Numerical study of the tidal interaction of a star and a massive black hole

We present a formalism well adapted to the numerical study of the encounter of an ordinary main sequence star with a massive black hole. Symmetry considerations , the use of a well adapted moving grid and a well adapted moving frame along with integration of the partial differential equations by means of pseudo-spectral methods result in a very powerful and accurate tool. The hydro-dynamical equations are written in a moving frame which mimics the bulk of the movement of the fluid, resulting in very small relative velocities and a well suited spatial resolution throughout the calculations. Therefore, the numerical calculations are considerably simplified, smoothing in particular the Courant condition. Typical runs are performed within a few hours on a workstation with the high accuracy linked to the spectral methods. Predictions of the so-called affine are tested against this full numerical simulation.