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Título:	An HDG formulation for incompressible and immiscible two-phase porous media flow problems
Autor/a:	Costa Solé, Albert; Ruiz Gironès, Eloi; Sarrate Ramos, Josep
Otros autores:	Universitat Politècnica de Catalunya. Doctorat en Enginyeria Civil; Universitat Politècnica de Catalunya. Departament d'Enginyeria Civil i Ambiental; Universitat Politècnica de Catalunya. LACÀN - Mètodes Numèrics en Ciències Aplicades i Enginyeria
Abstract:	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
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.
Abstract:	Peer Reviewed
Materia(s):	-Àrees temàtiques de la UPC::Matemàtiques i estadística::Matemàtica discreta::Teoria de grafs -Àrees temàtiques de la UPC::Matemàtiques i estadística::Anàlisi numèrica::Mètodes numèrics -Graph theory -Difference equations--Numerical solutions -Two-phase flow -Immiscible -Incompressible -Hybridisable discontinuous Galerkin method -Diagonally implicit Runge–Kutta method -Differential algebraic equations -Grafs, Teoria de -Equacions diferencials--solucions numèriques -Classificació AMS::05 Combinatorics::05C Graph theory -Classificació AMS::65 Numerical analysis::65L Ordinary differential equations
Derechos:	Attribution-NonCommercial-NoDerivs 3.0 Spain http://creativecommons.org/licenses/by-nc-nd/3.0/es/
Tipo de documento:	Artículo - Versión presentada Artículo
Editor:	Taylor & Francis
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