Stable Numerical Schemes for Fluids, Structures and their Interactions

  • ID: 4226576
  • Book
  • 208 Pages
  • Elsevier Science and Technology
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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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  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
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Murea, Cornel Marius
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.
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