7.2 Combination with other methods

Spectral methods have also demonstrated that they can be a valuable tool when combined with other methods. For instance, when shocks are present, spectral methods alone have trouble dealing with discontinuities at the shock interface. However, this can be efficiently dealt with using Godunov methods. Such a combination has already been successfully applied to the simulation of the oscillations of compact stars in [71] and of core collapse [164].

Spectral methods have also been used in conjunction with a description of the fluid based on SPH (smoothed particle hydrodynamics) in the case of neutron star binaries [75] and for the merger of a neutron star with a black hole [74]. In both cases, the fluid is described by an ensemble of particles to which forces are applied. Such technique can account for complicated fluid configurations, like the spiral arms that are formed during the merger. Such arms would be tricky to follow by means of spectral methods alone. On the other hand, the equations describing gravity are nicely solved by spectral solvers.

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