ALE Modeling of Surface Waves

An Arbitrary Lagrange Euler formulation for the propagation of surface waves is developed in LS-DYNA®. The ALE computational time step in this code is divided in two cycles: a Lagrangian cycle in which the mesh follows the material deformation and an advection cycle in which the users through remapping algorithms control the mesh motion. The new feature presented in this paper is one of these remapping algorithms. It enables a Lagrangian behavior of free ALE mesh boundaries whereas, in the direction of the wave propagation, the ALE mesh is Eulerian to avoid distortions. Nodes on the ALE mesh borders moves with the surface waves during the Lagrangian cycle. During the advection cycle, the remap positions of these nodes are computed by interpolating the Lagrangian positions of their neighbors with biquadratic polynomials. If the wave amplitudes are too important, ALE smoothing can be used for the internal nodes and a specific smoothing is applied on the mesh surfaces.