High-Order Hybridizable Discontinuous Galerkin Formulation for One-Phase Flow Through Porous Media

We present a stable high-order hybridizable discontinuous Galerkin (HDG) formulation coupled with diagonal implicit Runge–Kuta (DIRK) schemes to simulate slightly compressible one-phase flow through porous media. The HDG stability depends on the selection of single parameter and its definition is crucial ensure achieve properties method. Thus, we extend work Nguyen et al. in J Comput Phys 228, 8841–8855, 2009 deduce an analytical expression for stabilization using material parameters problem Engquist-Osher monotone flux scheme. accurate pressure, velocity same convergence rate P+1, being P polynomial degree approximation. This important because methods have potential reduce computational cost while obtaining more solutions less dissipation dispersion errors than low order methods. can use unstructured meshes capture heterogeneous reservoir. In addition, it conservative at element level, which when solving PDE’s form. Moreover, hybridization procedure be applied size global linear system. To keep these advantages, DIRK perform time integration. are memory footprint. show numerical evidence optimal rates obtained proposed formulation. Finally, several examples illustrate capabilities