Commun. Comput. Phys., 2 (2007), pp. 760-782.

Numerical Method for Boltzmann Equation with Soroban-Grid CIP Method

Youichi Ogata 1, Hyo-Nam Im 1, Takashi Yabe 1*

1 Department of Mechanical Sciences and Engineering, Tokyo Institute of Technology, 2-12-1 Meguro-ku, Ookayama 152-8552, Japan.

Received 6 October 2006; Accepted (in revised version) 25 November 2006
Available online 29 January 2007


A new numerical scheme to solve the Boltzmann equation in phase space for rarefied gas is described on the basis of the Cubic Interpolated Propagation (CIP) method. The CIP procedure is extended to adaptive unstructured grid system by the Soroban grid. The grid points in velocity space can move dynamically following the spread of velocity space in a spatially localized manner. Such adaptively moving points in velocity space are similar to the particle codes but can provide higher-order-accurate solutions. Numerical solutions obtained by the Soroban-grid CIP are examined and the validity is discussed.

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PACS: 02.70.-c, 47.11.-j, 47.45.-n
Key words: CIP, Boltzmann equation, Soroban grid.

*Corresponding author.
Email: (Y. Ogata), (H.-N. Im), (T. Yabe)

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