Commun. Comput. Phys., 15 (2014), pp. 1029-1044.

Remapping-Free Adaptive GRP Method for Multi-Fluid Flows I: One Dimensional Euler Equations

Jin Qi 1, Yue Wang 2*, Jiequan Li 1

1 School of Mathematical Sciences, Beijing Normal University, Beijing 100875, China.
2 Institute of Applied Physics and Computational Mathematics, Beijing 100094, China.

Received 14 March 2013; Accepted (in revised version) 11 October 2013
Available online 21 January 2014


In this paper, a remapping-free adaptive GRP method for one dimensional (1-D) compressible flows is developed. Based on the framework of finite volume method, the 1-D Euler equations are discretized on moving volumes and the resulting numerical fluxes are computed directly by the GRP method. Thus the remapping process in the earlier adaptive GRP algorithm [17, 18] is omitted. By adopting a flexible moving mesh strategy, this method could be applied for multi-fluid problems. The interface of two fluids will be kept at the node of computational grids and the GRP solver is extended at the material interfaces of multi-fluid flows accordingly. Some typical numerical tests show competitive performances of the new method, especially for contact discontinuities of one fluid cases and the material interface tracking of multi-fluid cases.

AMS subject classifications: 76M12, 76N15, 76T99

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Key words: The GRP method, multi-fluid flows, the Euler equations, the adaptive mesh method.

*Corresponding author.
Email: (J. Qi), (Y. Wang), (J. Li)

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