  Saturation overshoot and pressure overshoot are studied by incorporating
dynamic capillary pressure, capillary pressure hysteresis and hysteretic
dynamic coefficient with a traditional fractional flow equation in one
dimension. Using the method of lines, the discretizations are constructed by
applying Castillo-Grone's mimetic operators in the space direction and explicit
trapezoidal integrator in the time direction. Convergence tests and
conservation property of the schemes are presented. Computed profiles capture
both the saturation overshoot and pressure overshoot phenomena. Comparisons
between numerical results and experiments illustrate the effectiveness and
different features of the models.
