  A recent third-order, essentially non-oscillatory central scheme to advance
the equations of single-fluid magnetohydrodynamics (MHD) in time has been
implemented into a new numerical code. This code operates on a 3-D Cartesian,
non-staggered grid, and is able to handle shock-like gradients without
producing spurious oscillations. To demonstrate the suitability of our code for
the simulation of coronal mass ejections (CMEs) and similar heliospheric
transients, we present selected results from test cases and perform studies of
the solar wind expansion during phases of minimum solar activity. We can
demonstrate convergence of the system into a stable Parker-like steady state
for both hydrodynamic and MHD winds. The model is subsequently applied to
expansion studies of CME-like plasma bubbles, and their evolution is monitored
until a stationary state similar to the initial one is achieved. In spite of
the model's (current) simplicity, we can confirm the CME's nearly self-similar
evolution close to the Sun, thus highlighting the importance of detailed
modelling especially at small heliospheric radii. Additionally, alternative
methods to implement boundary conditions at the coronal base, as well as
strategies to ensure a solenoidal magnetic field, are discussed and evaluated.
