Linear stability of lattice Boltzmann models with non-ideal equation of state

Detailed study of spectral properties and of linear stability is presented for a class of lattice Boltzmann models with a non-ideal equation of state. Examples include the van der Waals and the shallow water models. Both analytical and numerical approaches demonstrate that linear stability requires boundedness of propagation speeds of normal eigen-modes. The study provides a basis for the construction of unconditionally stable lattice Boltzmann models.