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Published October 2006 | Published
Journal Article Open

A multidimensional, adiabatic hydrodynamics code for studying tidal excitation

Abstract

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.

Additional Information

© 2006 The Authors. Journal compilation © 2006 RAS. Accepted 2006 August 3. Received 2006 July 21; in original form 2006 May 16. Article first published online: 8 Sep. 2006. The authors would like to thank Anatoly Spitkovsky, Ruben Krasnopolsky, Michele Vallisneri, Andrew MacFadyen, Joel Tohline and Michael Norman for a number of helpful conversations. AEB would especially like to thank Jim Stone for a number of useful suggestions regarding the presentation of this material. This research used resources of the National Center for Computational Sciences at Oak Ridge National Laboratory, which is supported by the Office of Science of the US Department of Energy under Contract No. DE-AC05-00OR22725. This work was supported under NASA grant NAGWS-2837.

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