Journal
SIAM JOURNAL ON NUMERICAL ANALYSIS
Volume 55, Issue 4, Pages 2085-2109Publisher
SIAM PUBLICATIONS
DOI: 10.1137/M1111449
Keywords
IMEX Runge-Kutta methods; hyperbolic conservation laws with sources; diffusion equations; hydrodynamic limits; stiff systems; asymptotic-preserving schemes
Categories
Funding
- Numerical Methods for Uncertainty Qualification in Hyperbolic and Kinetic Equations of the group GNCS of INdAM
- ITN-ETN Marie-Curie Horizon program ModCompShock, Modeling and Computation of Shocks and Interface [642768]
- INDAM-GNCS research grant Numerical Methods for Hyperbolic and Kinetic Equation and Applications
- Marie Curie Actions (MSCA) [642768] Funding Source: Marie Curie Actions (MSCA)
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In this paper we consider the development of Implicit-Explicit (IMEX) Runge-Kutta schemes for hyperbolic systems with multiscale relaxation. In such systems the scaling depends on an additional parameter which modifies the nature of the asymptotic behavior, which can be either hyperbolic or parabolic. Because of the multiple scalings, standard IMEX Runge-Kutta methods for hyperbolic systems with relaxation lose their efficiency, and a different approach should be adopted to guarantee asymptotic preservation in stiff regimes. We show that the proposed approach is capable of capturing the correct asymptotic limit of the system independently of the scaling used. Several numerical examples con firm our theoretical analysis.
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