Variable-h and energy conserving SPH formulation with application in aerospace engineering

  • M.-A. Lavoie
  • A. Gakwaya
  • M. Nejad Ensan


This paper presents a variable-$h$ and energy conserving SPH formulation developed from the Hamilton variational principle. The evolution of $h$ is treated in a rigorous coupled manner consistent with the discretized form of the conservation equations by explicitly using a variable smoothing length kernel gradient. A boundary correction function is applied to address the boundary inconsistency issue and its efficiency is discussed and compared with that of the normalization correction. The resulting formulation is applied to the shear cavity and dam collapse problems with success. The obtained results are compared with those from the standard SPH formulation and comments are made regarding the efficiency and capabilities of the developed equations and corrections. Finally, two applications related to bird strike and hail impact to the field of aerospace engineering are given.