A high-order asymptotic-preserving scheme for kinetic equations using projective integration
| Autor: | Giovanni Samaey, Annelies Lejon, Pauline Lafitte |
|---|---|
| Přispěvatelé: | Mathématiques et Informatique pour la Complexité et les Systèmes (MICS), CentraleSupélec, Fédération de Mathématiques de l'Ecole Centrale Paris (FR3487), Ecole Centrale Paris-CentraleSupélec-Centre National de la Recherche Scientifique (CNRS), Department of Computer Science (KU Leuven - CS), Catholic University of Leuven - Katholieke Universiteit Leuven (KU Leuven), Centre National de la Recherche Scientifique (CNRS)-Ecole Centrale Paris-CentraleSupélec |
| Jazyk: | angličtina |
| Rok vydání: | 2014 |
| Předmět: |
Numerical Analysis
Applied Mathematics Mathematical analysis Relaxation (iterative method) 010103 numerical & computational mathematics Numerical Analysis (math.NA) 01 natural sciences Stability (probability) Projective Integration Kinetic equations 010101 applied mathematics Computational Mathematics symbols.namesake Consistency (statistics) Simple (abstract algebra) Time derivative Euler's formula symbols FOS: Mathematics [MATH.MATH-AP]Mathematics [math]/Analysis of PDEs [math.AP] Order (group theory) Mathematics - Numerical Analysis 0101 mathematics Scaling Mathematics |
| Zdroj: | SIAM Journal on Numerical Analysis SIAM Journal on Numerical Analysis, Society for Industrial and Applied Mathematics, 2016, 54 (1), pp.1-33. ⟨10.1137/140966708⟩ |
| ISSN: | 0036-1429 |
| DOI: | 10.1137/140966708⟩ |
| Popis: | We investigate a high-order, fully explicit, asymptotic-preserving scheme for a kinetic equation with linear relaxation, both in the hydrodynamic and diffusive scalings in which a hyperbolic, resp. parabolic, limiting equation exists. The scheme first takes a few small (inner) steps with a simple, explicit method (such as direct forward Euler) to damp out the stiff components of the solution and estimate the time derivative of the slow components. These estimated time derivatives are then used in an (outer) Runge-Kutta method of arbitrary order. We show that, with an appropriate choice of inner step size, the time-step restriction on the outer time step is similar to the stability condition for the limiting macroscopic equation. Moreover, the number of inner time steps is also independent of the scaling parameter. We analyse stability and consistency, and illustrate with numerical results. 32 pages, 8 figures |
| Databáze: | OpenAIRE |
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