An efficient and rigorous criterion for the admissible time step of deforming grids in generalized Lagrangian and ALE methods

It is mathematically proved that a sufficient condition for deformed grid to remain valid is that the Jacobian determinant of the deformation remains positive within each element and the boundary is preserved under the deformation throughout the time interval. This result provides a rigorous and element-wise check method for users of the generalized Lagrangian scheme and the arbitrary Lagrangian-Eulerian scheme to assess grid validity.