Volume 16, Issue 2 (10-2021)
IJMSI 2021, 16(2): 197-208 |
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Abstract:
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.
Keywords: Ideal compressible isentropic fluid, Lie-Poisson system, Semidirect product, Geometric integration, Coadjoint orbit.
Type of Study: Research paper |
Subject:
Special
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