A multidimensional, adiabatic hydrodynamics code for studying tidal excitation

We have developed a massively parallel, simple and fast hydrodynamics code for multidimensional, self-gravitating and adiabatic flows. Our primary motivation is the study of the non-linear development of white dwarf oscillations excited via tidal resonances, typically over hundreds of stellar dynamical times. Consequently, we require long-term stability, low diffusivity and high-numerical efficiency. This is accomplished by an Eulerian finite-difference scheme on a regular Cartesian grid. This choice of coordinates provides uniform resolution throughout the flow as well as simplifying the computation of the self-gravitational potential, which is done via spectral methods. In this paper, we describe the numerical scheme and present the results of some common diagnostic problems. We also demonstrate the stability of a cold white dwarf in three dimensions over hundreds of dynamical times. Finally, we compare the results of the numerical scheme to the linear theory of adiabatic oscillations, finding numerical quality factors on the order of 6000 and excellent agreement with the oscillation frequency obtained by the linear analysis.