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.

arXiv comment22 pages, 22 figures, accepted in MNRAS

References in corpus (42)

• The cosmological simulation code GADGET-2
• E pur si muove: Galiliean-invariant cosmological hydrodynamical simulations on a moving mesh
• GIZMO: A New Class of Accurate, Mesh-Free Hydrodynamic Simulation Methods
• FIRE-2 Simulations: Physics versus Numerics in Galaxy Formation
• Shocks and cold fronts in galaxy clusters
• Improving convergence in smoothed particle hydrodynamics simulations without pairing instability
• Smoothed Particle Hydrodynamics and Magnetohydrodynamics
• Fundamental differences between SPH and grid methods
• A General Class of Lagrangian Smoothed Particle Hydrodynamics Methods and Implications for Fluid Mixing Problems
• Modelling discontinuities and Kelvin-Helmholtz instabilities in SPH
• MUFASA: Galaxy Formation Simulations With Meshless Hydrodynamics
• Inviscid SPH
• Gasoline2: A Modern SPH Code
• Stirring Up the Pot: Can Cooling Flows In Galaxy Clusters Be Quenched By Gas Sloshing?
• Chandra estimate of the magnetic field strength near the cold front in A3667
• SPHGal: Smoothed Particle Hydrodynamics with improved accuracy for Galaxy simulations
• Gas sloshing, cold front formation, and metal redistribution: the Virgo cluster as a quantitative test case
• A Well-Posed Kelvin-Helmholtz Instability Test and Comparison
• On viscosity, conduction and sound waves in the intracluster medium
• Impact of stochastic gas motions on galaxy cluster abundance profiles
• Astrophysical Weighted Particle Magnetohydrodynamics
• Computational Eulerian Hydrodynamics and Galilean Invariance
• A Validated Nonlinear Kelvin-Helmholtz Benchmark for Numerical Hydrodynamics
• Physical viscosity in smoothed particle hydrodynamics simulations of galaxy clusters
• rpSPH: a novel Smoothed Particle Hydrodynamics Algorithm
• Kelvin-Helmholtz instabilities at the sloshing cold fronts in the Virgo cluster as a measure for the effective ICM viscosity
• The Effect of Anisotropic Viscosity on Cold Fronts in Galaxy Clusters
• Is there a giant Kelvin-Helmholtz instability in the sloshing cold front of the Perseus cluster?
• Buoyant Bubbles in Intracluster Gas: Effects of Magnetic Fields and Anisotropic Viscosity
• Astrophysical hydrodynamics with a high-order discontinuous Galerkin scheme and adaptive mesh refinement
• Calibrating an updated SPH scheme within GCD+
• Viscous Kelvin-Helmholtz instabilities in highly ionised plasmas
• GANDALF - Graphical Astrophysics code for N-body Dynamics And Lagrangian Fluids
• Hydrodynamic simulations with the Godunov SPH
• Modelling Shear Flows with SPH and Grid Based Methods
• 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
• Numerical viscosity in simulations of the two-dimensional Kelvin-Helmholtz instability
• A Switch for Artificial Resistivity and Other Dissipation Terms
• The Kelvin-Helmholtz instability and smoothed particle hydrodynamics

Cited by in corpus (7)

• The Cosmological Simulation Code OpenGadget3 -- Implementation of Meshless Finite Mass
• Euclid: Modelling massive neutrinos in cosmology -- a code comparison
• Vortex-p: a Helmholtz-Hodge and Reynolds decomposition algorithm for particle-based simulations
• Density Fluctuations in the Intracluster Medium: An Attempt to Constrain Viscosity with Cosmological Simulations
• Novel Hydrodynamic Schemes Capturing Shocks and Contact Discontinuities and Comparison Study with Existing Methods
• Braginskii Viscosity in Cosmological Simulations of Galaxy Clusters: Implementation, Validation, and First Application
• OpenGadget3 GPU solver tests