"Introduction to the ALE formulation of the NAVIER--STOKES equations"

Consider a problem with a moving interface between a fluid and a body. Lagrangian description of the fluid motion makes it convenient to treat the compatibility conditions and equilibrium between fluid and body. But it is practically impossible to employ the Lagrangian description throughout the entire domain; vortices and the outflow will cause heavy mesh distortion. A mixed Lagrangian--Eulerian formulation resolves these problems and is widely used for fluid--structure interaction problems. The lecture will commence by introducing the three co-ordinate systems (called material, spatial and referential) used by the arbitrary Lagrangian Eulerian (ALE) formulation, proceed by ALE kinematics and eventually derive the ALE version of the Navier--Stokes equations. The material is not very difficult; the objective is to provide a basis for the talk by Achim Schroll the 31. of May.

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