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Simulation Techniques

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Numerical Modelling of Astrophysical Turbulence

Part of the book series: SpringerBriefs in Astronomy ((BRIEFSASTRON))

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Abstract

An often used method to produced turbulence in numerical simulations is random forcing. Although this method is a mathematical idealization, it allows us to perform numerical experiments in the sense that a statistically stationary and isotropic turbulent state is prepared, with well defined statistical properties that can be compared to analytical theories. For more realistic astrophysical applications, adaptive methods are indispensable. Adaptive mesh refinement was introduced to efficiently treat flows with inhomogeneous structure. The basic idea is that the numerical resolution is dynamically adjusted such that subregions of the flow with strong fluctuations or steep gradients are well resolved, while smoother regions are covered by relatively coarse grids. The treatment of turbulent flows with adaptive mesh refinement, however, is still a challenging problem, mainly because refinement criteria that are sensitive to turbulent eddies or shocks in supersonic turbulence are difficult to formulate. The need to fully resolve turbulence, however, might be ameliorated by subgrid scale models, which approximate the effect of numerically unresolved turbulent eddies and shocks through turbulent viscosity and pressure in large eddy simulations.

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Notes

  1. 1.

    See Eq. (3.4) in Sect. 3.1. For consistency with Eq. (2.37), however, \(\omega _\mathrm{rms}^{2}\) is replaced by \(\langle |S^{*}|^{2}\rangle = \langle \omega ^{2}+\frac{4}{3}d^{2}\rangle \).

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  1. Institut für Astrophysik, Georg-August-Universität, Friedrich-Hund-Platz 1, 37077, Göttingen, Germany

    Wolfram Schmidt

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Schmidt, W. (2014). Simulation Techniques. In: Numerical Modelling of Astrophysical Turbulence. SpringerBriefs in Astronomy. Springer, Cham. https://doi.org/10.1007/978-3-319-01475-3_2

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