Commun. Comput. Phys., 16 (2014), pp. 956-982.


A Local Velocity Grid Approach for BGK Equation

Florian Bernard 1*, Angelo Iollo 2, Gabriella Puppo 3

1 Department of Mechanical and Aerospace Engineering, Politecnico di Torino, 10129 Torino, Italy; Univ. Bordeaux, IMB, UMR 5251, F-33400 Talence, France; INRIA, F-33400 Talence, France.
2 Univ. Bordeaux, IMB, UMR 5251, F-33400 Talence, France; INRIA, F-33400 Talence, France.
3 Dip. di Scienza ed Alta Tecnologia, Universita dell'Insubria, Como, Italy.

Received 29 October 2013; Accepted (in revised version) 24 March 2014
Available online 8 August 2014
doi:10.4208/cicp.291013.240314a

Abstract

The solution of complex rarefied flows with the BGK equation and the Discrete Velocity Method (DVM) requires a large number of velocity grid points leading to significant computational costs. We propose an adaptive velocity grid approach exploiting the fact that locally in space, the distribution function is supported only by a sub-set of the global velocity grid. The velocity grid is adapted thanks to criteria based on local temperature, velocity and on the enforcement of mass conservation. Simulations in 1D and 2D are presented for different Knudsen numbers and compared to a global velocity grid BGK solution, showing the computational gain of the proposed approach.

AMS subject classifications: 76P05

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Key words: Kinetic models, BGK model, discrete velocity method.

*Corresponding author.
Email: florian.bernard@polito.it (F. Bernard), angelo.iollo@math.u-bordeaux1.fr (A. Iollo), gabriella.puppo@uninsubria.it (G. Puppo)
 

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