On 16/06/17 01:19, Matthew Knepley wrote:
The way dual porosity is normally implemented in a finite volume context is to add an extra matrix rock cell 'inside' each of the original cells (which now represent the fractures, and have their volumes reduced accordingly), with a connection between the fracture cell and its corresponding matrix rock cell, so fluid can flow between them.Thanks for those ideas, very helpful. If I try this approach (forming whole Jacobian matrix and using PCFieldSplit Schur), I guess I will first need to set up a modified DMPlex for the whole fracture + matrix mesh- so I can use it to create vectors and the Jacobian matrix (with the right sparsity pattern), and also to work out the coloring for finite differencing. Would that be straight-forward to do? Currently my DM just comes from DMPlexCreateFromFile(). Presumably you can use DMPlexInsertCone() or similar to add points into it?You can certainly modify the mesh. I need to get a better idea what kind of modification, and then I can suggest a way to do it. What do you start with, and what exactly do you want to add?
More generally there can be multiple matrix rock cells for each fracture cell, in which case further matrix rock cells are nested inside the first one, again with connections between them. There are formulae for computing the appropriate effective matrix rock cell volumes and connection areas, typically based on a 'fracture spacing' parameter which determines how fractured the rock is.
So in a DMPlex context it would mean somehow adding extra DAG points representing the internal cells and faces for each of the original cells. I'm not sure how that would be done.
Another approach, which might be easier, would be not to construct a DM for the whole dual-porosity mesh, but create the Jacobian matrix as a MatNest, with the fracture cell part created using DMCreateMatrix() as now, with the original DM, and the other parts of the Jacobian (representing fracture-matrix and matrix-matrix interactions) created 'by hand'- because of the local one-dimensional nature of the matrix rock cell parts of the mesh, these would be just a bunch of block diagonal matrices anyway.
I've just been looking at SNES example ex70.c where something a bit like this is done.
I think once the Jacobian matrix is created, you can create a coloring for finite differencing on it just from the matrix itself, and don't actually need a corresponding DM. So this approach might work, without needing to construct a dual-porosity DM.
- Adrian -- Dr Adrian Croucher Senior Research Fellow Department of Engineering Science University of Auckland, New Zealand email: a.crouc...@auckland.ac.nz tel: +64 (
