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.