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Nordita Astrophysics seminars

The timestep constraint in solving the gravitational wave equations sourced by hydromagnetic turbulence

by Axel Brandenburg (Nordita)

112:028 ()


Hydromagnetic turbulence produced during phase transitions in the early universe can be a powerful source of stochastic gravitational waves (GWs). GWs can be modeled by the linearized spatial part of the Einstein equations sourced by the Reynolds and Maxwell stresses. We have implemented a GW solver into the {\sc Pencil Code}, which uses a third order timestep and sixth order finite differences. We study the appearance of a numerical degradation of the GW amplitude at the highest wavenumbers, which depends on the length of the timestep---even when the Courant-Friedrichs-Lewy condition is ten times below the stability limit. This degradation leads to a numerical error, which is found to scale with the third power of the timestep. A similar degradation is not seen in the magnetic and velocity fields. Yet, we argue that such degradation could also occur in those fields, but it is being masked by the forward cascade of energy, which populates all higher wavenumbers in a timestep-independent fashion. A similar process is not possible for the GWs, because their evolution equations are linear.