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Arbitrary Lagrangian-Eulerian methods
Donea, J; Huerta, Antonio; Ponthot, J -Ph; Rodríguez Ferran, Antonio
Universitat Politècnica de Catalunya. Departament de Matemàtica Aplicada III; Universitat Politècnica de Catalunya. LACÀN - Centre Específic de Recerca de Mètodes Numèrics en Ciències Aplicades i Enginyeria
Aim of the present chapter is to provide an in-depth survey of arbitrary Lagrangian-Eulerian (ALE) methods, including both conceptual aspects of the mixed kinematical description and numerical implementation details. Applications are discussed in °uid dynamics, nonlinear solid mechanics and coupled problems describing fluid-structure interaction. The need for an adequate mesh update strategy is underlined and various automatic mesh displacement prescription algorithms are reviewed. This includes mesh regularization methods essentially based on geometrical concepts, as well as mesh adaptation techniques aiming at optimizing the computational mesh according to some error indicator. Emphasis is then placed on particular issues related to the modeling of compressible and incompressible flow and nonlinear solid mechanics problems. This includes the treatment of convective terms in the conservation equations for mass, momentum and energy, as well as a discussion of stress update procedures for materials with history-dependent constitutive behaviour.
Peer Reviewed
Àrees temàtiques de la UPC::Matemàtiques i estadística::Anàlisi numèrica
Lagrange equations--Numerical solutions
Numerical analysis
nonlinear solid mechanics
stress update procedures
fluid-structure interaction
ALE description
convective transport
finite elements
stabilization techniques
mesh regularization and adaptation
fluid dynamics
Lagrange, Equacions de
Euler, Equacions d'
John Wiley & Sons

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