HP adaptive DG scheme for twophase flow problem

(notebook) (script)

Section author: Andreas Dedner <a.s.dedner@warwick.ac.uk>, Birane Kane <birane.kane@ians.uni-stuttgart.de>, Robert Klöfkorn <robert dot klofkorn at math dot lu dot se>, Martin Nolte <nolte.mrtn@gmail.com>

We solve a two phase flow model using an hp adaptive higher order discontinuous Galerkin scheme [DKKN18].

This examples presents a framework for solving two-phase flow problems in porous media. The discretization is based on a Discontinuous Galerkin method and includes local grid adaptivity and local choice of polynomial degree. The method is implemented using the Python frontend described here. The example contains a number of time stepping approaches ranging from a classical IMPES method to a fully coupled implicit scheme. The implementation of the discretization is very flexible allowing to test different formulations of the two-phase flow model and adaptation strategies. For further details we refer to [DKKN18].