We performed 2D magnetohydrodynamical numerical experiments to study the response of the coronal magnetic configuration to the newly emerging magnetic flux. The configuration includes an electric current-carrying flux rope modeling the prominence floating in the corona, and the background magnetic field produced by two separated magnetic dipoles embedded in the photosphere. Parameters for one dipole are fixed in space and time to model the quiet background, and those for another one are time-dependent to model the new flux. These numerical experiments duplicate important results of the analytic solution, but also reveal new results. Unlike previous works, the configuration here possesses no symmetry, and the flux rope could move in any direction. The non-force-free environment causes the deviation of the flux rope equilibrium in the experiments from that determined in the analytic solution. As the flux rope radius decreases, the equilibrium could be found, and evolves quasi-statically until the flux rope reaches the critical location at which the catastrophe occurs. As the radius increases, no equilibrium exists at all. During the catastrophe, two current sheets (CS1 and CS2) form in different ways. CS1 forms as the surrounding closed magnetic field is stretched by the catastrophe, and CS2 forms as the flux rope squeezes the magnetic field nearby. Although reconnection happens in both the current sheets, CS1 is quickly erased by reconnection, and CS2 is enhanced by reconnection in CS1. These results reveal the impact of the asymmetry on the system evolution, and the implication for understanding related observations of solar eruptions.
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