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CATEGORIES:Isaac Newton Institute Seminar Series
SUMMARY:A Numerical Scheme for the Quantum Boltzmann Equat
ion Efficient in the Fluid Regime - Filbert\, F (C
laude Bernard Lyon 1)
DTSTART;TZID=Europe/London:20101216T100000
DTEND;TZID=Europe/London:20101216T110000
UID:TALK28423AThttp://talks.cam.ac.uk
URL:http://talks.cam.ac.uk/talk/index/28423
DESCRIPTION:Numerically solving the Boltzmann kinetic equation
s with the small Knudsen number is challenging due
to the stiff nonlinear collision term. A class of
asymptotic preserving schemes was introduced in [
5] to handle this kind of problems. The idea is to
penalize the stiff collision term by a BGK type o
perator. This method\, however\, encounters its ow
n difficulty when applied to the quantum Boltzmann
equation. To define the quantum Maxwellian (Bose-
Einstein or Fermi-Dirac distribution) at each tim
e step and every mesh point\, one has to invert a
nonlinear equation that connects the macroscopic q
uantity fugacity with density and internal energy.
Setting a good initial guess for the iterative me
thod is troublesome in most cases because of the c
omplexity of the quantum functions (Bose-Einstein
or Fermi- Dirac function). In this paper\, we prop
ose to penalize the quantum collision term by a 'c
lassical' BGK operator instead of the quantum one.
This is based on the observation that the classic
al Maxwellian\, with the temperature replaced by t
he internal energy\, has the same first five momen
ts as the quantum Maxwellian. The scheme so design
ed avoids the aforementioned difficulty\, and one
can show that the density distribution is still dr
iven toward the quantum equilibrium. Numerical res
ults are present to illustrate the efficiency of t
he new scheme in both the hydrodynamic and kinetic
regimes. We also develop a spectral method for th
e quantum collision operator.
LOCATION:Seminar Room 1\, Newton Institute
CONTACT:Mustapha Amrani
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