An HDG formulation for incompressible and immiscible two-phase porous media flow problems

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hdl:2117/165655
Document typeArticle
Defense date2019-05-27
PublisherTaylor & Francis
Rights accessOpen Access
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Attribution-NonCommercial-NoDerivs 3.0 Spain
ProjectINTEGRACION DE NUEVAS METODOLOGIAS PARA LA PLANIFICACION Y ANALISIS MEDIOAMBIENTAL DE YACIMIENTOS PETROLIFEROS (MINECO-CTM2014-55014-C3-3-R)
SIMULACION IN VIVO DEL EFECTO DE LA HIPOXIA Y LA DOSIS DEL FARMACO EN EL CRECIMIENTO DEL GLIOBLASTOMA (AEI-PGC2018-097257-B-C33)
SIMULACION IN VIVO DEL EFECTO DE LA HIPOXIA Y LA DOSIS DEL FARMACO EN EL CRECIMIENTO DEL GLIOBLASTOMA (AEI-PGC2018-097257-B-C33)
Abstract
We develop a high-order hybridisable discontinuous Galerkin (HDG) formulation to solve the immiscible and incompressible two-phase flow problem in a heterogeneous porous media. The HDG method is locally conservative, has fewer degrees of freedom than other discontinuous Galerkin methods due to the hybridisation procedure, provides built-in stabilisation for arbitrary polynomial degrees and, if the error of the temporal discretisation is low enough, the pressure, the saturation and their fluxes converge with order P+1 in L2-norm, being P the polynomial degree. In addition, an element-wise post-process can be applied to obtain a convergence rate of P+2 in L2-norm for the scalar variables. All of these advantages make the HDG method suitable for solving multiphase flow trough porous media. We show numerical evidence of the convergences rates. Finally, to assess the capabilities of the proposed formulation, we apply it to several cases of water-flooding technique for oil recovery.
Description
This is an Accepted Manuscript of an article published by Taylor & Francis Group in International journal of computational fluid dynamics on 27/05/2019, available online at: https://tandfonline.com/doi/abs/10.1080/10618562.2019.1617855
CitationCosta, A.; Ruiz Gironès , E.; Sarrate, J. An HDG formulation for incompressible and immiscible two-phase porous media flow problems. "International journal of computational fluid dynamics", 27 Maig 2019, vol. 33, núm. 4, p. 137-148.
ISSN1061-8562
Publisher versionhttps://tandfonline.com/doi/abs/10.1080/10618562.2019.1617855
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