Modeling variable-density flow in saturated-unsaturated porous media: An advanced numerical model

•An advanced model is developed for variable density flow in unsaturated media.•Sophisticated methods for spatial and temporal discretizations are combined.•Performance of the new model are shown against standard strategies in COMSOL.•SWI under climate change stresses is simulated in an unconfined aquifer in Lebanon.•Due to its robustness, the model is suitable for sustainable resources management.