en تخصصي Special پژوهشي Research paper In this paper we apply a geometric integrator to the problem of<br> Lie-Poisson system for ideal compressible isentropic fluids (ICIF)<br> numerically. Our work is based on the decomposition of the phase<br> space, as the semidirect product of two infinite dimensional Lie<br> groups. We have shown that the solution of (ICIF)&nbsp; stays in<br> coadjoint orbit and this result extends a similar result<br> for matrix group discussed in [6] (Hairer, et al). By using the coadjoint action of the Lie<br> group on the dual of its Lie algebra to advance the numerical flow,<br> we (as in Engo, et al. [2]) devise methods that automatically stay on the<br> coadjoint orbit. The paper concludes with a concrete example. Ideal compressible isentropic fluid, Lie-Poisson system, Semidirect product, Geometric integration, Coadjoint orbit. 197 208 http://ijmsi.ir/browse.php?a_code=A-10-3458-1&slc_lang=en&sid=1 E. Nobary e.nobari@mazust.ac.ir 10031947532846008566 10031947532846008566 Yes Department of Mathematics, University of Science and Technology of Mazandaran S. M. Hosseini hossei_m@modares.ac.ir 10031947532846008567 10031947532846008567 No Department of Mathematics, Tarbiat Modares University