High-order kinetic flux vector splitting schemes in general coordinates for ideal quantum gas dynamics

  • Authors:

  • Jaw-Yen Yang;Tse-Yang Hsieh;Yu-Hsin Shi;Kun Xu

  • Affiliations:

  • Institute of Applied Mechanics, National Taiwan University, Taipei, Taiwan;Institute of Applied Mechanics, National Taiwan University, Taipei, Taiwan;Institute of Applied Mechanics, National Taiwan University, Taipei, Taiwan;The Hong Kong University of Science and Technology, Clear Water Bay, Kowloon, Hong Kong

  • Venue:
  • Journal of Computational Physics
  • Year:
  • 2007

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Abstract

A class of high-order kinetic flux vector splitting schemes are presented for solving ideal quantum gas dynamics based on quantum statistical mechanics. The collisionless quantum Boltzmann equation approach is adopted and both Bose-Einstein and Fermi-Dirac gases are considered. The formulas for the split flux vectors are derived based on the general three-dimensional distribution function in velocity space and formulas for lower dimensions can be directly deduced. General curvilinear coordinates are introduced to treat practical problems with general geometry. High-order accurate schemes using weighted essentially non-oscillatory methods are implemented. The resulting high resolution kinetic flux splitting schemes are tested for 1D shock tube flows and shock wave diffraction by a 2D wedge and by a circular cylinder in ideal quantum gases. Excellent results have been obtained for all examples computed.