Add adaptive mesh refinement based on solution variables

[ktbolt]

Problem

The svMulltiPhysics solver currently implements remeshing operations for the fluid mesh in FSI simulations. The solver monitors element Jacobians as the measure of element distortion and performs an on-the-fly remeshing if the Jacobian <= 0.

There is currently no support for adaptive mesh refinement based on solution variables (e.g., pressure, velocity).

Solution

Implement adaptive mesh refinement based on solution variables.

Additional context

The SimVascular application did support adaptive mesh refinement base on the svSolver simulation results (e.g., ybar).

Code of Conduct

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[alisonmarsden]

I think this should be two different issues, as they serve somewhat different purposes:

1. adaptive meshing based on CFD simulation results. The procedure here is 1) run steady (or short unsteady) CFD simulation, 2) compute hessian (ybar), 3) adapt mesh according to areas of high gradients, 4) repeat 2-3x, 5) use this adapted mesh to run final unsteady CFD simulation. This is all done in advance of running a simulation, not "on line" with the simulation. We used to do this very frequently in the Taylor lab using adaptive meshing features in meshsim, but I suspect other meshers (tetgen / netgen) have similar capabilities.

2. "on the fly" rememshing for FSI simulations. This is needed when the mesh deformation during an FSI simulation is large and results in poor quality meshes, as measured by the Jacobian. This is needed for valve FSI and for ventricular contraction when mesh motion is large. This is done "on line" during the simulation. Vijay implemented this and it has been used some, but not too extensively.

They are related but I think two different capabilities - one is "off line" the other is "on line."

[ktbolt]

@alisonmarsden The FSI remeshing seems to work for the tests I've run although the implementation could be improved.

I consider the CFD adaptive mesh refinement to be a dynamic process that modifies the mesh during a simulation, computing the Hessian at a user-set time increment, and remesh if needed. This method can of course be used just like the workflow you outlined in 1.

The old SimVascular performed CFD adaptive mesh refinement like 1. using the following steps

• running svSolver
• compute and write out ybar results
• convert svSolver results to VTK
• read in the VTK file into SimVascular Meshing Tool
• remesh using TetGen
• write out new svSolver files

We should implement mesh generator interface in svMultiPhysics so we can use TetGen and whatever else we want.

[alisonmarsden]

I agree that ideally we could have adaptive meshing that runs alongside a simulation. But as a step towards that ultimate goal I would like to first get back the functionality we had in the Taylor lab previously, namely to run adaptive meshing in advance of running the "production simulation" using the steps you outline above. Once we get that working again, we could extend it to the dynamic case you're referring to and make it more efficient. The steps you list above are what I remember doing as a postdoc in the Taylor lab (but we were using Meshsim). As far as I know, no one is currently able to do this because it either doesn't work or they don't know how. Not sure which it is. It was incredibly useful in reducing computational time by concentrating areas of high mesh resolution only where you need it (e.g. in small branches, etc).

[ktbolt]

@alisonmarsden OK, I will focus on getting this working in SimVascular; just need to have svMultiPhysics write out ybar to the VTK results files I guess.