The finite volume code d3f++ has been developed to meet the needs of far field modelling as part of long-term safety analyses for nuclear waste repositories. The development started in 1994 with the computer codes d3f (distributed density-driven flow, Fein & Schneider, 1999) and r3t (radionuclides, reaction, retardation, and transport, Fein, 2004). Both codes were based on the simulation toolbox UG (unstructured grids, Bastian et al, 1997), a software framework for the numerical solution of coupled systems of partial differential equations developed by a research group of the Frankfurt University. The smart Kd-concept was originally implemented in the code r3t during the project ESTRAL (Noseck et al, 2012). With the transfer to the new code version Vogel et al, 2013), d3f and r3t were combined to the code d3f++ (Schneider, 2016). The code is fully parallelized.

Today, d3f++ allows to simulate density-driven flow in porous as well as fractured media at regional scale considering heat transport as well as free surface flow. The transport of radionuclides or other substances can be modelled regarding the effects that are relevant for safety assessments, e. g. radioactive decay, equilibrium and kinetically controlled sorption, precipitation and colloid-borne transport. The smart Kd‑concept (Coupling with transport, Noseck et al, 2018) provides the equilibrium sorption model with input parameters depending on certain environmental parameters.

Fig. 2: Results of the Äspö site descriptive model as example for a d3f++ simulation on a regional scale.


Contact: Anne Gehrke



Bastian, P., Birken, K., Johannsen, K., Lang, S., Neuß, N., Rentz-Reichert, H., Wieners, C.: UG – A flexible software tool for solving partial differential equations. Computing and Visualization in Science 1, 27-40, 1997.

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

Fein, E., Software Package r3t. Model for Transport and Retention in Porous Media, GRS-192, BMWA-FKZ 02E9148/2, Gesellschaft für Anlagen- und Reaktorsicherheit (GRS) gGmbH, Braunschweig (2004) 319 p.

Noseck, U., Brendler, V., Flügge, J., Stockmann, M., Britz, S., Lampe, M., Schikora, J., Schneider, A.: Realistic integration of sorption processes in transport codes for long-term safety assessments, Final Report GRS-297, BMWi-FKZ 02E10518 und 02E10528, Gesellschaft für Anlagen- und Reaktorsicherheit (GRS) gGmbH, Braunschweig (2012) 293 p.

Noseck, U., Brendler, V., Britz, S., Stockmann, M., Fricke, J., Richter, C., Lampe, M., Gehrke, A., Flügge, J.: Smart Kd-Concept for Long-term Safety Assessment – Extension towards more Complex Applications, Final Report GRS-500, BMWi-FKZ 02E11072A and 02E11072B, Gesellschaft für Anlagen- und Reaktorsicherheit (GRS) gGmbH, Braunschweig (2018), 346 p.

Schneider, A. (ed.), Modelling of Data Uncertainties on Hybrid Computers, GRS-392, BMWi-FKZ 02E11062A, Gesellschaft für Anlagen- und Reaktorsicherheit (GRS) gGmbH, Braunschweig (2016) 187 p.

Vogel, A., Reiter, S., Rupp, M., Nägel, A., Wittum, G.: UG 4 - A Novel Flexible Software System for Simulating PDE Based Models on High Performance Computers. Computing and Visualization in Science, 16 (4), pp 165-179, 2014.