Computing gravity-driven viscous fingering in complex subsurface geometries: A high-order discontinuous Galerkin approach

We present a formulation of the discontinuous Galerkin method aimed for simulations of gravity-driven viscous fingering instabilities occurring in porous media flow. Specifically, we are targeting applications characterized by complex geometrical features. Viscous fingering instabilities play a very important role in carbon sequestration in brine aquifers. The proposed method has the ability to preserve high order of accuracy on completely unstructured meshes, a feature that makes it ideal for high-fidelity computations of the challenging fingering flow patterns and very complex geometries of actual reservoirs and aquifers. An extensive set of numerical computations is also included, to confirm the stability, accuracy, and robustness of the method.