Current CFD models are computationally extremely expensive such that detailed, long-term simulations of transient flows are practically impossible. Current limits (obviously dependent on the case size, etc) are in the order of seconds or at most a few minutes. Recently, the novel, data-driven method recurrence CFD was introduced to describe passive or weakly coupled processes on highly dynamic, recurrent backgrounds with a high degree of spatial details. On small-scale test cases, rCFD produced speed-ups of more than two orders of magnitude.

The discrete element method (DEM) has proven to be a viable tool to analyse granular flows in great detail on the micromechanical level. However, this level of detail comes with a major drawback, namely high computational costs due to resolving individual particle contacts. This inherent feature of the DEM severely limits the maximum time step that can be applied in any DEM simulation. Any larger time step may lead to missed contacts or wrong energy dissipation. To some extent the critical time step depends on the material of the particles but usually is in the range of microseconds or even lower for very stiff materials. Typical time scales of industrial processes on the other hand range from several hours to days which leaves us with a difference of several orders of magnitude that needs to be bridged. The vast amount of particles in industrial facilities further aggravates the computational demands. While the latter may be handled by a coarse-graining approach to reduce the effectively computed number of particles significantly, the time step shows only a linear dependence on particle size and cannot be increased at the same rate.


While rCFD allows for speed-ups of more than two orders of magnitude, it requires substantial further developments for practical applicability concerning industrial needs. Large-scale flows impose serious memory demands such that proper data reduction strategies (e.g. filtering) need to be devised, which have to be accompanied by corresponding sub-grid closure models. To capture the existence of multiple process conditions (e.g. low vs high inlet velocity), we will use several databases and switch between them. For large cases, “loading on demand” will prevent too large memory demands.

To overcome the limitation on the time scale for DEM simulations, we propose a method that combines a short-term DEM simulation with a long-term information transportation method using the particle positions at the end of the DEM simulation as nodes for the information network. This may be extended to a tick-tock scheme where DEM simulation and transport information model may be executed alternatingly.

Results and Application

The methods rCFD and synDEM aim to allow long-term simulations of Eulerian and Lagrangian frame of reference simulations while maintaining high temporal and spatial resolution. As data-driven methods, they can be used on desktop computers with sufficient memory without the need of expensive computer clusters to picture the behavior of various types of flows on process-relevant time scales. This will significantly increase the usefulness of computer models as numerical experiments to gain insights into industrial processes involving granular materials or multiple fluid phases.