flow

Cited by 8 publications

References 25 publications

An explicit P1 finite element scheme for Maxwell's equations with constant permittivity in a boundary neighborhood

An explicit P1 finite element scheme for Maxwell's equations with constant permittivity in a boundary neighborhood

Formation Mechanism of Trailing Oil in Product Oil Pipeline

Numerical validation of an explicit P1 finite-element scheme for Maxwell's equations in a polygon with variable permittivity away from its boundary

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