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.

In filtration processes it is necessary to consider both, the interaction of the fluid with the solid parts, as well as the effect of particles carried in the fluid and accumulated on the solid. In this first part a closer look is taken on the influence of the fluid on the solid regions. The required algorithm to couple the governing differential equations is derived on the basis of the equations, governing the solid and fluid regions. For discretization, only one single computational mesh is used and this is adjusted to the deformation at each time-step. The simulation of the fluid-structure interaction is realised in a single finite volume flow solver on the basis of the OpenSource software OpenFoam.

A Lagrangian solver to realistically model large, non-spherical dirt particles and their behaviour in the vicinity of deformable filtration fibres has been programmed. While this paper focuses on basic solver concepts as well as drag force implementations, a related article, concerning the realisation of interaction effects and result verification, is forthcoming, [3].Within the framework of a digitally reconstructed, deformable filter fibre geometry, the solver traces the governing multi physics effects down to the occurrence of single force-and torque vectors. In order to go from an initial, spherical particle model [2], to a more sophisticated, non-spherical model, the capabilities of a Six Degrees of Freedom Solver have been included in the programming. A panel model and the concept of satellite help points are used to handle particles that encompass several fluid calculation cells.An innovative drag force implementation allows the consideration of rotational-and shear flow effects on particle motion. Results are evaluated and compared to an analytical formulation.

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