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High-Order Asymptotic-Preserving Projective Integration Schemes for Kinetic Equations

  • Pauline Lafitte
  • Annelies Lejon
  • Ward Melis
  • Dirk Roose
  • Giovanni Samaey
Conference paper
Part of the Lecture Notes in Computational Science and Engineering book series (LNCSE, volume 103)

Abstract

We study a projective integration scheme for a kinetic equation in both the diffusive and hydrodynamic scaling, on which a limiting diffusion or advection equation exists. The scheme first takes a few small steps with a simple, explicit method, such as a spatial centered flux/forward Euler time integration, and subsequently projects the results forward in time over a large, macroscopic time step. With an appropriate choice of the inner step size, the time-step restriction on the outer time step is similar to the stability condition for the limiting equation, whereas the required number of inner steps does not depend on the small-scale parameter. The presented method is asymptotic-preserving, in the sense that the method converges to a standard finite volume scheme for the limiting equation in the limit of vanishing small parameter. We show how to obtain arbitrary-order, general, explicit schemes for kinetic equations as well as for systems of nonlinear hyperbolic conservation laws, and provide numerical results.

Keywords

Kinetic Equation Projective Integration Collision Kernel Asymptotic Preserve Semiconductor Equation 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer International Publishing Switzerland 2015

Authors and Affiliations

  • Pauline Lafitte
    • 1
  • Annelies Lejon
    • 2
  • Ward Melis
    • 2
  • Dirk Roose
    • 2
  • Giovanni Samaey
    • 2
  1. 1.Laboratoire de Mathématiques Appliquées aux SystémesEcole Centrale ParisChâtenay-MalabryFrance
  2. 2.Department of Computer ScienceKU LeuvenLeuvenBelgium

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