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