|Abstract:|| This paper presents an algebraic dynamic multilevel method with local time-stepping (ADM-LTS) for transport equations of sequentially coupled flow in heterogeneous porous media. The method employs an adaptive multilevel space-time grid determined on the basis of two error estimators, one in time and one in space.
More precisely, at each time step, first a coarse time step on a coarsest space-grid resolution is taken. Then, based on the error estimators, the transport equation is solved by taking different time step sizes at different spatial resolutions within the computational domain.
In this way, the method is able to use a fine grid resolution, both in space and in time, only at the moving saturation fronts.
In order to ensure local mass conservation, two procedures are developed. First, finite-volume restriction operators and constant prolongation (interpolation) operators are developed to map the system across different space-grid resolutions. Second, the fluxes at the interfaces across two different time resolutions are approximated with an averaging scheme in time.
Several numerical experiments have been performed to analyze the efficiency and accuracy of the proposed ADM-LTS method for both homogeneous and heterogeneous permeability field. The results show that the method provides accurate solutions, at the same time it reduces the number of fine grid-cells both in space and in time. |