Arbitrary Lagrangian Eulerian

Donea, J., 1992. Arbitrary Lagrangian-Eulerian finite element methods. In Belytschko, T. and Hughes, T. J. R. (eds), Computational Methods for Transient Analysis, Elsevier Science, Amsterdam. 

Figure 5.4 The finite element mesh configurations in the Arbitrary Lagrangian-Eulerian scheme...

Arbitrary-Lagrangian-Eulerian (ALE) codes dynamically position the mesh to optimize some feature of the solution. An ALE code has tremendous flexibility. It can treat part of the mesh in a Lagrangian fashion (mesh velocity equation to particle velocity), part of the mesh in an Eulerian fashion (mesh velocity equal to zero), and part in an intermediate fashion (arbitrary mesh velocity). All these techniques can be applied to different parts of the mesh at the same time as shown in Fig. 9.18. In particular, an element can be Lagrangian until the element distortion exceeds some criteria when the nodes are repositioned to minimize the distortion. 

G. Luttwak and R.L. Rabie, The Multimaterial Arbitrary Lagrangian-Eulerian Code MMALE and its Application to Some Problems of Penetration and Impact, LA-UR-2311, Los Alamos National Laboratory, Los Alamos, NM, 1985. 

J. Donea, Arbitrary Lagrangian-Eulerian Finite Element Methods, Computational Methods for Transient Analysis (edited by J.D. Achenbach), North-Holland, Amsterdam, 1983. 

Solve Eqs. (5) and (6) to obtain the velocity distribution in the flow field Vn+1 using the Arbitrary-Lagrangian-Eulerian (ALE) scheme (Kashiwa et al., 1994). 

The computational code used in solving the hydrodynamic equation is developed based on the CFDLIB, a finite-volume hydro-code using a common data structure and a common numerical method (Kashiwa et al., 1994). An explicit time-marching, cell-centered Implicit Continuous-fluid Eulerian (ICE) numerical technique is employed to solve the governing equations (Amsden and Harlow, 1968). The computation cycle is split to two distinct phases a Lagrangian phase and a remapping phase, in which the Arbitrary Lagrangian Eulerian (ALE) technique is applied to support the arbitrary mesh motion with fluid flow. 

Lagrangian- or arbitrary Lagrangian-Eulerian (ALE) methods [36] [37], and were first reported by Hirt et al. [68]. In this book this particular framework is termed the general Lagrangian approach, see Fig 1.1(C). This approach also involves quite complex mathematics and is thus hardly ever used in chemical reactor analysis. 

Donea J, Giuliani S, Halleux JP (1982) An Arbitrary Lagrangian-Eulerian Finite Element Method for Transient Dynamic Fluid-Structure Interactions. Computer Methods in Applied Mechanics and Engineering 33 689-723... 

Donea J, Huerta A, Ponthot JP, Rodrfguez-Ferran A (2004) Arbitrary Lagrangian-Eulerian Methods. Encyclopedia of Computational Mechanics. 

Hirt CW, Amsden AA, Cook JL (1974) An Arbitrary Lagrangian-Eulerian Computing Method for All Flow Speeds. J Comput Phys 14 227-253 Hoff KA, Poplsteinova J, Jakobsen HA, Falk-Pedersen O, Juhussen O, Svendsen HF (2003) Modeling of Membrane Reactor. International Journal of Chemical Reactor Engineering 1 1-12, Article A9, (http //www.bepress. com/ijcre/voll/articles.html)... 

The model formulation used with moving meshes is of the arbitrary-Lagrangian-Eulerian (ALE) type. The integral form of the equations governing the incompressible Newtonian fluid in a time-varying control-volume V(t) is written as ... 

Donea J, Huerta A, Ponthot J-P, Rodrfguez-Ferran A (2004) Arbitrary Lagrangian-Eulerian Methods. In Stein E, de Borst R, Hughes TJR (eds) Encyclopedia of Computational Mechanics, Volume 1 Fundamentals, Chapter 14, pp 1-25, John Wiley Sons Ltd ISBN 0-470-84699-2... 

Hirt, C. W. Amsden, A. A., Cook, J. L. "An Arbitrary Lagrangian-Eulerian Computing Method for All Flow Speeds," J. Comput. Phys. 1974, 14, 227. 

Mohamed G, Soutis C, Hodzic A. Multi-material Arbitrary-Lagrangian-Eulerian formulation for blast-induced fluid-stmcture interaction in fibre metal laminates. AIAA J Am Inst Aeronaut Astronaut Struct Mech Mater 2012 50(9) 1826—33. 

The actual solution algorithm is often based on the arbitrary Lagrangian-Eulerian (ALE) method of Hirt et al. [22]. In this method, in order to make the solution computationally more efficient, a decoupling of the convective and nonconvective gas-phase terms in each time step is introduced. In the Lagrangian phase, where the computational cells move with the fluid flow, the spray PDE is updated and the source terms due to liquid and chemistry are evaluated. Also, the nonconvective... 

A1 Quddus N, Moussa WA, Bhattacharjee S (2008) Motion of a spherical particle in a cylindrical channel using arbitrary Lagrangian-Eulerian method. J Colloid Interface Sci 17 20-630... 

A three-dimensional arbitrary Lagrangian Eulerian finite element code SPLASH has been applied to the flow-induced vibration analysis of the thermocouple probe. Equations of... 

Hirt, C.W. An arbitrary lagrangian-eulerian computing method for all speeds. Journal of Computational Physics 14, 227-253 (1974)... 

Arbitrary Lagrangian Eulerian and Fluid-structure Interaction... 

In order to account for boundary deformation in the fluid mesh, the fluid governing equations are recast in an Arbitrary Lagrangian-Eulerian (ALE) description in CFX, where the fluid mesh deformation and velocity are solved based on a Lapladan diffusion model. The fluid-structure interaction is achieved by matching the forces and velocities at the common interface between the fluid and structure, via... 

Donea J, Giuliam S, HaUeux JP (1982) An arbitrary Lagrangian-Eulerian finite element method for transient dynamic fluid-structure interactions. Comput Methods Appl Mech Eng 33 689-723... 

Hirt CW, Amsden AA, Cook JL (1974) An arbitrary Lagrangian-Eulerian computing method for all flow speeds. J Comput Phys 14 227-253... 

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