The code d³f (distributed density-driven flow) has been developed to meet the needs of far field modelling as a part of long-term safety analyses for nuclear waste repositories in rock salt (Fein & Schneider, 1999). It is able to model density-driven flow in the geological overburden of salt domes and other host rock formations, i.e. in areas up to 10 000 km² with complex hydrogeological situations over time periods of some ten thousands of years (Fig. 1). The development began in 1995 as a joint project of GRS together with five university institutes, funded by BMWi, and is still ongoing. The result is a powerful tool that is able to handle salt and heat transport in porous as well as fractured media, salt concentrations up to saturation and complex hydrogeological structures with high permeability contrasts. Besides safety analyses, d³f has been applied to other fields, too, such as laboratory and field experiments or coastal aquifers.

All numerical algorithms applied in this code are based on finite volume methods with robust solvers in form of multigrid algorithms. Spatial and temporal adaptivity can be taken into account using a-posteriori error estimators. The code is fully parallelized and can be run on workstations, LINUX-PC, clusters and massively parallel computers.


Fig. 1: Example for the application of the computer code d3f: Relative salt concentration (colors) and velocity field (arrows) in the overburden of a salt formation in Northern Germany (Keesmann et al., 2005).



Fein, E., and Schneider, A., d³f – Ein Programmpaket zur Modellierung von Dichteströmungen, GRS-139, BMWi-FKZ 02C04650, Gesellschaft für Anlagen- und Reaktorsicherheit (GRS) mbH, Braunschweig, 245 p (1999).

Keesmann, S., Noseck, U., Fein, E., Schneider, A., Buhmann, D., Modellrechnungen zur Langzeitsicherheit von Endlagern für abgebrannte Brennelemente in Salz- und Granitformationen, GRS-206, BMWA-FKZ 02E9239, Gesellschaft für Anlagen- und Reaktorsicherheit (GRS) mbH, Braunschweig, 75 p (2005).