In this report, I will present two types of numerical simulations which are relevant to high resolution observations of the nearby galaxies, either optical or radio. The first type is the simulation of a rapidly rotating bar driving spiral density waves at both the outer Lindblad resonance (OLR) and the inner Lindblad resonance (ILR) simultaneously. We will show it leads to the observed starburst ring outside (at OLR) and the formation of the dense circumnuclear molecular disks near the center (at ILR). The latter has been seen by the recent SMA observations. The second type is the simulation of a slowly rotating, but strong bar of the size of a major bar seen in the major-bar galaxies, such as NGC1300 and NGC1097. In this study, we will show that many of the detailed features revealed in the recent observations can be reproduced by such a bar at the ILR. A strong bar, however, has always been a challenge to the numerical simulation community, because the high amplitude of the perturbation often leads to chaos and numerical instabilities. The Antares codes we have developed, prove to be an effective tool for such problems. We will report the results of our high resolution simulations and show that, with a sufficient strong bar potential, the straight dust lanes and a central star formation spiral-ring, similar to those seen in NGC1300 and NGC1097, can be generated in the process and remain stable for sufficiently long time.