Dear deal.ii community I would like to solve a coupling problem, where fracture flow (1D interface flow, generating pressure p) and solid deformation (2D elasticity problem, generating displacement u) interact.
In my case, the matrix of this coupling problem can be expressed as [ K, C; C^T, H] where K and H are the stiffness matrices for the 2D solid and the 1D fracture flow, respectively. The matrix C is a coupling matrix. For the 2D solid deformation, I have used the FE_Q<2> as the finite element and distribute the variable u at each 2D node. For the 1D fracture flow, I would like to use the FE_Q<1> as the finite element and assign the degree of freedom (variable p) at points where the fracture and 2D grids intersect (see the attached figure). I have several questions about how to implement the 1D fracture flow in a 2D solid domain in deal.ii. 1. How do I discretize the 1D fracture flow? 2. If I use a FE_Q<1> for fracture flow, it seems like I should distribute u dofs and p dofs separately. In this way, how can I consider the coupling effect of the displacement u and pressure p? 3. How deal.ii deal with problems with different dimensional configurations (like 2D for solid deformation and 1D for fluid flow)? 4. Is there any example in the tutorial related to my problem? I will be grateful for any help you can provide. Sincerely, Chong Liu -- The deal.II project is located at http://www.dealii.org/ For mailing list/forum options, see https://groups.google.com/d/forum/dealii?hl=en --- You received this message because you are subscribed to the Google Groups "deal.II User Group" group. To unsubscribe from this group and stop receiving emails from it, send an email to [email protected]. To view this discussion on the web visit https://groups.google.com/d/msgid/dealii/CAKCBbH86VRzxZz%2BnoVQAone64Tqxz14VUTYekJ9hvBrOvqzPnw%40mail.gmail.com.
