DORiE – The DUNE Operated Richards Equation Solving Environment

  • Narrow water flux entering a heterogeneous unsaturated medium. The grid is adaptively refined (or coarsened) depending on the estimated error in numeric flux across a grid intersection. Visualized with Paraview.


DORiE is a software suite for solving Richards Equation. The core feature is a C++ PDE-solver powered by DUNE. It implements a Discontinous Galerkin (DG) discretization scheme on structured rectangular / cuboid and unstructured simplex grids in two and three spatial dimensions, and makes use of advanced features like adaptive grid refinement.

The suite encapsulates a documentation and various tools for program setup, program testing, and output analysis, which are mostly written in Python.

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


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.

Associated Theses and Workshop Contributions

Lukas Riedel, Dion Häfner, Ole Klein, and Kurt Roth: DORiE – a versatile discontinuous Galerkin Richards solver, poster presentation, EGU General Assembly 2018, April 8 – 13, 2018, Vienna, Austria.
See abstract & poster.

Lukas Riedel: DORiE – From Numeric Routine to Simulation Suite, oral presentation, DUNE User Meeting, March 13 – 14, 2017, Heidelberg, Germany.

Lukas Riedel: DORiE – Solving Richards Equation with DUNE-PDELab, oral presentation, DUNE User Meeting, September 28 – 29, 2015, Heidelberg, Germany.

Dion Häfner: Numerical Simulations of Soil Water Flow: Implementing and Benchmarking Adaptive Grid Refinement, B.Sc. Thesis, Faculty of Physics and Astronomy, Heidelberg University, 2015.

Felix Riexinger: An Extension of the Richards Equation Solver DORiE, B.Sc. Thesis, Faculty of Physics and Astronomy, Heidelberg University, 2015.

Lukas Riedel: DORiE – A New Richards Solver based on the Distributed and Unified Numerics Environment (DUNE), B.Sc. Thesis, Faculty of Physics and Astronomy, Heidelberg University, 2014.