Improving a SPH code by alternative interpolation schemes

A still unconventional discretization approach for numerical simulation codes to solve the conservation equations was invented within the last years by the so called particle methods. As a gridless interpolation scheme Smooth Particle Hydrodynamics (SPH) turned out to be very useful for applications where large deformations or multiple fracture and fragmentation shall be calculated. Deep penetration, brittle material behaviour and fluid structure interaction in combination with fragmentation are typical scenarios where particle methods have clear advantage over grid based methods. Originally invented by astrophysicists in the late 70’s, SPH is meanwhile also used for structural mechanics since material strength was implemented during the early 90’s. However the method still suffers from some particular problems like inconsistency and numerical instability. The SPH code SOPHIA [ 5 ], developed at Emst-Mach-Institut Freiburg and the Federal Armed Forces University Munich, allows for implementation and use of arbitrary material strength and failure models. Different schemes have been tested recently in order to improve the numerical stability. Kernel renormalisation and conservative smoothing were first steps. This article demonstrates the implementation of Moving Least Squares (MLS) into SOPHIA. MLS is an alternative interpolation scheme that provides consistency and thus improves the standard SPH kernel functions. Two example applications are given to demonstrate the resulting differences.