A distributed Lagrange formulation of the Finite Element Immersed Boundary Method for fluids interacting with compressible solids
Incremental improvement to fluid-structure interaction methods for computational mechanics researchers.
The paper generalizes a previous fluid-solid coupling method using distributed Lagrange multipliers for cleaner variational formulation, with stability estimates and numerical validation.
We present a distributed Lagrange multiplier formulation of the Finite Element Immersed Boundary Method to couple incompressible fluids with compressible solids. This is a generalization of the formulation presented in Heltai and Costanzo (2012), that offers a cleaner variational formulation, thanks to the introduction of distributed Lagrange multipliers, that acts as intermediary between the fluid and solid equations, keeping the two formulation mostly separated. Stability estimates and a brief numerical validation are presented.