A particle-particle hybrid method for kinetic and continuum equations

  • Authors:

  • Sudarshan Tiwari;Axel Klar;Steffen Hardt

  • Affiliations:

  • Fachbereich Mathematik, TU Kaiserslautern, Gottlieb-Daimler-Strasse, 67663 Kaiserslautern, Germany;Fachbereich Mathematik, TU Kaiserslautern, Gottlieb-Daimler-Strasse, 67663 Kaiserslautern, Germany;Center of Smart Interfaces, TU Darmstadt, Petersenstr. 32, 64287 Darmstadt, Germany

  • Venue:
  • Journal of Computational Physics
  • Year:
  • 2009

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Abstract

We present a coupling procedure for two different types of particle methods for the Boltzmann and the Navier-Stokes equations. A variant of the DSMC method is applied to simulate the Boltzmann equation, whereas a meshfree Lagrangian particle method, similar to the SPH method, is used for simulations of the Navier-Stokes equations. An automatic domain decomposition approach is used with the help of a continuum breakdown criterion. We apply adaptive spatial and time meshes. The classical Sod's 1D shock tube problem is solved for a large range of Knudsen numbers. Results from Boltzmann, Navier-Stokes and hybrid solvers are compared. The CPU time for the hybrid solver is 3-4 times faster than for the Boltzmann solver.