An h-adaptive mesh method for Boltzmann-BGK/hydrodynamics coupling

  • Authors:

  • Zhenning Cai;Ruo Li

  • Affiliations:

  • School of Mathematical Sciences, Peking University, Beijing, China;CAPT, LMAM and School of Mathematical Sciences, Peking University, Beijing 100871, China

  • Venue:
  • Journal of Computational Physics
  • Year:
  • 2010

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Abstract

We introduce a coupled method for hydrodynamic and kinetic equations on 2-dimensional h-adaptive meshes. We adopt the Euler equations with a fast kinetic solver in the region near thermodynamical equilibrium, while use the Boltzmann-BGK equation in kinetic regions where fluids are far from equilibrium. A buffer zone is created around the kinetic regions, on which a gradually varying numerical flux is adopted. Based on the property of a continuously discretized cut-off function which describes how the flux varies, the coupling will be conservative. In order for the conservative 2-dimensional specularly reflective boundary condition to be implemented conveniently, the discrete Maxwellian is approximated by a high order continuous formula with improved accuracy on a disc instead of on a square domain. The h-adaptive method can work smoothly with a time-split numerical scheme. Through h-adaptation, the cell number is greatly reduced. This method is particularly suitable for problems with hydrodynamics breakdown on only a small part of the whole domain, so that the total efficiency of the algorithm can be greatly improved. Three numerical examples are presented to validate the proposed method and demonstrate its efficiency.