Hydrodynamics of accretion discs of variable thickness

We present a new model for the hydrodynamics of thin accretion discs. In th e (r, phi) plane full hydrodynamics is taken into account, while the time e volution of the disc thickness H is followed by assuming uniform expansion and contraction in the vertical direction. This amounts to a 'one-zone' app roximation for the vertical equation of motion. We show that the model corr ectly incorporates the fundamental mode of vertical oscillation of a disc f or waves long compared with the disc thickness. A numerical scheme to solve these equations on an Eulerian grid is introduced and tested for validity. As an application we compute the excitation of disc thickness oscillations by the tidal field of a companion. Strong excitation occurs at the 2:1 res onance, at r similar or equal to 0.32 a, where a is the binary separation.