The role of physical and numerical viscosity in hydrodynamical instabilities

Abstract

The evolution of the Kelvin-Helmholtz Instability (KHI) is widely used to assess the performance of numerical methods. We employ this instability to test both the smoothed particle hydrodynamics (SPH) and the meshless finite mass (MFM) implementation in OpenGadget3. We quantify the accuracy of SPH and MFM in reproducing the linear growth of the KHI with different numerical and physical set-ups. Among them, we consider: $i)$ numerical induced viscosity, and $ii)$ physically motivated, Braginskii viscosity, and compare their effect on the growth of the KHI. We find that the changes of the inferred numerical viscosity when varying nuisance parameters such as the set-up or the number of neighbours in our SPH code are comparable to the differences obtained when using different hydrodynamical solvers, i.e. MFM. SPH reproduces the expected reduction of the growth rate in the presence of physical viscosity and recovers well the threshold level of physical viscosity needed to fully suppress the instability. In the case of galaxy clusters with a virial temperature of $3\times 10^7$ K, this level corresponds to a suppression factor of $\approx 10^{-3}$ of the classical Braginskii value. The intrinsic, numerical viscosity of our SPH implementation in such an environment is inferred to be at least an order of magnitude smaller (i.e. $\approx 10^{-4}$), re-ensuring that modern SPH methods are suitable to study the effect of physical viscosity in galaxy clusters.

22 pages, 22 figures, accepted in MNRAS

References in corpus (11)

• Shocks and cold fronts in galaxy clusters
• Smoothed Particle Hydrodynamics and Magnetohydrodynamics
• Modelling discontinuities and Kelvin-Helmholtz instabilities in SPH
• Inviscid SPH
• Physical viscosity in smoothed particle hydrodynamics simulations of galaxy clusters
• The Effect of Anisotropic Viscosity on Cold Fronts in Galaxy Clusters
• GANDALF - Graphical Astrophysics code for N-body Dynamics And Lagrangian Fluids
• Mixing matters
• Chandra and XMM-Newton observations of A2256: cold fronts, merger shocks, and constraint on the IC emission
• The Mergers in Abell 2256: Displaced Gas and its Connection to the Radio-emitting Plasma
• Role of magnetic fields in ram pressure stripped galaxies

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• Braginskii Viscosity in Cosmological Simulations of Galaxy Clusters: Implementation, Validation, and First Application
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