Arbitrary Lagrangian Eulerian

The arbitrary Lagrangian-Eulerian method (ALE method) is a way of coupling an Eulerian with a Lagrangian formulation in numerical fluid mechanics in order to solve , for example, free surface problems, multiphase flow problems or fluid-structure-coupling problems.

There are two different ways of looking at the description of movement in space, which are called Lagrange or Euler's formulation . In a Lagrange description, the observer moves with the moving body. The Lagrangian description is often used in solid mechanics. In fluid mechanics, it is often easier to describe the flow field in a fixed volume without having to worry about the paths of individual particles. This is called Euler's mode of description. The ALE method combines the advantages of the Euler and Lagrange approaches.

At the beginning of a simulation calculation, the output network is discretized in Lagrangian form. If individual sub-areas of the network get an unfavorable geometry due to a change, the element nodes are shifted to such an extent that a numerically unstable network is avoided. This method has the advantage over other adaptation methods that both the number of nodes and the number of elements are retained.

Application examples for the arbitrary Lagrangian-Eulerian method

The following questions can be considered when using the arbitrary Lagrangian-Eulerian method:

• Inflow of gas into an airbag (fluid-structure coupling).
• Splashing a fluid in a tank (free surface).

literature

• Dahong, Chen "Numerical simulation of flow processes with the" Arbitrary Lagrangian-Eulerian method "(ALE method)" Aachen: Mainz, 1997. XVII, 139 pp. ISBN 3-89653-610-9 .
• Hirt, CW, Amsden, AA, and Cook, JL, An Arbitrary Lagrangian-Eulerian Computing Method for all Flow Speeds, J. Comp. Phys., 14 (1974), p. 227