"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.
Back
to seminars