Commun. Comput. Phys., 12 (2012), pp. 162-192.

Efficient Deterministic Modelling of Three-Dimensional Rarefied Gas Flows

V. A. Titarev 1*

1 Dorodnicyn Computing Centre of Russian Academy of Sciences, Vavilov st. 40, Moscow, Russia, 119333; and Cranfield University, Cranfield, UK, MK43 0AL.

Received 22 January 2011; Accepted (in revised version) 14 July 2011
Available online 20 January 2012


The paper is devoted to the development of an efficient deterministic framework for modelling of three-dimensional rarefied gas flows on the basis of the numerical solution of the Boltzmann kinetic equation with the model collision integrals. The framework consists of a high-order accurate implicit advection scheme on arbitrary unstructured meshes, the conservative procedure for the calculation of the model collision integral and efficient implementation on parallel machines. The main application area of the suggested methods is micro-scale flows. Performance of the proposed approach is demonstrated on a rarefied gas flow through the finite-length circular pipe. The results show good accuracy of the proposed algorithm across all flow regimes and its high efficiency and excellent parallel scalability for up to 512 cores.

AMS subject classifications: 82D05, 76P05, 82B40, 82C40, 76M12, 65N08, 65B99

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Key words: Kinetic, S-model, unstructured, mixed-element, micro channel, rarefied, implicit.

*Corresponding author.
Email:, (V. A. Titarev)

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