On the construction of kinetic schemes

  • Authors:

  • Taku Ohwada

  • Affiliations:

  • Department of Aeronautics and Astronautics, Graduate School of Engineering, Kyoto University, Kyoto 606-8501, Japan

  • Venue:
  • Journal of Computational Physics
  • Year:
  • 2002

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Abstract

A general method for the construction of kinetic schemes of evolutionary equations is illustrated with the simple example of the linear advection equation, where the role of the collision effect is clarified theoretically and numerically. The application to the compressible Euler equation and Navier-Stokes equation is explained. The theoretical backgrounds of the existing kinetic schemes, such as the Pullin scheme for the Euler equation and Chou-Baganoff scheme and modified Prendergast-Xu scheme for the Navier-Stokes equation, are unified and their intrinsic errors are revealed.