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Combining Face Based And Nodal Based Discretizations For Multiphase Darcy Flow Problems
- Publisher: European Association of Geoscientists & Engineers
- Source: Conference Proceedings, ECMOR XVI - 16th European Conference on the Mathematics of Oil Recovery, Sep 2018, Volume 2018, p.1 - 31
Abstract
A new methodology is introduced in this work to combine face based (Hybrid Finite Volume, HFV or Two Point Flux Approximation, TPFA) and nodal based (Vertex Approximate Gradient, VAG) discretizations on hybrid meshes in order to adapt the numerical scheme to the different types of cells and medium properties in different parts of the mesh. The stability and convergence of the combined VAG-HFV schemes is studied in the gradient scheme framework and is shown to hold on arbitrary partitions of the cells for the unstabilised version and on arbitrary partitions of the faces for the stabilised version. The framework preserves at the interface the discrete conservation properties of the VAG and HFV schemes with fluxes based on local to each cell transmissibility matrices. This discrete conservative form allows to naturally extend the VAG and HFV discretizations of two-phase Darcy flow models to the combined VAG-HFV schemes. Numerical results on different types of meshes show the accuracy and efficiency of the combined schemes which are compared to the stand alone VAG and HFV (or TPFA) discretizations.