Discontinuous Galerkin method for Krause's consensus models and pressureless Euler equations

نویسندگان

  • Yang Yang
  • Dongming Wei
  • Chi-Wang Shu
چکیده

In this paper, we apply discontinuous Galerkin (DG) methods to solve two model equations: Krause’s consensus models and pressureless Euler equations. These two models are used to describe the collisions of particles, and the distributions can be identified as density functions. If the particles are placed at a single point, then the density function turns out to be a δ-function and is difficult to be well approximated numerically. In this paper, we use DG method to approximate such a singularity and demonstrate the good performance of the scheme. Since the density functions are always positive, we apply a positivity-preserving limiter to them. Moreover, for pressureless Euler equations, the velocity satisfies the maximum principle. We also construct special limiters to fulfill this requirement.

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عنوان ژورنال:
  • J. Comput. Physics

دوره 252  شماره 

صفحات  -

تاریخ انتشار 2013