Abstract

Summary We introduce a new, efficient control volume finite element method that improves the modelling of multi-phase flow in heterogeneous porous media. The method uses discontinuous piecewise linear functions enriched with bubble functions for velocity and discontinuous piecewise linear functions for pressure evaluated on control volumes (CVs). LBB stability is maintained with a very efficient velocity:pressure degrees of freedom ratio of 1.25 on tetrahedral meshes. Classical CVFE methods on the other hand may reach a ratio of 5. The method does not require CVs to span element boundaries and as a result is able to accurately preserve saturation discontinuities across material boundaries. Finally, the use of control volume representation for pressure yields significant improvements in stability of the method on challenging meshes.

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