  Motivated by observations of saturation overshoot, this paper investigates
numerical modeling of two-phase flow incorporating dynamic capillary pressure.
The effects of the dynamic capillary coefficient, the infiltrating flux rate
and the initial and boundary values are systematically studied using a
travelling wave ansatz and efficient numerical methods. The travelling wave
solutions may exhibit monotonic, non-monotonic or plateau-shaped behaviour.
Special attention is paid to the non-monotonic profiles. The travelling wave
results are confirmed by numerically solving the partial differential equation
using an accurate adaptive moving mesh solver. Comparisons between the computed
solutions using the Brooks-Corey model and the laboratory measurements of
saturation overshoot verify the effectiveness of our approach.
