Novel fractional-step higher resolution hybrid cell-centred finite-volume formulations are presented for twophase and three component two-phase flow with gravity on structured and unstructured grids. We note that previous hybrid methods [1] are first order and presented for structured grids.

The Darcy-flux is approximated by a control-volume distributed multipoint flux approximation (CVD-MPFA) coupled with a higher resolution approximation for convective transport. The CVD-MPFA method is used for Darcy-flux approximations involving pressure and gravity flux operators, leading to a novel formulation for two-phase and three-component two-phase flow on unstructured grids.

Comparisons with both higher resolution and standard first order characteristic based upwind methods and classical phase upwinding is presented.

Results demonstrate the benefits of the new methods for a range of problems including channel flow and shale-barrier problems.

[1] S. Lee, Y. Efendiev, H. Tchelepi, Hybrid upwind discretization of nonlinear two phase flow with gravity, Advances in Water Resources 82 (2015) 27–38.


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