Discussion Forum

I’m trying to solve a 2D coupled biological problem where the concentration of diluted species inside a body sunk in water is calculated by a diffusion problem (to simplify). The most important part of the model is that the concentration of the diluted species determines the area of the body. To simplify, [Area = x*Concentration + Initial area]. This means that somehow the body swells when concentration increases.
The body is an “infinite” layer stuck to a fixed boundary (wall), so there is only one free side. The transient concentration is spatially heterogeneous in the two dimensions. Because the concentration is local the growth/swelling of the body is anisotropic.
1- First, I tried to compute the moving boundary by using the mesh velocity tool (in Mathematics > Deformed mesh > Deformed geometry). I set the mesh velocity equal to the change in concentrations. I could obtain nice results but I think that this command only computes the deformation from the concentration measured in the boundary (interface body-water). I’m not sure about this. Maybe it accounts for the local deformation of all the nodes but I don’t think so.
2- Second and instead of following the steps in 1, I divided all the body in many smaller domains. I used surface integration (in Derived values) to estimate the mass in each sub-domain and I repeated the steps in 1 using these values. To capture the whole heterogeneity it is necessary to create sub-domains as small as the mesh elements.
3- Finally, I recalculated the concentrations both in 1 and 2 solving the conservative form of the transport equation by setting the convection term equal to mesh velocity.
Results using 1-3 and 2-3 are completely different. I don’t know which approach is best. Maybe any of them. Any advice is welcome. Thanks