دوره 16، شماره 2 - ( 7-1400 )
جلد 16 شماره 2 صفحات 208-197 |
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Nobary E, Hosseini S M. A Geometric Numerical Integration of Lie-Poisson System for Ideal Compressible Isentropic Fluid. IJMSI 2021; 16 (2) :197-208
URL: http://ijmsi.ir/article-1-1313-fa.html
URL: http://ijmsi.ir/article-1-1313-fa.html
A Geometric Numerical Integration of Lie-Poisson System for Ideal Compressible Isentropic Fluid. مجله علوم ریاضی و انفورماتیک. 1400; 16 (2) :197-208
چکیده:
In this paper we apply a geometric integrator to the problem of
Lie-Poisson system for ideal compressible isentropic fluids (ICIF)
numerically. Our work is based on the decomposition of the phase
space, as the semidirect product of two infinite dimensional Lie
groups. We have shown that the solution of (ICIF) stays in
coadjoint orbit and this result extends a similar result
for matrix group discussed in [6] (Hairer, et al). By using the coadjoint action of the Lie
group on the dual of its Lie algebra to advance the numerical flow,
we (as in Engo, et al. [2]) devise methods that automatically stay on the
coadjoint orbit. The paper concludes with a concrete example.
Lie-Poisson system for ideal compressible isentropic fluids (ICIF)
numerically. Our work is based on the decomposition of the phase
space, as the semidirect product of two infinite dimensional Lie
groups. We have shown that the solution of (ICIF) stays in
coadjoint orbit and this result extends a similar result
for matrix group discussed in [6] (Hairer, et al). By using the coadjoint action of the Lie
group on the dual of its Lie algebra to advance the numerical flow,
we (as in Engo, et al. [2]) devise methods that automatically stay on the
coadjoint orbit. The paper concludes with a concrete example.
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