Linearized hydro-elasticity: A numerical study
| Autor: | Daniel Toundykov, Lorena Bociu, Steven Derochers |
|---|---|
| Rok vydání: | 2016 |
| Předmět: |
Control and Optimization
Discretization Applied Mathematics 010102 general mathematics Mathematical analysis Stokes flow Curvature 01 natural sciences Finite element method 010101 applied mathematics Linearization Modeling and Simulation Stability theory Shape optimization 0101 mathematics Elasticity (economics) Mathematics |
| Zdroj: | Evolution Equations and Control Theory. 5:533-559 |
| ISSN: | 2163-2480 |
| Popis: | In view of control and stability theory, a recently obtained linearization around a steady state of a fluid-structure interaction is considered. The linearization was performed with respect to an external forcing term and was derived in an earlier paper via shape optimization techniques. In contrast to other approaches, like transporting to a fixed reference configuration, or using transpiration techniques, the shape optimization route is most suited to incorporating the geometry of the problem into the analysis. This refined description brings up new terms---missing in the classical coupling of linear Stokes flow and linear elasticity---in the matching of the normal stresses and the velocities on the interface. Later, it was demonstrated that this linear PDE system generates a $C_0$ semigroup, however, unlike in the standard Stokes-elasticity coupling, the wellposedness result depended on the fluid's viscosity and the new boundary terms which, among other things, involve the curvature of the interface. Here, we implement a finite element scheme for approximating solutions of this fluid-elasticity dynamics and numerically investigate the dependence of the discretized model on the ``new" terms present therein, in contrast with the classical Stokes-linear elasticity system. |
| Databáze: | OpenAIRE |
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