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SUMMARY:Modelling and numerical approximation for the nonconservative bi-t
emperature MHD model
DTSTART;VALUE=DATE-TIME:20160615T101500Z
DTEND;VALUE=DATE-TIME:20160615T105000Z
DTSTAMP;VALUE=DATE-TIME:20191017T135949Z
UID:indico-contribution-2972@indico.math.cnrs.fr
DESCRIPTION:Speakers: Xavier Lhebrard (Centre Lasers Intenses et Applicati
ons)\nIn order to achieve inertial confinement fusion\, one has to improve
the knowledge of the laser-plasma interaction. There exists two main ways
of describing this phenomenon\, the microscopic (kinetic) approach and th
e macroscopic (hydrodynamic) approach. The kinetic approach is not competi
tive since it is too expensive in computational time. This is why we inves
tigate an intermediate model in thermal nonequilibrium\, which is between
the kinetic model and the hydrodynamic model.\n\nIn the first stage of the
confinement the magnetic field is negligible\, the relevant intermediate
model is than the nonconservative bitemperature Euler model. Recently in [
1]\, an entropic approximation of this system has been derived thanks to n
umerical schemes based on an underlying conservative kinetic model.\n\nHow
ever in the last stage of the confinement the target is penetrated by rela
tivistic electrons\, which induces a strongly variable magnetic field. Thi
s is why we want to deal with an intermediate model which takes into accou
nt the magnetic field.\n\nIn this work we propose to study a bitemperature
MHD model. This system consists in four conservation equations for mass\,
impulsion and magnetic field and two nonconservation equations\, that is
to say\, one for each energy. Physically\, the model describes the interac
tion of a mixture of one species of ions and one species of electrons in t
hermal nonequilibrium subjected to a transverse variable magnetic field.\n
\nA first result is to have been able to established the hydrodynamic mode
l from an underlying kinetic model. More precisely\, using an out of equil
ibrium Chapman-Enskop procedure\, the bitemperature MHD model is construct
ed from a BGK model coupled with Maxwell equations with full Lorentz force
\, which includes the magnetic field.\n\nFinally\, we approximate the weak
solutions of the bitemperature MHD model using a kinetic scheme\, based o
n the underlying kinetic model.\n\n\n\nReferences\n\n[1] D. Aregba-Driolle
t\, S. Brull\, J.Breil\, B. Dubroca and E. Estibal\, Modelling and numeric
al ap-\nproximation for the nonconservative bitemperature Euler model\, pr
eprint\, 2015.\n\nhttps://indico.math.cnrs.fr/event/939/contributions/2972
/
LOCATION: Salle de Réunion - Bâtiment M2
URL:https://indico.math.cnrs.fr/event/939/contributions/2972/
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