Pressure-related algorithm for fluid structure interaction

Coupling fluid and structure equations is not a simple task, specially when the fluid is considered incompressible. A first problem is that the main variable is not the same at the interface for the fluid and the structure. The main fluid variable is its velocity while the main structure variable is its position. Moreover the coupling is essentially done by equalizing the dual stress variable, which is essentially the pressure which acts as a Lagrange multiplier for the incompressible fluid equation. Both side of the interface are evolving with different and incompatible laws so it is impossible to satisfy at the same time and all the time the equality of all the relevant quantities: position, velocity, acceleration and normal stress. This work is an improvement and in direct continuation of Jaubert & Moreau (1997) ([3]) with essentially the same notations. In this paper, we will try to use the fluid pressure indetermination and the fluid evolution algorithm to match the evolution of the interface.

@TechReport{Mor97b,
  author       = {Moreau, V.},
  title        = {Pressure-related algorithm for fluid structure interaction},
  institution  = {CRS4},
  month        = {july},
  year         = {1997},
  address      = {(changed to) Loc. Piscina Manna, Edificio 1 09050 Pula (CA)},
  type         = {Research note},
  keywords     = {ALE, NSE, Navier-Stokes, FSI},
  url          = {https://publications.crs4.it/pubdocs/1997/Mor97b},
}