DORiE – The DUNE Operated Richards Equation Solving Environment


DORiE is an open-source software framework for modelling and simulating transient water flow and passive solute transport in unsaturated porous media with finite volume (FV) and discontinuous Galerkin (DG) methods, powered by the Distributed and Unified Numerics Environment (DUNE). It supports computations with higher-order function spaces on structured and unstructured, non-conforming grids and features advanced numerical routines like flux reconstruction and adaptive grid refinement. The framework encapsulates a documentation and various tools for program setup, program testing, and output analysis, which are mostly written in Python.

Combining high numerical precision and an accurate physical process representation, DORiE is tailored to soil physicists and computational scientists. The application can be controlled with configuration input files and a command line interface. Its source code additionally allows modifications and for integrating the entire model stack into encapsulating frameworks.

DORiE is developed and maintained by the DORiE Developers, in collaboration with Ole Klein and the Scientific Computing Group of IWR Heidelberg.

Simulation Examples

  • Simulation of a strong infiltration into a hill-shaped domain consisting of a small-scale heterogeneous porous medium.
  • Simulation of salinization through steady-state evaporation from a heterogeneous domain consisting of a coarse- and fine-grained material.

Simulation showcases from the JOSS publication available at


DORiE v2.0 was reviewed and published in the Journal of Open Source Software (JOSS).

Stable versions of DORiE are available as pre-compiled Docker applications or can be compiled from the most recent source code.


The dynamics of soil water inside the unsaturated vadose zone above the groundwater table and directly below the surface have a prominent role in soil physics. Described by the Richards Equation, they are the connecting link between soil, atmosphere, and vegetation and therefore play a dominant role in landscape formation and diversification. As the parameters of the soil as well as the actual behavior of the water are difficult to observe, reliable simulations are needed in order to deduce information. The highly non-linear parameterization characteristics encountered additionally demand for very stable numeric solutions.

To meet these requirements, DORiE is set up as a module of the Distributed and Unified Numerics Environment (DUNE), an actively developed generic C++ template library containing multiple modules for the computation of Partial Differential Equations (PDEs) on multidimensional domains using various Finite Element Methods (FEMs). It uses the DUNE-PDELab discretization module to implement spatial and temporal local operators for residual assembly, linear and non-linear solvers, an implicit time stepping scheme, and local grid refinement.


Publications on DORiE:

  • Riedel, Lukas, Santiago Ospina Los De Ríos, Dion Häfner, and Ole Klein. 2020. “DORiE: A Discontinuous Galerkin Solver for Soil Water Flow and Passive Solute Transport Based on DUNE.” Journal of Open Source Software 5 (52): 2313.

Publications using DORiE:

  • Bauser, Hannes H., Lukas Riedel, Daniel Berg, Peter A. Troch, and Kurt Roth. 2020. “Challenges with Effective Representations of Heterogeneity in Soil Hydrology Based on Local Water Content Measurements.” Vadose Zone Journal 19 (1): e20040.

Conference Contributions and Theses

Presentations on DORiE:

  • Riedel, Lukas, Dion Häfner, Ole Klein, and Kurt Roth. 2018. “DORiE – a Versatile Discontinuous Galerkin Richards Solver.” Poster Presentation presented at the European Geosciences Union (EGU) General Assembly 2018, Vienna, Austria, April 9.
  • Riedel, Lukas. 2017. “DORiE – From Numeric Routine to Simulation Suite.” Oral Presentation presented at the DUNE User Meeting, Heidelberg, Germany, March 13.
  • Riedel, Lukas. 2015. “DORiE – Solving the Richards Equation with DUNE-PDELab.” Oral Presentation presented at the DUNE User Meeting, Heidelberg, Germany, September 29.

Presentations using DORiE:


  • Riedel, Lukas. 2017. “Advancing Data Assimilation of Soil Water Flow with a DG-Based Richards Solver.” Master’s Thesis, Heidelberg, Germany: Heidelberg University.
  • Häfner, Dion. 2015. “Numerical Simulations of Soil Water Flow: Implementing and Benchmarking Adaptive Grid Refinement.” Bachelor’s Thesis, Heidelberg, Germany: Heidelberg University.
  • Riexinger, Felix. 2015. “An Extension of the Richards Equation Solver DORiE.” Bachelor’s Thesis, Heidelberg, Germany: Heidelberg University.
  • Riedel, Lukas. 2014. “DORiE – A New Richards Solver Based on the Distributed and Unified Numerics Environment (DUNE).” Bachelor’s Thesis, Heidelberg, Germany: Heidelberg University.