A framework for late-time/stiff relaxation asymptotics

Details A framework for late-time/stiff relaxation asymptotics A framework for late-time/stiff relaxation asymptotics

2011-05-07

arxiv.org/abs/1105.1415v2

Proc. " CFL condition - 80 years gone by'', Rio de Janeiro Aug. 2010, C.S. Kubrusly et al. (editors), Springer Proc. Math., 20

Mathematics

Analysis of PDEs

15 pages

Scientific paper

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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