The test calculations show that ionizing shock waves evolving in partially ionized gases may produce, due to the finite-rate ionization and recombination processes present, temperature and density discontinuities that are substantially different from those of conventional shock waves.In the case of cylindrical shocks evolving around particle sources, the expanding shock wave may be stopped and reflected because of the interaction of the fully ionized peripheral layer with the magnetic field, in full agreement with observations pertaining to pellet plasmas and barium cloud release experiments in the magnetosphere.The computed ionization and confinement radii, the shape and size of the two-dimensional wakes enveloping moving pellets are in agreement with experimental observations in toroidal confinement machines.The tests show that more complex scenarios such as the counter-parallel injection of two 'gazing pellets' can also be analysed with the help of the computational model described. The work presented represents a first attempt to treat pellet ablation phenomena, with full account for the neutral gas component present, in a multi-dimensional approach.