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

Abstract : 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.
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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. Computer and mathematics with applications, Elsevier, 2014, Volume 68 (Issue 12, Part B), pp.2331-2347. ⟨10.1016/j.camwa.2014.08.008⟩. ⟨hal-00856437v3⟩

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