Citation:
R. Vignjevic, J. Campbell, J. Jaric, S. Powell, Derivation of SPH equations in a
moving referential coordinate system, Computer Methods in Applied Mechanics and
Engineering, Volume 198, Issues 30-32, 1 June 2009, Pages 2403-2411
Abstract:
The conventional SPH method uses kernel interpolation to derive the spatial
semi-discretisation of the governing equations. These equations, derived using a
straight application of the kernel interpolation method, are not used in
practice. Instead the equations, commonly used in SPH codes, are heuristically
modified to enforce symmetry and local conservation properties. This paper
revisits the process of deriving these semi-discrete SPH equations. It is shown
that by using the assumption of a moving referential coordinate system and
moving control volume, instead of the fixed referential coordinate system and
fixed control volume used in the conventional SPH method, a set of new semi-
discrete equations can be rigorously derived. The new forms of semi-discrete
equations are similar to the SPH equations used in practice. It is shown through
numerical examples that the new rigorously derived equations give similar
results to those obtained using the conventional SPH equations.