Nitsche's method combined with spacetime finite elements for ALE fluidstructure interaction problems
Journal article, 2004
We propose a weak method for handling the fluidstructure interface in finite element fluidstructure interaction based on Nitsche's method [Abh. Math. Univ. Hamburg 36 (1971) 9]. We assume transient incompressible Newtonian flow and, for the structure, undamped linear elasticity. For the time-discretization, we use the time-continuous (energy conserving) Galerkin method for the structure, and for the fluid we employ the time-discontinuous Galerkin method. This means that the velocity becomes piecewise constant on each timestep for the fluid, matching the time-derivative of the displacements in the solid which is also piecewise constant over a time step. We formulate the method and report some numerical examples using spacetime oriented elements for the fluid in order to mimic Lagrangian or ALE-type simulations.