Robin BCs for mesh motion equation

[Tanmay Shidhore]

In svFSI, can a Robin BC be imposed on the mesh motion equation? My impression is that imposing a traction BC would mean that the simplification from Johnson et al. (doi: 10.1016/0045-7825(94)00077-8) about using a single parameter (lambda/mu) would not be valid. Does that mean that to impose a Robin BC, I would also have to specify the Young's modulus in the input file? Thank you.

[Vijay Vedula]

For FSI simulations, solving the mesh equation involves solving a weighted Laplace equation in the fluid domain. While the interface is implicitly treated using Dirichlet boundary conditions, in principle, you can apply any boundary condition at the caps of the fluid domain. It is, however, unconventional to apply Robin BC at the caps for the mesh equation.

In the absence of any traction (or Robin BC), the equation only depends on the Poisson ratio (or the parameter lambda/mu as noted in the paper you referred to). In svFSI, Young's modulus for the mesh equation is set to 1 and you cannot specify the value as it will be overwritten. Instead, you could scale the Robin BC parameters with the shear modulus (mu) to get the same effect.

[Tanmay Shidhore]

Got it! Thanks, Vijay.