Analysis of a semi-augmented mixed finite element method for double-diffusive natural convection in porous media

Alvarez, Mario; Colmenares, Eligio; Sequeira, Filánder A.

doi:10.1016/j.camwa.2022.03.032

Cited by 7 publications

(27 citation statements)

References 22 publications

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“…In this section we recall from [2] the mathematical model that is addressed in the present work. About that, we consider the Oberbeck-Boussinesq approximation framework, along with the double-diffusive natural convection phenomenon in a porous media.…”

Section: The Mathematical Modelmentioning

confidence: 99%

“…Up to the authors knowledge, in the literature only a few works are available concerning to the numerical analysis of a similar double-diffusive natural convection in porous media problem like we studied in [2] (see [8,9,12,19,22,31,36]). Moreover, only [8] is devoted to the a posteriori error analysis for the corresponding numerical method.…”

Section: Introductionmentioning

confidence: 99%

“…The mathematical model and the weak formulation are outlined in Sections 2 and 3, respectively. Therein, we recall from [2] the corresponding Galerkin scheme. In Section 4 we derive a reliable and efficient residual-based a posteriori error estimator for our Galerkin scheme.…”

Section: Introductionmentioning

confidence: 99%

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A posteriori error analysis of a semi‐augmented finite element method for double‐diffusive natural convection in porous media

Álvarez,

Colmenares,

Sequeira

2024

Numerical Methods Partial

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This paper presents our contribution to the a posteriori error analysis in 2D and 3D of a semi‐augmented mixed‐primal finite element method previously developed by us to numerically solve double‐diffusive natural convection problem in porous media. The model combines Brinkman‐Navier‐Stokes equations for velocity and pressure coupled to a vector advection‐diffusion equation, representing heat and concentration of a certain substance in a viscous fluid within a porous medium. Strain and pseudo‐stress tensors were introduced to establish scheme solvability and provide a priori error estimates using Raviart‐Thomas elements, piecewise polynomials and Lagrange finite elements. In this work, we derive two reliable residual‐based a posteriori error estimators. The first estimator leverages ellipticity properties, Helmholtz decomposition as well as Clément interpolant and Raviart‐Thomas operator properties for showing reliability; efficiency is guaranteed by inverse inequalities and localization strategies. An alternative estimator is also derived and analyzed for reliability without Helmholtz decomposition. Numerical tests are presented to confirm estimator properties and demonstrate adaptive scheme performance.

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Section: The Mathematical Modelmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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A posteriori error analysis of a semi‐augmented finite element method for double‐diffusive natural convection in porous media

Álvarez,

Colmenares,

Sequeira

2024

Numerical Methods Partial

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“…The authors established the existence and uniqueness results for the continuous problem and the discrete schemes. In addition, a semi-augmented mixed finite element method for double-diffusive natural convection in porous media was analyzed in Alvarez et al [17]. Besides, for the stationary double-diffusive natural convection equations, three iterative methods were designed, and their convergence intervals were given in Wei and Huang [18].…”

Section: Introductionmentioning

confidence: 99%

Convergence of several iterations for double‐diffusive natural convection model

Wei

Huang

2023

Math Methods in App Sciences

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Several iterative finite element methods are analyzed for a steady‐state double‐diffusive natural convection model, which contains the diffusion of temperature and concentration and can simulate heat and mass transfer phenomena. These iterations include the Stokes‐type, Newton‐type, and Oseen‐type iterative methods. Then, based on the uniqueness condition, stability and convergence of these iterative methods are proved for the considered model. Finally, some numerical examples are presented for validating the correctness of the theoretical analysis.

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“…Hybrid nanofluids may be commonly applied to improve thermal characteristics in a stationary DDNC issue. Álvarez et al (2022) used a vector advection–diffusion equation in conjunction with a Navier–Stokes/Brinkman type system to describe the velocity and pressure. Teamah and El-Maghlany (2010) investigated DDNC inside a lid-driven area with the composed buoyancy effects.…”

Section: Introductionmentioning

confidence: 99%

Second law and thermal analyses of non-Newtonian nanofluid double-diffusive natural convection within a two-hot-baffles-equipped C-shaped domain impacted by magnetic field

Irshad,

Pasha,

Mesfer

et al. 2023

HFF

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Purpose The entropy and thermal behavior analyses of non-Newtonian nanofluid double-diffusive natural convection inside complex domains may captivate a bunch of scholars’ attention because of the potential utilizations that they possess in modern industries, for example, heat exchangers, solar energy collectors and cooling of electronic apparatuses. This study aims to investigate the second law and thermal behavior of non-Newtonian double-diffusive natural convection (DDNC) of Al2O3-H2O nanofluid within a C-shaped cavity emplacing two hot baffles and impacted by a magnetic field. Design/methodology/approach For the governing equations of the complicated and practical system with all considered parameters to be solved via a formidable numerical approach, the finite element method acts as an approach to achieving the desired solution. This method allows us to gain a detailed solution to the studied geometry. Findings This investigation has been executed for the considered parameters of range, such as power-law index, baffle length, Lewis number, buoyancy ratio, Hartmann number and Rayleigh number. The main results reveal that isothermal and concentration lines are significantly more distorted, indicating intensified concentration and temperature distributions because of the growth of baffle length (L). Nuave decreases by 8.4% and 0.8% while it enhances by 49.86% and 33.87%, respectively, because of growth in the L from 0.1 to 0.2 and 0.2 to 0.3. Originality/value Such a comprehensive study on the second law and thermal behavior of DDNC of Al2O3-H2O nanofluid within a C-shaped cavity emplacing two hot baffles and impacted by magnetic field has not yet been carried out.

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Analysis of a semi-augmented mixed finite element method for double-diffusive natural convection in porous media

Cited by 7 publications

References 22 publications

A posteriori error analysis of a semi‐augmented finite element method for double‐diffusive natural convection in porous media

A posteriori error analysis of a semi‐augmented finite element method for double‐diffusive natural convection in porous media

Convergence of several iterations for double‐diffusive natural convection model

Second law and thermal analyses of non-Newtonian nanofluid double-diffusive natural convection within a two-hot-baffles-equipped C-shaped domain impacted by magnetic field

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