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 interactions
- Provides a numerical analysis of schemes for Stokes and Navier-Stokes equations
- Covers dynamic linear and non-linear elasticity and fluid-structure interaction
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- Mixed Finite Elements for Stokes Equations
- Numerical Schemes for Navier-Stokes Equations
- The ALE Method for Navier-Stokes Equations in a Moving Domain
- Linear Elastodynamics
- Nonlinear Elastodynamics
- Numerical Schemes for the Fluid-Structure Interaction
Cornel Marius Murea is a lecturer at the University of Haute Alsace, France. His research area includes numerical analysis and scientific computing of fluid-structure interaction problems.