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Vertex Approximate Gradient Scheme for Hybrid Dimensional Two-Phase Darcy Flows in Fractured Porous Media

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Academic year: 2021

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Figure 1: Example of a 2D domain Ω and 3 intersecting fractures Γ i , i = 1, 2, 3.
Figure 2: Degrees of freedom of the VAG scheme: cell unknowns v K , v L , fracture face unknown v σ , and node unknowns v s , v s 1 , v s 2 , v s 3 , v s 4
Figure 3: For VAG-1 (left) and VAG-2 (right), example of the choices of the control volumes at cells, fracture face, and nodes, in the case of two cells K and L splitted by one fracture face σ (the width of the fracture has been enlarged in this figure).
Figure 4: Inverses of the extended monotone graphs of the capillary pressures S 1 1 (in blue in subdomain Ω 1 and in the fault Γ f ) and S 2 1 (in red in subdomain Ω 2 )
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