Stable anisotropic heat conduction in smoothed particle hydrodynamics

Abstract

We investigate how to simulate anisotropic heat conduction in a stable manner in Smoothed Particle Hydrodynamics. We show that the requirement for stability is that entropy must increase. From this, we deduce that methods involving direct second derivatives in SPH are unstable, as found by previous authors. We show that the only stable method is to use two first derivatives with alternating differenced and symmetric SPH derivative operators, with the caveat, that one may need to apply smoothing or use an artificial conductivity term if the initial temperature jump is discontinuous. Furthermore, we find that with two first derivatives the stable timestep can be 3--8 times larger even for isotropic diffusion.

9 pages, 10 figures, accepted to MNRAS

References in corpus (6)

• Smoothed Particle Hydrodynamics and Magnetohydrodynamics
• Modelling discontinuities and Kelvin-Helmholtz instabilities in SPH
• Constrained Hyperbolic Divergence Cleaning for Smoothed Particle Magnetohydrodynamics
• An implementation of radiative transfer in the cosmological simulation code GADGET
• Physical viscosity in smoothed particle hydrodynamics simulations of galaxy clusters
• Ambipolar diffusion in smoothed particle magnetohydrodynamics

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