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.

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

• Presents a self-contained monograph of schemes for fluid and elastic structures, including their interactions
• Provides a numerical analysis of schemes for Stokes and Navier-Stokes equations
• Covers dynamic linear and non-linear elasticity and fluid-structure interaction