Stable Numerical Schemes for Fluids, Structures and their Interactions

This book presents numerical algorithms for solving incompressible fluids, elastic structures and fluid-structure interactions. It collects some of the fundamental finite element methods as well as new approaches. For Stokes and Navier-Stokes equations, the mixed finite element method is employed. An arbitrary Lagrangian Eulerian framework is used for fluids in a moving domain. Schemes for linear and St Venant-Kirchhoff non-linear dynamic elasticity are presented. For fluid-structure interaction, two schemes are analyzed: the first is fully implicit and the second is semi-implicit, where the fluid domain is computed explicitly and consequently the computational time is considerably reduced. The stability of the schemes is proven in this self-contained book. Every chapter is supplied with numerical tests for the reader. These are aimed at Masters students in Mathematics or Mechanical Engineering.

Presents a self-contained monograph of schemes for fluid and elastic structures, including their interactionsProvides a numerical analysis of schemes for Stokes and Navier-Stokes equationsCovers dynamic linear and non-linear elasticity and fluid-structure interaction

1. Mixed Finite Elements for Stokes Equations 2. Numerical Schemes for Navier-Stokes Equations 3. The ALE Method for Navier-Stokes Equations in a Moving Domain 4. Linear Elastodynamics 5. Nonlinear Elastodynamics 6. Numerical Schemes for the Fluid-Structure Interaction