Fast Solvers for Flow in Porous Media Based on Discontinuous Galerkin Methods and Optimal Reordering

We present a family of efficient solvers for hyperbolic transport equations modelling flow in porous media. The solvers are based on discontinuous Galerkin spatial discretisations and implicit temporal discretisation. By applying an optimal reordering algorithm, the corresponding discrete system of (non)linear equations can be solved in one grid-block at a time. This way, we avoid assembly of a full (non)linear system. Our approach allows us to handle large numbers of grid blocks with modest requirements on memory.