Cosmological analogies, Lagrangians, and symmetries for convective–radiative heat transfer

Faraoni, Valerio; Atieh, Farah; Dussault, Steve

doi:10.1140/epjc/s10052-020-8292-0

Cited by 4 publications

(2 citation statements)

References 46 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…It is also well known that the solutions of Equation (1) present steep fronts and shocks, which need to be accurately resolved in applications and often cause severe numerical challenges. Lagrangian methods are among the numerical techniques used in the literature to handle these difficulties generated from the presence of convective terms in the governing equations, see for instance [9, 21]. The main shortcoming for these methods is the grid distortion drawback specially when characteristic curves are required to be computed for time‐dependent velocity fields.…”

Section: Introductionmentioning

confidence: 99%

A priori error estimates for a semi‐Lagrangian unified finite element method for coupled Darcy‐transport problems

Salhi

El‐Amrani

Seaı̈d

2023

Numerical Methods Partial

View full text Add to dashboard Cite

A semi‐Lagrangian unified finite element method is investigated for solving time‐dependent coupled Darcy‐transport problems. In this method, the modified method of characteristics is combined with a Galerkin finite element discretization allowing the same finite element space to be used for all solutions of the problem including the pressure, velocity and concentration. Convergence and stability of the method are also analyzed in this study and error estimates in the ‐norm are established for the numerical solutions. For the time integration we consider a second‐order implicit method and discrete error estimates are provided. Due to the Lagrangian treatment of convection terms in the considered problems, the conventional Courant‐Friedrichs‐Lewy condition is relaxed and the time truncation errors are reduced in the diffusion‐reaction part. Numerical results are presented for several test examples to demonstrate the reliability and efficiency of the proposed method. The computed results support our expectations for an accurate and highly efficient semi‐Lagrangian unified finite element method for time‐dependent coupled Darcy‐transport problems.

show abstract

Section: Introductionmentioning

confidence: 99%

A priori error estimates for a semi‐Lagrangian unified finite element method for coupled Darcy‐transport problems

Salhi

El‐Amrani

Seaı̈d

2023

Numerical Methods Partial

View full text Add to dashboard Cite

show abstract

“…Moreover, numerical solutions need an accurate approximation in order to resolve possible steep fronts and shocks, see for instance [19,21,38,44]. To deal with the difficulties generated by the presence of convective terms in the governing equations, it is possible to opt for numerical techniques based on Lagrangian methods, see for example [13,26]. However, the main disadvantage of these methods is the grid distortion drawback specially when characteristic curves are required to be computed for time-dependent velocity fields.…”

Section: Introductionmentioning

confidence: 99%

Analysis of a Galerkin-characteristic finite element method for convection-diffusion problems in porous media

Salhi¹,

El‐Amrani²,

Seaı̈d³

2021

APAM

View full text Add to dashboard Cite

L'objectif de ce travail est l'étude d'une méthode de résolution numérique par éléments finis semilagrangiennes afin de résoudre les problémes évolutifs de convection-diffusion issus des milieux poreux. La méthode proposée permet d'utiliser une approximation par éléments finis d'ordre égal pour toutes les solutions du probléme. En outre, la condition standard de Courant-Friedrichs-Lewy est assouplie avec le traitement lagrangien des termes de convection, et les erreurs de troncature sont réduites dans la partie diffusion-réaction du probléme. Dans cette étude, une analyse de la convergence et de la stabilité de la méthode proposée est aussi présentée, ainsi que les estimations des erreurs dans la norme L 2 dérivées pour toutes les solutions numériques. Les tests numériques sont illustrées par quelques exemples afin de vérifier les estimations théoriques et de démontrer la grande précision et l'efficacité de la méthode proposée. ABSTRACT. We present a Galerkin-characteristic finite element method for the numerical solution of time-dependent convection-diffusion problems in porous media. The proposed method allows the use of equal-order finite element approximations for all solutions in the problem. In addition, the standard Courant-Friedrichs-Lewy condition is relaxed with the Lagrangian treatment of convection terms, and the time truncation errors are reduced in the diffusion-reaction part. Analysis of convergence and stability of the proposed method is also investigated in this study and error estimates in the L 2 -norm are established for the numerical solutions. Numerical performance of the method is examined using two examples to verify the theoretical estimates and to demonstrate the high accuracy and efficiency of the proposed Galerkin-characteristic finite element method. MOTS-CLÉS. Problémes de convection-diffusion, Équation de Darcy, Milieux poreux, Méthode semi-lagrangienne, Éléments finis, Estimation des erreurs a priori.

show abstract

Non-singular non-flat universes

et al. 2022

View full text Add to dashboard Cite

Cosmological analogies, Lagrangians, and symmetries for convective–radiative heat transfer

Cited by 4 publications

References 46 publications

A priori error estimates for a semi‐Lagrangian unified finite element method for coupled Darcy‐transport problems

A priori error estimates for a semi‐Lagrangian unified finite element method for coupled Darcy‐transport problems

Analysis of a Galerkin-characteristic finite element method for convection-diffusion problems in porous media

Non-singular non-flat universes

Contact Info

Product

Resources

About