Adaptive Discontinuous Galerkin Methods for Flow in Porous Media
We present an adaptive Discontinuous Galerkin discretization for the solution of porous media flow problems. The considered flows are immiscible and incompressible. The fully adaptive approach implemented allows for refinement and coarsening in both the element size, the polynomial degree and the time step size.
Birane Kane would like to thank the German Research Foundation (DFG) for financial support of the project within the Cluster of Excellence in Simulation Technology (EXC 310/1) at the University of Stuttgart. Robert Klöfkorn acknowledges the Research Council of Norway and the industry partners; ConocoPhillips Skandinavia AS, Aker BP ASA, Eni Norge AS, Maersk Oil Norway AS, DONG Energy A/S, Denmark, Statoil Petroleum AS, ENGIE E&P NORGE AS, Lundin Norway AS, Halliburton AS, Schlumberger Norge AS, Wintershall Norge AS, DEA Norge AS of The National IOR Centre of Norway for support. The authors would like to thank the reviewers for helpful comments to improve this work.
- 5.B. Kane, Using dune-fem for adaptive higher order discontinuous galerkin methods for strongly heterogenous two-phase flow in porous media. Arch. Numer. Softw. 5:1 (2017).Google Scholar
- 11.M. Wolff, Y. Cao, B. Flemisch, R. Helmig, B. Wohlmuth, Multi-point flux approximation l-method in 3d: numerical convergence and application to two-phase flow through porous media, in Simulation of Flow in Porous Media: Applications in Energy and Environment. Radon Series on Computational and Applied Mathematics, vol. 12 (De Gruyter, Berlin, 2013), pp. 39–80Google Scholar