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

  • Authors:

  • Xihua Xu;Guoxi Ni;Song Jiang

  • Affiliations:

  • LCP, Institute of Applied Physics and Computational Mathematics, Beijing, China 100088;LCP, Institute of Applied Physics and Computational Mathematics, Beijing, China 100088;LCP, Institute of Applied Physics and Computational Mathematics, Beijing, China 100088

  • Venue:
  • Journal of Scientific Computing
  • Year:
  • 2013

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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.