The fixed-mesh ALE approach applied to solid mechanics and fluid-structure interaction problems

• Published in: International journal for numerical methods in engineering Vol. 81; no. 12; pp. 1529 - 1557
• Main Authors: Baiges, Joan, Codina, Ramon
• Format: Journal Article
• Language: English
• Published: Chichester, UK John Wiley & Sons, Ltd 19.03.2010; Wiley
• Subjects: ALE formulations; Boundaries; Computational fluid dynamics; Computational techniques; Discretization; Exact sciences and technology; fixed-mesh methods; Fluid dynamics; Fluid flow; Fluid-structure interaction; Fluids; Fundamental areas of phenomenology (including applications); General theory; immersed boundaries; Mathematical methods in physics; Mathematical models; Physics; Solid mechanics; Structural and continuum mechanics; Vibration, mechanical wave, dynamic stability (aeroelasticity, vibration control...); Solid mechanics; High strain; Euler Lagrange equation; Lagrangian; Vibration; Computational fluid dynamics; Fluid structure interaction; Advection; fixed-mesh methods; fluid-structure interaction; immersed boundaries; ALE formulations; Stretching
• ISSN: 0029-5981; 1097-0207
• DOI: 10.1002/nme.2740

In this paper we propose a method to solve Solid Mechanics and fluid–structure interaction problems using always a fixed background mesh for the spatial discretization. The main feature of the method is that it properly accounts for the advection of information as the domain boundary evolves. To achieve this, we use an Arbitrary Lagrangian–Eulerian (ALE) framework, the distinctive characteristic being that at each time step results are projected onto a fixed, background mesh. For solid mechanics problems subject to large strains, the fixed‐mesh (FM)‐ALE method avoids the element stretching found in fully Lagrangian approaches. For FSI problems, FM‐ALE allows for the use of a single background mesh to solve both the fluid and the structure. Copyright © 2009 John Wiley & Sons, Ltd.