An efficient discontinuous Galerkin method for advective transport in porous media

Fast computation of multiphase flow in porous media by implicit discontinuous Galerkin schemes with optimal ordering of elements

“…In the linear case (with f ðuÞ ¼ u, see [24]), this results in a reducible block-structured linear system Ax ¼ b. Furthermore, there exists a symmetric permutation P that maps the global coefficient matrix A to a lower block-triangular matrix L ¼ PAP T .…”

“…For instance, if one uses a two-point flux-approximation scheme for the pressure Eq. (2), a simple monotonicity argument on the pressure shows that the discrete velocity field is guaranteed to contain no cyclic dependencies, see [24]. More general schemes like mixed finite elements, multipoint flux-approximation schemes [1], or mimetic finite differences [5,6] may produce velocity fields or fluxes with cyclic dependencies.…”

“…In [24] we presented a family of efficient discontinuous Galerkin schemes for stationary linear transport, i.e., for the special case with f ðuÞ ¼ u and a ¼ 0. In the next section, we will extend these schemes to include (3).…”

The localized reduced basis multiscale method for two‐phase flows in porous media

“…Consistent with our discretization of the saturation and pressure equation we use the DG-discretization introduced in [39]…”

“…In the absence of gravitational forces, the discretized time-of-flight equation can be permuted to a lower block-triangular form-if the computational mesh is reordered according to the direction of the flow-and hence solved very efficiently in a per-element fashion by a simple backsubstitution method; see [39] for details.…”