Can I read A Mixed Variational Formulation for the Wellposedness and Numerical Approximation of a PDE Model Arising in a 3-D Fluid-Structure Interation on EtoBox?

A Mixed Variational Formulation for the Wellposedness and Numerical Approximation of a PDE Model Arising in a 3-D Fluid-Structure Interation by Avalos, George; Clark, Thomas J. is a scholarly article available to read on EtoBox.

What is A Mixed Variational Formulation for the Wellposedness and Numerical Approximation of a PDE Model Arising in a 3-D Fluid-Structure Interation about?

We will present qualitative and numerical results on a partial differential equation (PDE) system which models a certain fluid-structure dynamics. The wellposedness of this PDE model is established by means of constructing for it a nonstandard semigroup generator representation; this representation is essentially accomplished by an appropriate elimination of the pressure. This coupled PDE model involves the Stokes system which evolves on a three dimensional domain $\mathcal{O}$ being coupled to a fourth order plate equation, possibly with rotational inertia parameter $\rho >0$, which evolves on a flat portion $\Omega$ of the boundary of $\mathcal{O}$. The coupling on $\Omega$ is implemented via the Dirichlet trace of the Stokes system fluid variable - and so the no-slip condition is necessarily not in play - and via the Dirichlet boundary trace of the pressure, which essentially acts as a forcing term on this elastic portion of the boundary. We note here that inasmuch as the Stokes fluid velocity does not vanish on $\Omega$, the pressure variable cannot be eliminated by the classic Leray projector; instead, the pressure is identified as the solution of a certain elliptic boundary v

Author

Avalos, George; Clark, Thomas J.

Published

2013

Language

EN