Arbitrary Lagrangian-Eulerian method is of common use in nonlinear structural mechanics and also in fluid mechanics with free interphases. The Lagrangian boundary conditions applied in the normal direction restrict to transient analysis in fluid mechanical problems and may lead to large mesh deformation in structural ones.
We have developed a method to extend this method to the boundary which removes the restriction and allows to a better control of the mesh deformation. Analogously, we named it Boundary Arbitrary Lagrangian-Eulerian method.
If you want to learn more about this method, you can find more details in our manuscript. A revised version is in progress. For an application of this method, go to the section on inertial migration or elongated bubbles.