12 MESH MOVEMENT
In many instances, the fluid interacts with rigid or flexible bodies that are either totally submerged in it or partly wetted. These bodies will tend to react to the forces exerted by the fluid, producing a change of the fluid domain. Examples of this type of interaction are structures submerged in water, aeroelastic applications like flutter or buzz, or simply the movement of flags due to wind forces. Another possibility is the forced movement of a body through a flowfleld. Examples that fall under this category are store separation for military aircraft, torpedo launch and trains entering tunnels. The important new phenomenon that has to be addressed carefully for these classes of problems is the change of the domain itself as the simulation proceeds. The present chapter discusses the changes required for the PDEs describing the fluid, the algorithms employed and the possibilities for mesh movement.
12.1. The ALE frame of reference
The most convenient form to treat problems with changing domains is to re-write the equations describing the fluid in an arbitrary Lagrangian Eulerian (ALE) frame of reference. Given a mesh velocity field w = (wx, wy, wz), the Euler equations become
Observe that in the case of no element movement (w = 0) we recover the usual Eulerian conservation law form of the Euler equations. If, however, the elements move with the particle velocity ...