High performance computation of radiative transfer equation using the finite element method

Badri, M.A.; Jolivet, Pierre; Rousseau, Benoı̂t; Favennec, Yann

doi:10.1016/j.jcp.2018.01.027

Cited by 44 publications

(28 citation statements)

References 54 publications

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“…Our deterministic simulations are based on tightly coupled vectorial FE for solving the radiation physics and Galerkin FE for solving the conduction physics. Our vectorial FE solver [33,34] was previously developed only for handling the radiation physics within participating media. In this article, we extend its capabilities to solve conduction-radiation physics efficiently.…”

Section: Introductionmentioning

confidence: 99%

Conductive-radiative heat transfer within SiC-based cellular ceramics at high-temperatures: A discrete-scale finite element analysis

Badri

Favennec

Jolivet

et al. 2020

Finite Elements in Analysis and Design

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Cellular ceramic materials possess many favorable properties that allow to develop efficient modern-day hightemperature thermal energy conversion systems and processes. The energy conversion within these porous media is governed by tightly coupled conduction-radiation physics. To efficiently design and optimize these systems, a comprehensive understanding of the conduction-radiation behavior within these materials becomes important. In this study, by performing large-scale numerical experiments, we analyze the conduction-radiation coupling characteristics within different (with respect to topology and porosity) SiC-based open-cell cellular ceramics surrounded by fictitious vacuum up to temperatures of 1800 K. To induct minimal approximations, our finite element simulations are based on a discrete-scale approach within which realistic discrete (porelevel) representations of the cellular ceramics are used as numerical media. The results presented in this study provide means to better understand the role of radiation in the coupled conduction-radiation physics within the ceramic samples. A detailed comparison on effectiveness of energy conversion is established for SiC-based full-scale cubic-cell, Kelvin-cell, and pseudo-random-cell ceramic structures which are at 80 % and 90 % porosity each. In conclusion, among the different standalone and full-scale ceramic samples, the Kelvin-cell structures at 90% porosity have proven to benefit the most from radiation coupling.

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Section: Introductionmentioning

confidence: 99%

Conductive-radiative heat transfer within SiC-based cellular ceramics at high-temperatures: A discrete-scale finite element analysis

Badri

Favennec

Jolivet

et al. 2020

Finite Elements in Analysis and Design

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“…Note that this test is run on an ordinary laptop with 8 processors, using the domain decomposition method (the lighter blue contours present in Figure 5 represent the internal boundaries of the different domains). Note that such simulations have been highly studied and validated in previous papers [3,10]. Figure 6 presents a series of ad hoc refined meshes of the unit sphere, starting from the first level of uniform refinement of the octahedron.…”

Section: Test 2: Absorbing and Scattering Medium Impinged By A Laser mentioning

confidence: 94%

“…In order to model the involved physics accurately, it was proven that a unit sphere discretization with at least 320 directions was necessary. As such, high computational resources and time were required to solve such problem without considering the setting of vectorial finite elements [9] and associate parallelization tools [10]. A similar scenario was noticed in [11,12], who used the FEM-FEM discretization and ended up using 1280 directions with an adaptive mesh for astrophysics problems.…”

Section: Introductionmentioning

confidence: 92%

Ad hoc angular discretization of the radiative transfer equation

Favennec

Mathew

Badri

et al. 2019

Journal of Quantitative Spectroscopy and Radiative Transfer

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Solving the radiative transfer equation with the finite element method requires both angular and spatial discretizations. We develop a novel algorithm of angular mesh discretization based on a posteriori calculations. The obtained angular discretizations are optimized in such a way that they suit the particular physics under consideration. Such ad hoc angular discretizations are implemented for increasing the finite element solution efficiency. Using comparative numerical tests based on the solution accuracy, the solutions provided by the obtained ad hoc discretizations are proven to be better than the ones provided by the standard uniform angular discretizations. The algorithm is drafted in such a way that it could be easily implemented using pre-existing open-source mathematical libraries.

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“…To find the numerical solution, the finite difference method, finite element method and finite volume method are the prominent methods. Out of these, the finite element method [39][40][41][42][43][44][45] is a powerful tool to encounter the boundary value problems. The conforming element pair p 2 − p 1 is utilized for the velocity and pressure approximations.…”

Section: Computational Schemementioning

confidence: 99%

A potential alternative CFD simulation for steady Carreau–Bird law-based shear thickening model: Part-I

Rehman

Malik

Mahmood

et al. 2019

J Braz. Soc. Mech. Sci. Eng.

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The current article provides the numerical investigation into an infinite-length circular cylinder placed as an obstacle in the flow of non-Newtonian fluid. To be more specific, a channel of length 2.2 m and height 0.41 m is considered. The Power law fluid model is carried out with Carreau-Bird law as a non-Newtonian fluid model, and both the Power law linear (constant) and parabolic velocity profiles are initiated simultaneously at an inlet of the channel. The right wall as an outlet is carried with Neumann condition. The relative velocity of Power law fluid particles with both the lower and upper walls is taken zero. A mathematical model is structured in terms of nonlinear differential equations. A well-trusted numerical technique named finite element method is adopted commercially. The LBB-stable element pair is utilized to approximate the velocity and pressure. The nonlinear iterations are stopped when the residual is dropped by 10 −6. The impact of Power law index and Reynolds number on the primitive variables is inspected. The obtained observations in this direction are provided by means of both the contour plots and line graphs. Due to a circular obstacle, both the drag and lift coefficients are evaluated around the outer surface of an obstacle towards the higher values of the Power law index. The numerical values of drag and lift coefficients up to various refinement mesh levels of domain are provided by way of tables. It is noticed that the parabolic velocity profile at an inlet of channel is compatible as compared to the linear velocity profile. Further, both the drag and lift coefficients are increasing function of Power law index. Keywords Power law fluid model • Linear and parabolic profiles • Finite element method • Drag and lift coefficients List of symbols (x, y, z) Space variables ⃗ V = (u, v, w) Velocity field Fluid density p Pressure ↔ Stress tensor ⃗ B Body force Fluid viscosity Apparent viscosity n Power law index K Consistency coefficient U mean Mean velocity D Characteristic length (diameter of circular cylinder) Re Reynolds number U max Maximum velocity F D Drag force F L Lift force C D Drag coefficient C L Lift coefficient

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High performance computation of radiative transfer equation using the finite element method

Cited by 44 publications

References 54 publications

Conductive-radiative heat transfer within SiC-based cellular ceramics at high-temperatures: A discrete-scale finite element analysis

Conductive-radiative heat transfer within SiC-based cellular ceramics at high-temperatures: A discrete-scale finite element analysis

Ad hoc angular discretization of the radiative transfer equation

A potential alternative CFD simulation for steady Carreau–Bird law-based shear thickening model: Part-I

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