Abstract
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-spherical particle behaviour are pointed out.
Highlights
Numerical implementation schemes of drag force effects on Lagrangian particles can lead to instabilities or inefficiencies if static particle time stepping is used
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
Summary
Lagrangian particle solver, based on the Open Source Computational Fluid Dynamics (CFD) software OpenFOAM® [18, 19] was developed as described in (Boiger & Mataln, 2008, [1, 2] & [20, 21]). The simple relationship between fluid time step ∆tf, particle time step ∆tp and the number of particle Subcycles J reads: J. This work presents a way to quantify the degree of numerical particle stability, that goes along with each chosen particle sub time step Based on these results an adaptive time stepping method is worked out, that allows the user to select accuracy and efficiency of the explicit EULER force effect modelling. Issues concerning numerical instability, stemming from the explicit EULER, temporal discretization, are at the focus of this paper Those instabilities are limited to particle–fluid interaction force effects and do not concern momentary forces caused by events such as particle–particle, particle-wall or particle-fibre impacts (Boiger, Mataln, 2008, [2, 21]). Particle-fluid forces have to be inspected in detail
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