BERNARD, Florian; IOLLO, Angelo; RIFFAUD, Sébastien

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BERNARD, Florian
Institut de Mathématiques de Bordeaux [IMB]
Modeling Enablers for Multi-PHysics and InteractionS [MEMPHIS]

IOLLO, Angelo
Institut de Mathématiques de Bordeaux [IMB]
Modeling Enablers for Multi-PHysics and InteractionS [MEMPHIS]

RIFFAUD, Sébastien
Institut de Mathématiques de Bordeaux [IMB]
Modeling Enablers for Multi-PHysics and InteractionS [MEMPHIS]

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Communication dans un congrès

Ce document a été publié dans

6th European Conference on Computational Mechanics (ECCM 6) - 7th European Conference on Computational Fluid Dynamics (ECFD 7), 2018-06-11, Glasgow.

Résumé en anglais

A reduced-order model of the BGK equation leading to fast and accurate computations is presented. The BGK model describes the dynamics of a gas flow in both hydrodynamic and rarefied regimes. In the reduced-order model, the distribution functions are approximated in velocity space by a small number of basis functions computed offline. In the offline phase, the BGK equation is sampled in order to collect information on the distribution functions. Then, optimal transportation provides additional samples by interpolating the distribution functions to complete the sampling. Finally, the basis functions are built by Proper Orthogonal Decomposition. During the online phase, the offline knowledge is used to compute approximations ofthe density distribution function at low cost. The BGK equation is projected onto the basis functions, leading to an hyperbolic system of partial differential equations. Moreover, the projection is modified to conserve mass, momentum and energy of the gas. The resulting system is then solved by an IMEX Runge-Kutta scheme in time and a finite-volume scheme in space. The results show the significant reduction of the computational cost and the accuracy of the reduced-order model.< Réduire

Mots clés en anglais

Rarefied flows

Proper Orthogonal Decomposition

Reduced-order model

Optimal transportation

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Reduced-order model of the BGK equation based on POD and optimal transport

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