[PDF][PDF] A posteriori error estimates with application of adaptive mesh refinement for thermal multiphase compositional flows in porous media
Computers and Mathematics with Applications, 2013•hal.science
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 …
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 …
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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