Solving density driven flow problems with efficient spatial discretizations and higher-order time integration methods

An implicit numerical model for multicomponent compressible two-phase flow in porous media

“…(13) and Eq. (17) 2) If the element K is in two-phase and K′ is in single phase then the derivative of the phase in K′ is set to one and the derivative of the absent phase is set to zero.…”

“…The total flux is calculated by the hybridized mixed finite element method (MFE). The latter provides accurate calculation of the velocity field even in highly heterogeneous media when compared to the traditional finite element and finite volume methods [1,5,7,13,14,15,16,17,18,19,20]. The strength of the MFE method is from the calculation of the pressure inside a finite element and the traces of the pressures at the interfaces of each finite element in the computational domain.…”

Modelling variable density flow problems in heterogeneous porous media using the method of lines and advanced spatial discretization methods

“…As in [3,36], the Mixed Finite Element (MFE) method is used for the flow equation since it is locally conservative and produces accurate and consistent velocity field even for highly heterogeneous domains [10]. For the transport equation, the Discontinuous Galerkin (DG) method is used to discretize the advection equation and combined with the Multi-Point Flux Approximation (MPFA) method for the discretization of the dispersion equation [35].…”

Hydraulic and transport parameter assessment using column infiltration experiments

“…A uniform mesh of 600 cells is employed. Temporal discretization is performed with the highorder method of lines (MOL) (e.g., Miller et al, 1998;Tocci et al, 1997;Younes et al, 2009;Fahs et al, 2011). Error checking, robustness, order selection and adaptive time step features, available in sophisticated solvers, are applied to the time integration of partial differential equations (Tocci et al, 1997).…”