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Title:
Modelling discontinuities and Kelvin Helmholtz instabilities in SPH
Authors:
Price, Daniel J.
Affiliation:
School of Physics, University of Exeter, Stocker Road, Exeter EX4 4QL, UK. Present address: School of Mathematical Sciences, Monash University, Clayton Vic 3168, Australia. Tel.: +44 1392 264138; fax: +44 1392 264111.
Publication:
Journal of Computational Physics, Volume 227, Issue 24, p. 10040-10057.
Publication Date:
12/2008
Origin:
ELSEVIER
Abstract Copyright:
Elsevier Inc.
DOI:
10.1016/j.jcp.2008.08.011
Bibliographic Code:
2008JCoPh.22710040P

Abstract

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, Å. 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.
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