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A numerical study of two-phase flow models with dynamic capillary pressure and hysteresis

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.