A parallel mixed–hybrid finite element method for two phase flow problems in porous media using MPI
Jakub Solovský 
, Radek Fučík
Faculty of Nuclear Sciences and Physical Engineering, Czech Technical University in Prague, Trojanova 13, 120 00 Prague, Czech Republic.
DOI:
https://doi.org/10.7494/cmms.2017.2.0593
Abstract:
This paper deals with a numerical solution of two–phase flow problems in porous media. To solve this type of problems, we propose a numerical method based on mixed–hybrid finite element method. The method is briefly introduced for arbitrary dimension but only a 2D case is considered in this work. We implement several variations of this method using The accuracy and the computational efficiency of the method is verified using a problem with a known exact solution. Numerical experiments show that the errors are similar for all variations of the method. The method is convergent and the experimental order of convergence is slightly less than one. There are differences in the computational time in favor to the iterative solvers, especially when using finer meshes. For computations on fine meshes it is also advantageous to use the parallelism that significantly speeds-up the computation.different approaches to solve the resulting system of linear algebraic equations. Direct and iterative solvers are used and a parallel implementation of this method based on the domain decomposition method using MPI is described.
Cite as:
Solovský , J., Fučík, R. (2017). A parallel mixed–hybrid finite element method for two phase flow problems in porous media using MPI. Computer Methods in Materials Science, 17(2), 84 – 93. https://doi.org/10.7494/cmms.2017.2.0593
Article (PDF):
Keywords:
Mixed–Hybrid Finite Element Method, MPI, Parallel Implementation, Two Phase Flow in Porous Media
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