Journal
JOURNAL OF COMPUTATIONAL PHYSICS
Volume 227, Issue 24, Pages 10040-10057Publisher
ACADEMIC PRESS INC ELSEVIER SCIENCE
DOI: 10.1016/j.jcp.2008.08.011
Keywords
Hydrodynamics; Methods: numerical; Smoothed particle hydrodynamics (SPH); Kelvin-Helmholtz instability; Contact discontinuities; Artificial surface tension
Funding
- Royal Society University Research Fellowship
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In this paper we discuss the treatment of discontinuities in smoothed particle hydrodynamics (SPH) simulations. In particular we discuss the difference between integral and differential representations of the fluid equations in an SPH context and how this relates to the formulation of dissipative terms for the capture of shocks and other discontinuities. This has important implications for many problems, in particular related to recently highlighted problems in treating Kelvin-Helmholtz instabilities across entropy gradients in SPH. The specific problems pointed out by Agertz et al. [O.Agertz, B. Moore, J. Stadel, D. Potter, F. Miniati, J. Read, L. Mayer, A. Gawryszczak, A. Kravtsov, A. Nordlund, F. Pearce, V. Quilis, D. Rudd, V. Springel, J. Stone, E. Tasker, R. Teyssier, J. Wadsley, R. Walder, Fundamental differences between SPH and grid methods, MNRAS 380 (2007) 963-978] are shown to be related in particular to the (lack of) treatment of contact discontinuities in standard SPH formulations which can be cured by the simple application of an artificial thermal conductivity term. We propose a new formulation of artificial thermal conductivity in SPH which minimises dissipation away from discontinuities and can therefore be applied quite generally in SPH calculations. (C) 2008 Elsevier Inc. All rights reserved.
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