A shock-capturing finite-element technique for unsaturated-saturated flow and transport problems

A shock-capturing technique is introduced for a finite element approach of the governing balance equations of flow, contaminant mass and heat transport in variably saturated porous media. It represents a nonlinear method which depends itself on the numerical solution and is characterized by an additional discontinuity-capturing term controlling the derivatives in the direction of the solution gradient. The technique is embedded in a predictor-corrector scheme of first and second order in time to handle the solution implicitly. The impact of the shock-capturing technique is studied for selected applications.