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CATEGORIES:Isaac Newton Institute Seminar Series
SUMMARY:On the time discretization of kinetic equations in
stiff regimes - Pareschi\, L (Ferrara)
DTSTART;TZID=Europe/London:20100910T100000
DTEND;TZID=Europe/London:20100910T110000
UID:TALK26075AThttp://talks.cam.ac.uk
URL:http://talks.cam.ac.uk/talk/index/26075
DESCRIPTION:We review some results concerning the time discret
ization of kinetic equations in stiff regimes and
their stability properties. Such properties are pa
rticularly important in applications involving sev
eral lenght scales like in the numerical treatment
of fluid-kinetic regions. We emphasize limitation
s presented by several standard schemes and focus
our attention on a class of exponential Runge-Kutt
a integration methods. Such methods are based on a
decomposition of the collision operator into an e
quilibrium and a non equilibrium part and are exac
t for relaxation operators of BGK type. For Boltzm
ann type kinetic equations they work uniformly for
a wide range of relaxation times and avoid the so
lution of nonlinear systems of equations even in s
tiff regimes. We give sufficient conditions in ord
er that such methods are unconditionally asymptoti
cally stable and asymptotic preserving. Such stabi
lity properties are essential to guarantee the cor
rect asymptotic behavior for small relaxation time
s. The methods also offer favorable properties suc
h as nonnegativity of the solution and entropy ine
quality. For this reason\, as we will show\, the m
ethods are suitable both for deterministic as well
as probabilistic numerical techniques.
LOCATION:Seminar Room 1\, Newton Institute
CONTACT:Mustapha Amrani
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