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

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 h...

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Vydáno v:International journal of computational fluid dynamics Ročník 33; číslo 4; s. 137 - 148
Hlavní autoři: Costa-Solé, A., Ruiz-Gironés, E., Sarrate, J.
Médium: Journal Article Publikace
Jazyk:angličtina
Vydáno: Taylor & Francis 21.04.2019
Témata:
05 Combinatorics
05C Graph theory
65 Numerical analysis
65L Ordinary differential equations
Anàlisi numèrica
Classificació AMS
Diagonally implicit Runge–Kutta method
Difference equations
Differential algebraic equations
Equacions diferencials
Grafs, Teoria de
Graph theory
Hybridisable discontinuous Galerkin method
Immiscible
Incompressible
Matemàtica discreta
Matemàtiques i estadística
Mètodes numèrics
Numerical solutions
solucions numèriques
Teoria de grafs
Two-phase flow
Àrees temàtiques de la UPC
ISSN:1061-8562, 1029-0257
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Popis
Shrnutí: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 -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 -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.
ISSN:1061-8562
1029-0257
DOI:10.1080/10618562.2019.1617855