An HDG formulation for incompressible and immiscible two-phase porous media flow problems. Issue 4 (21st April 2019)

• Record Type: Journal Article
• Authors: Costa-Solé, A.; Ruiz-Gironés, E.; Sarrate, J.
• Is Part Of: International journal of computational fluid dynamics. Volume 33:Issue 4(2019)
• Page Start: 137
• Page End: 148
• Publication Date: 2019-04-21
• Subjects: Two-phase flow -- immiscible -- incompressible -- hybridisable discontinuous Galerkin method -- diagonally implicit Runge–Kutta method -- differential algebraic equations; Fluid dynamics -- Data processing -- Periodicals; 532.05
• DOI: 10.1080/10618562.2019.1617855
• Languages: English
• ISSNs: 1061-8562

Abstract

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 L 2 -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 L 2 -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.