Adaptive local grid refinement to solve nonlinear transport problems with moving fronts

Highly nonlinear advection-dispersion-reactive equations govern numerous transport phenomena in subsurface media. Robust, accurate, and efficient algorithms to solve these equations hold the key to the success of applying numerical models to field problems. This paper presents the development and verification of a computational algorithm to approximate the highly nonlinear transport equations of multiphase flow and reactive chemical transport. The algorithm was developed based on the Lagrangian-Eulerian decoupling method with an adaptive ZOOMing and Peak/valley Capture (LEZOOMPC) scheme. It consisted of both backward and forward node tracking, rough element determination, peak/valley capturing, and adaptive local grid refinement. A second-order implicit tracking was implemented to accurately and efficiently track all fictitious particles. The unique feature of the algorithm is the adaptive mechanism. Unlike other adaptive local grid refinement methods, the adaptive mechanism of LEZOOMPC was based on the almost 'true' error estimates. The accuracy and efficiency of the algorithm were verified with the Burger's equation for a variety of cases. The robustness of the algorithm to achieve convergent solutions was demonstrated for highly nonlinear multiphase flow and reactive contaminant transport problems.