Commun. Comput. Phys., 8 (2010), pp. 427-444.

Implicit Unstructured-Mesh Method for Calculating Poiseuille Flows of Rarefied Gas

V. A. Titarev 1*

1 Fluid Mechanics and Computational Sciences Group, Aerospace Sciences Department, Cranfield University, Cranfield, MK43 0AL, UK.

Received 18 September 2009; Accepted (in revised version) 28 December 2009
Available online 12 March 2010


An implicit high-order accurate method for solving model kinetic equations is proposed. The method is an extension of earlier work on the construction of an explicit TVD method for hybrid unstructured meshes in physical space and is illustrated on the Poiseuille flow of rarefied gas. Examples of calculations are provided for different Knudsen numbers and mesh resolutions, which illustrate the efficiency and high accuracy of the new scheme.

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

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Key words: Poiseuille, kinetic, unstructured, mixed-element, micro, rarefied, implicit.

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

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