Adaptive time stepping for explicit euler implementation of spherical and non-spherical particle speed up

Numerical implementation schemes of drag force effects on Lagrangian particles can lead to instabilities or inefficiencies if static particle time stepping is used. Despite well known disadvantages, the programming structure of the underlying, C++ based, Lagrangian particle solver led to the choice of an explicit EULER, temporal discretization scheme. To optimize the functionality of the EULER scheme, this paper proposes a method of adaptive time stepping, which adjusts the particle sub time step to the need of the individual particle. A user definable adjustment between numerical stability and calculation efficiency is sought and a simple time stepping rule is presented. Furthermore a method to quantify numerical instability is devised and the importance of the characteristic particle relaxation time as numerical parameter is underlined. All derivations are being conducted for (non-)spherical particles and finally for a generalized drag force implementation. Important differences in spherical and non-sph...