A spherically symmetric adiabatic single-fluid model is outlined for simulating the nonlinear time-dependent response of the corona to solar events that are simulated by perturbations in the appropriate physical variables from their steady-state values at the coronal base. Several observed features of the coronal transient that occurred on June 10, 1973, are simulated by using a particular steady-state solar wind, a specific combination of density and temperature perturbations, and a particular time dependence of the perturbations. A different steady-state solar wind, a perturbation of shorter duration, and other perturbation combinations are also employed to simulate the same transient so that the effect of each quantity can be determined. It is found that the model cannot adequately simulate all the observational results for the investigated transient, that the steady-state solar wind is relatively unimportant in such numerical simulations, and that studies which attempt only to reproduce observed shock trajectories may lead to erroneous conclusions regarding the physics of the solar event that produced the transient.