Exponential Runge-Kutta for the inhomogeneous Boltzmann equations with high order of accuracy

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Abstract

We consider the development of exponential methods for the robust time discretization of space inhomogeneous Boltzmann equations in stiff regimes. Compared to the space homogeneous case, or more in general to the case of splitting based methods, studied in Dimarco Pareschi [7] a major difficulty is that the local Maxwellian equilibrium state change with respect to time and thus needs a proper numerical treatment. We show how to derive asymptotic-preserving (AP) schemes of arbitrary order, and in particular by using the Shu-Osher representation of Runge-Kutta methods we explore the monotonicity properties of such schemes, like strong stability preserving (SSP) and positivity preserving. Several numerical results confirm our analysis.

Original languageEnglish
Pages (from-to)402-420
Number of pages19
JournalJournal of Computational Physics
Volume259
DOIs
StatePublished - 15 Feb 2014
Externally publishedYes

Keywords

  • Asymptotic-preserving schemes
  • Boltzmann equation
  • Exponential Runge-Kutta methods
  • Fluid limits
  • Stiff equations
  • Strong stability preserving schemes

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