Journal
JOURNAL OF COMPUTATIONAL PHYSICS
Volume 259, Issue -, Pages 402-420Publisher
ACADEMIC PRESS INC ELSEVIER SCIENCE
DOI: 10.1016/j.jcp.2013.11.020
Keywords
Exponential Runge-Kutta methods; Stiff equations; Boltzmann equation; Fluid limits; Asymptotic-preserving schemes; Strong stability preserving schemes
Funding
- Research Project of National Interest (PRIN) Advanced numerical methods for kinetic equations and balance laws with source terms
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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. (C) 2013 Elsevier Inc. All rights reserved.
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