Parallel algorithms for compressible fluid flows in the subsurface

Parallel algorithms for the numerical simulation of compressible fluid flows in the subsurface are presented. From a general velocity-pressure mixed model, dual macro-hybrid variational formulations are developed on the basis of nonoverlapping domain decompositions. Then, multidomain mixed finite element approximations are introduced as semidiscrete variational models, defined on independent subdomain meshes and compatible interface meshes, and numerical time integration schemes are applied for fully discrete versions. Specifically the implicit time marching scheme of Euler and the semi-implicit scheme of Peaceman-Rachford are considered, which can be implemented in parallel via resolvent or proximation characterizations, generalizing Uzawa and augmented Lagrangian numerical procedures.