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A High-Order Moving Mesh Kinetic Scheme Based on WENO Reconstruction for Compressible Flows on Unstructured Meshes

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Abstract

In this paper, we present a high-order moving mesh (HMM) kinetic scheme for compressible flow computations on unstructured meshes. To construct the scheme, we employ the frame of the remapping-free ALE-type kinetic method (Ni et al. in J Comput Phys 228:3154–3171, 2009) to get the discretization of compressible system. For the space accuracy, we use the weighted essential non-oscillatory reconstruction on the adaptive moving mesh from Tang and Tang (SIAM J Numer Anal 41:487–515 2003) to achieve time accuracy,we make use of the kinetic flux which includes time accurate integral, and thus obtain a HMM scheme. A number of numerical examples are given, especially an isentropic vortex problem to show the convergence order of the scheme. Numerical results demonstrate the accuracy and robustness of the scheme.

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Acknowledgments

The authors wish to thank Prof. K. Xu and the referees for the useful suggestions which improve this paper. S. Jiang is supported by the National Basic Research Program under the Grant 2011CB309705 and NSFC (Grant No. 11229101), and G. X. Ni is supported by the NSFC (Grant No. 10971016, 91130020).

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  1. LCP, Institute of Applied Physics and Computational Mathematics, P.O. Box 8009, Beijing, 100088, China

    Xihua Xu, Guoxi Ni & Song Jiang

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  1. Xihua Xu
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  2. Guoxi Ni
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  3. Song Jiang
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Correspondence to Xihua Xu.

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Xu, X., Ni, G. & Jiang, S. A High-Order Moving Mesh Kinetic Scheme Based on WENO Reconstruction for Compressible Flows on Unstructured Meshes. J Sci Comput 57, 278–299 (2013). https://doi.org/10.1007/s10915-013-9705-0

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  • DOI: https://doi.org/10.1007/s10915-013-9705-0

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