An a posteriori-based, fully adaptive algorithm with adaptive stopping criteria and mesh refinement for thermal multiphasecompositional flows in porous media

Daniele Antonio Di Pietro (1) , Martin Vohralík (2) , Soleiman Yousef (3, 4)

1 I3M - Institut de Mathématiques et de Modélisation de Montpellier
2 POMDAPI - Environmental Modeling, Optimization and Programming Models
3 IFPEN - IFP Energies nouvelles
4 LJLL - Laboratoire Jacques-Louis Lions

We consider in this work thermal multiphase multicomponent flows in porous media. We derive fully computable a posteriori error estimates for the dual norm of the residual supplemented by a nonconformity evaluation term. The estimators are general and valid for a variety of discretization methods. We also show how to estimate separately the space, time, linearization, and algebraic errors giving the possibility to formulate adaptive stopping and balancing criteria. Moreover, a space--time adaptive mesh refinement algorithm based on the estimators is proposed. We consider the application of the theory to an implicit finite volume scheme with phase-upwind and two-point discretization of diffusive fluxes. Numerical results on an example of real-life thermal oil-recovery in a reservoir simulation illustrate the performance of the refinement strategy and in particular show that a significant gain in term of mesh cells can be achieved.

Mots clés: a posteriori error analysis; adaptive mesh refinement; compositional Darcy flow; thermal flow; finite volume method

Domaines: Analyse numérique [math.NA]

Daniele Antonio Di Pietro, Martin Vohralík, Soleiman Yousef. An a posteriori-based, fully adaptive algorithm with adaptive stopping criteria and mesh refinement for thermal multiphasecompositional flows in porous media. Computers & Mathematics with Applications, 2014, Volume 68 (Issue 12, Part B), pp.2331-2347. ⟨10.1016/j.camwa.2014.08.008⟩. ⟨hal-00856437v3⟩