Open AccessVariational principles for relativistic smoothed particle hydrodynamics
Author(s) -
Monaghan J.J.,
Price D.J.
Publication year - 2001
Publication title -
monthly notices of the royal astronomical society
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 2.058
H-Index - 383
eISSN - 1365-2966
pISSN - 0035-8711
DOI - 10.1046/j.1365-8711.2001.04742.x
Subject(s) - physics , classical mechanics , variational principle , equations of motion , angular momentum , conservation law , relativistic particle , smoothed particle hydrodynamics , dissipation , energy–momentum relation , mechanics , quantum mechanics , electron
In this paper we show how the equations of motion for the smoothed particle hydrodynamics (SPH) method may be derived from a variational principle for both non‐relativistic and relativistic motion when there is no dissipation. Because the SPH density is a function of the coordinates the derivation of the equations of motion through variational principles is simpler than in the continuum case where the density is defined through the continuity equation. In particular, the derivation of the general relativistic equations is more direct and simpler than that of Fock. The symmetry properties of the Lagrangian lead immediately to the familiar additive conservation laws of linear and angular momentum and energy. In addition, we show that there is an approximately conserved quantity which, in the continuum limit, is the circulation.