Multidimensional mixed–hybrid finite element method for compositional two-phase flow in heterogeneous porous media and its parallel implementation on GPU

• Published in: Computer physics communications 2019-05, Vol.238, p.165-180
• Main Authors: Fučík, Radek, Klinkovský, Jakub, Solovský, Jakub, Oberhuber, Tomáš, Mikyška, Jiří
• Format: Article
• Language: English
• Subjects: 47.11.fg; 47.56.+r; Mixed–hybrid finite element method; Parallel implementation on GPU
• ISSN: 0010-4655; 1879-2944
• DOI: 10.1016/j.cpc.2018.12.004

A general multidimensional numerical scheme, primarily designed to simulate two-phase compositional flow in porous media, is presented with serial and parallel implementations suitable for solving problems with degenerate (capillary) diffusion or capillary barrier effect in heterogeneous porous materials. The numerical scheme is based on the mixed–hybrid finite element method with the semi-implicitapproach for the time discretization in order to obtain a system of linear equations in each time step. The scheme is implemented in serial for CPU and in parallel for CPU and GPU using TNL that provides an efficient abstraction layer for accessing various parallel hardware architectures. In order to demonstrate the applicability of the numerical scheme, a numerical analysis is presented for problems of two-phase flow in 1D, 2D, and 3D for which exact (semi-analytical) solutions are known and a series of benchmark problems for two-phase flow in heterogeneous porous media is discussed to show correct simulation of the capillary barrier effect. The efficiency and accuracy of the implementations on CPU and GPU are discussed. Moreover, we construct an analytical solution and use it to demonstrate convergence of the numerical scheme for two-phase compositional flow problems in porous media.