From 3ad0db897d519d77f3c124db86a890b6a5638b4a Mon Sep 17 00:00:00 2001 From: =?UTF-8?q?Dennis=20Gl=C3=A4ser?= <dennis.glaeser@iws.uni-stuttgart.de> Date: Tue, 4 Apr 2023 21:34:06 +0000 Subject: [PATCH] [exercises][fractures][readme] rephrase issues with open fractures --- exercises/exercise-fractures/README.md | 4 ++-- 1 file changed, 2 insertions(+), 2 deletions(-) diff --git a/exercises/exercise-fractures/README.md b/exercises/exercise-fractures/README.md index e8a07c7e..bff1480d 100644 --- a/exercises/exercise-fractures/README.md +++ b/exercises/exercise-fractures/README.md @@ -165,7 +165,7 @@ BoundaryTypes interiorBoundaryTypes(const Element& element, const SubControlVolu } ``` -To summarize: when using Neumann-type interior boundary conditions, flux continuity conditions are evaluated on the two interfaces (the two sides of the fracture) between fracture and matrix ([see e.g. Martin et al. (2005)](https://link.springer.com/article/10.1007/s10596-012-9302-6)). Note that these interfaces geometrically coincide but allow for both different pressures and fluxes to prevail on the two sides of the fracture. When using Dirichlet-type interior boundary conditions, the pressure in the fracture is assumed to be invariant in normal direction of the fracture and is directly applied at the interfaces. While the fluxes still can be different on the two interfaces, the pressure is now the same. Thus, this is only valid for fractures that are highly permeable in normal direction (note that "open" fractures have infinite normal permeability). +To summarize: when using Neumann-type interior boundary conditions, flux continuity conditions are evaluated on the two interfaces (the two sides of the fracture) between fracture and matrix ([see e.g. Martin et al. (2005)](https://link.springer.com/article/10.1007/s10596-012-9302-6)). Note that these interfaces geometrically coincide but allow for both different pressures and fluxes to prevail on the two sides of the fracture. When using Dirichlet-type interior boundary conditions, the pressure in the fracture is assumed to be invariant in normal direction of the fracture and is directly applied at the interfaces. While the fluxes still can be different on the two interfaces, the pressure is now the same. Thus, this is only valid for fractures that are highly permeable in normal direction. This means we have to use Neumann-type interior boundary conditions here. Change this accordingly, compile and rerun the exercise again. You should now be able to see jumps in pressure in the matrix domain with an especially prominent one across the first vertical fracture (see image below). @@ -213,4 +213,4 @@ const auto fractureElement = couplingManager().getLowDimElement(element, scvf); const auto fractureElementMarker = fractureProblem.spatialParams().getElementDomainMarker(fractureElement); ``` -Note that this will not have a visible effect on the results, because the permeability chosen for the open fractures is very high, leading to identical results for the two approaches. However, as mentioned above, the use of interior Neumann-type boundary conditions involves the evaluation of flux continuity conditions at the interfaces between fracture and matrix on the basis of the fracture normal permeability. Here, we are defining scalar permeabilities on the fracture with the result that the normal and tangential permeabilities are the same (if you want them to be different, you have to define tensorial permeabilities). The high value for the "open" fractures leads to neglectable pressure jumps and seems to produce the right results. But, keep in mind that from a physical perspective we are using the wrong value as "open" fractures have infinite normal permeability. Using Dirichlet-type interior boundary conditions at the interfaces to "open" fractures is clearly the better choice. +Note that this will not have a visible effect on the results, because the permeability chosen for the open fractures is very high, leading to identical results for the two approaches. However, as mentioned above, the use of interior Neumann-type boundary conditions involves the evaluation of flux continuity conditions at the interfaces between fracture and matrix on the basis of the fracture normal permeability. Here, we are defining scalar permeabilities on the fracture with the result that the normal and tangential permeabilities are the same (if you want them to be different, you have to define tensorial permeabilities). The high value for the "open" fractures leads to neglectable pressure jumps and seems to produce the right results. But, keep in mind that from a physical perspective it makes little sense to define a permeability for an "open" fracture. Using Dirichlet-type interior boundary conditions at the interfaces to "open" fractures is clearly the better choice. -- GitLab