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Computational Fluid Dynamics

Chi Yuan and C.C. Yen have been developing hydro-dynamic codes for the last two years using relaxation scheme and high order Godunov methods for Cartesian and polar coordinates. These codes were implemented to simulate a two-dimensional flow in an infinitesimally thin gaseous disk driven by a rotating bar. Special attention is given to obtain correct radiation boundary conditions near the center. The codes were applied to NGC5248 and the 3-kpc 2 arm problem of the Milky Way with satisfactory results (Yuan, Yen and Li 2002; Yen and Yuan 2002).

NGC5248 is a nearby grand-design galaxy with a bright nucleus, classified as SAB(rs)b. The spiral arms can be traced inward from 7 kpc almost all the way to the center, with double circumnuclear rings, which are suspected to power the nuclear activities. The numerical results have demonstrated that the excitation of both leading and trailing wave will prevent the density waves from going into the center and form a spiral-ring structure. The results of simulations differ from that of nonlinear asymptotic theory developed by Chi Yuan and C. C. Yang. This discrepancy is likely due to the uncertainty of the parameters in the numerical computation. Furthermore, it is necessary to investigate the effects of driving force and the rotation curve, both of which can affect results.

A nonlinear asymptotic theory of spiral density waves was developed by Yuan & Cheng 1991 and applied to the 3 kpc arm of Milky Way. They have confirmed the earlier suggestion of Yuan (1984) that either a minor oval distortion or an uneven distribution of mass in the center region can excite spiral waves which has the radial velocity and mass concentration in excellent agreement with the observations of the 3 kpc arm. However, the dynamical evolution of disk can not be achieved by the asymptotic theory. For that, numerical simulations must be employed. In this experiment, Yen and Yuan calculated two cases for the evolution of the Milky Way. The first case is that a pair of spiral waves generated by a rapidly rotating bar at the outer Lindblad resonance, which is located at r = 3.0 kpc. The second case is a one-arm spiral generated by an off-set bar, to mimic an uneven distribution of matter. The outer Lindblad resonance for the latter is also located near r=3.0 kpc.

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