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Tregan JM, Amestoy JL, Bati M, Bezian JJ, Blanco S, Brunel L, Caliot C, Charon J, Cornet JF, Coustet C, d'Alençon L, Dauchet J, Dutour S, Eibner S, El Hafi M, Eymet V, Farges O, Forest V, Fournier R, Galtier M, Gattepaille V, Gautrais J, He Z, Hourdin F, Ibarrart L, Joly JL, Lapeyre P, Lavieille P, Lecureux MH, Lluc J, Miscevic M, Mourtaday N, Nyffenegger-Péré Y, Pelissier L, Penazzi L, Piaud B, Rodrigues-Viguier C, Roques G, Roger M, Saez T, Terrée G, Villefranque N, Vourc'h T, Yaacoub D. Coupling radiative, conductive and convective heat-transfers in a single Monte Carlo algorithm: A general theoretical framework for linear situations. PLoS One 2023; 18:e0283681. [PMID: 37023098 PMCID: PMC10079137 DOI: 10.1371/journal.pone.0283681] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Journal Information] [Subscribe] [Scholar Register] [Received: 10/21/2022] [Accepted: 03/14/2023] [Indexed: 04/07/2023] Open
Abstract
It was recently shown that radiation, conduction and convection can be combined within a single Monte Carlo algorithm and that such an algorithm immediately benefits from state-of-the-art computer-graphics advances when dealing with complex geometries. The theoretical foundations that make this coupling possible are fully exposed for the first time, supporting the intuitive pictures of continuous thermal paths that run through the different physics at work. First, the theoretical frameworks of propagators and Green's functions are used to demonstrate that a coupled model involving different physical phenomena can be probabilized. Second, they are extended and made operational using the Feynman-Kac theory and stochastic processes. Finally, the theoretical framework is supported by a new proposal for an approximation of coupled Brownian trajectories compatible with the algorithmic design required by ray-tracing acceleration techniques in highly refined geometry.
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Affiliation(s)
- Jean Marc Tregan
- LAPLACE, Université de Toulouse, CNRS, INPT, UPS, Toulouse, France
| | - Jean Luc Amestoy
- LAPLACE, Université de Toulouse, CNRS, INPT, UPS, Toulouse, France
| | - Megane Bati
- IRIT, Université de Toulouse, CNRS, UPS, Toulouse, France
| | - Jean-Jacques Bezian
- Université de Toulouse, Mines Albi, UMR 5302 - Centre RAPSODEE, Campus Jarlard, Albi, CT, France
| | - Stéphane Blanco
- LAPLACE, Université de Toulouse, CNRS, INPT, UPS, Toulouse, France
| | | | - Cyril Caliot
- CNRS, UPPA, E2S, LMAP, 1 Allée du Parc Montaury, Anglet, France
| | - Julien Charon
- ESTACA West Campus, Rue Georges Charpak, Laval, France
| | - Jean-Francois Cornet
- Université Clermont Auvergne, Clermont Auvergne INP, CNRS, Institut Pascal, Clermont-Ferrand, France
| | | | - Louis d'Alençon
- LAPLACE, Université de Toulouse, CNRS, INPT, UPS, Toulouse, France
- LMD/IPSL, Sorbonne Université, CNRS, École Polytechnique, ENS, Paris, France
| | - Jeremi Dauchet
- Université Clermont Auvergne, Clermont Auvergne INP, CNRS, Institut Pascal, Clermont-Ferrand, France
| | - Sebastien Dutour
- LAPLACE, Université de Toulouse, CNRS, INPT, UPS, Toulouse, France
| | - Simon Eibner
- Université de Toulouse, Mines Albi, UMR 5302 - Centre RAPSODEE, Campus Jarlard, Albi, CT, France
| | - Mouna El Hafi
- Université de Toulouse, Mines Albi, UMR 5302 - Centre RAPSODEE, Campus Jarlard, Albi, CT, France
| | | | - Olivier Farges
- Université de Lorraine, CNRS, LEMTA, Vandœuvre-lès-Nancy, France
| | | | - Richard Fournier
- LAPLACE, Université de Toulouse, CNRS, INPT, UPS, Toulouse, France
| | - Mathieu Galtier
- Univ. Lyon, CNRS, INSA-Lyon, Université Claude Bernard Lyon 1, CETHIL UMR5008, Villeurbanne, France
| | - Victor Gattepaille
- Université Clermont Auvergne, Clermont Auvergne INP, CNRS, Institut Pascal, Clermont-Ferrand, France
| | - Jacques Gautrais
- LAPLACE, Université de Toulouse, CNRS, INPT, UPS, Toulouse, France
- CRCA, CBI, Université de Toulouse, CNRS, Toulouse, France
| | - Zili He
- Université de Toulouse, Mines Albi, UMR 5302 - Centre RAPSODEE, Campus Jarlard, Albi, CT, France
| | - Frédéric Hourdin
- LMD/IPSL, Sorbonne Université, CNRS, École Polytechnique, ENS, Paris, France
| | | | - Jean-Louis Joly
- LAPLACE, Université de Toulouse, CNRS, INPT, UPS, Toulouse, France
| | - Paule Lapeyre
- Department of Mechanical and Mechatronics Engineering, University of Waterloo, Waterloo ON, Canada
| | - Pascal Lavieille
- LAPLACE, Université de Toulouse, CNRS, INPT, UPS, Toulouse, France
| | | | - Jacques Lluc
- LAPLACE, Université de Toulouse, CNRS, INPT, UPS, Toulouse, France
| | - Marc Miscevic
- LAPLACE, Université de Toulouse, CNRS, INPT, UPS, Toulouse, France
| | - Nada Mourtaday
- Inspe TOP, UMR EFTS, Université de Toulouse, Toulouse, France
| | | | | | - Lea Penazzi
- Université de Lorraine, CNRS, LEMTA, Vandœuvre-lès-Nancy, France
| | | | | | - Gisele Roques
- LAPLACE, Université de Toulouse, CNRS, INPT, UPS, Toulouse, France
| | - Maxime Roger
- Univ. Lyon, CNRS, INSA-Lyon, Université Claude Bernard Lyon 1, CETHIL UMR5008, Villeurbanne, France
| | - Thomas Saez
- LTZ Electronique, Saint Laurent du Var, France
| | - Guillaume Terrée
- Univ. Lyon, CNRS, INSA-Lyon, Université Claude Bernard Lyon 1, CETHIL UMR5008, Villeurbanne, France
| | - Najda Villefranque
- Centre National de Recherches Météorologiques, UMR 3589 CNRS, Météo France, Toulouse, France
| | - Thomas Vourc'h
- Université Clermont Auvergne, Clermont Auvergne INP, CNRS, Institut Pascal, Clermont-Ferrand, France
| | - Daniel Yaacoub
- Université Clermont Auvergne, Clermont Auvergne INP, CNRS, Institut Pascal, Clermont-Ferrand, France
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