... Eulerian framework by a {\it variational multi-scale} method, which allows to take into account the small-scale turbulence without explicitly model it. The multi-fluid problem has been solved through the convectively re-initialized level-set method to robustly deal with high density and viscosity ratio...

.... The level-set (LS) method and the extended finite element method (XFEM) are utilized to simulate flow of the CO₂ plume. The LS is employed to trace the plume front. A streamline upwind Petrov-Galerkin method is adopted to stabilize possible occurrence of spurious oscillations due to advection...