Abstract
We consider solutions to nonlinear hyperbolic systems of balance laws with stiff relaxation and formally derive a parabolic-type effective system describing the late-time asymptotics of these solutions. We show that many examples from continuous physics fall into our framework, including the Euler equations with (possibly nonlinear) friction. We then turn our attention to the discretization of these stiff problems and introduce a new finite volume scheme which preserves the late-time asymptotic regime. Importantly, our scheme requires only the classical CFL (Courant–Friedrichs–Lewy) condition associated with the hyperbolic system under consideration, rather than the more restrictive, parabolic-type stability condition.
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Acknowledgements
The author was partially supported by the Agence Nationale de la Recherche (ANR) through the grant 06-2-134423, and by the Centre National de la Recherche Scientifique (CNRS).
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LeFloch, P.G. (2013). A Framework for Late-Time/Stiff Relaxation Asymptotics. In: de Moura, C., Kubrusly, C. (eds) The Courant–Friedrichs–Lewy (CFL) Condition. Birkhäuser, Boston. https://doi.org/10.1007/978-0-8176-8394-8_8
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DOI: https://doi.org/10.1007/978-0-8176-8394-8_8
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