  We present a new lattice kinetic method to simulate fluid dynamics in
curvilinear geometries. A suitable discrete Boltzmann equation is solved in
contravariant coordinates, and the equilibrium distribution function is
obtained by a Hermite polynomials expansion of the Maxwell-Boltzmann
distribution, expressed in terms of the contravariant coordinates and the
metric tensor. To validate the model, we calculate the critical Reynolds number
for the onset of the Taylor-Couette instability between two concentric
cylinders, obtaining excellent agreement with the theory. In order to extend
this study to more general geometries, we also calculate the critical Reynolds
number for the case of two concentric spheres, finding good agreement with
experimental data. In the case of two concentric tori, we have found that the
critical Reynolds is about 10% larger than the respective value for the two
concentric cylinders.
