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 flowin porous media. The solvers are based on discontinuous Galerkin spatial discretisationsand implicit temporal discretisation. By applying an optimal reordering algorithm, thecorresponding discrete system of (non)linear equations can be solved in one grid-block ata time. This way, we avoid assembly of a full (non)linear system. Our approach allowsus to handle large numbers of grid blocks with modest requirements on memory.