We care a lot about the math and physics at the heart of 3Di’s hydrodynamic simulations.

The computational core is carefully designed to create an optimal balance between accuracy, robustness and speed.

We work closely with Prof. dr. Guus Stelling and use the latest mathematical insights to solve the full St. Venant equations with conservation of mass and momentum. 3Di solves this equation using subgrid and quadtrees.


Processes that can be simulated

  • The most relevant processes from the hydrological cycle: Sewerage, open water, freatic ground water table, sources & sinks, leakage, evapotranspiration, rainfall, wind.
  • Structures (including control) and breaches
  • Simplified rainfall run off processes 0D inflow conform Dutch NWRW or custom characteristiscs

Model components that are configurable as 2D Raster

  • DEM
  • Friction
  • Infiltration
  • Interception
  • Groundwater
  • Interflow
  • Initial water level

The 3Di computational core

The computational core is developed together with Stelling Hydraulics and is based on the latest scientific insights.

Models can be built using 0D, 1D and 2D components. When using multiple components 3Di solves the water equation in one and the same matrix. So no coupled model for surface flow and sewerage flow, but one fully integrated solution. The benefit of this is that 1D-2D exchange is extremely stable and has a very small mass balance error

Subgrid methodology

The computational core uses the subgrid methodology. This has the advantage that the high detail of the schematisation is used without the need for extra computational power.The computational core handles dryfall in cells really well. Subgrid hugely reduces the need for extra time step iterations.

The size of the computational cells are user defined in the shape of a quadtree grid. The mathematical characteristisc of this grid are chosen to ensure the highest possible accuracy in solving the water equations.

The grid generator is an integral part of the modelling process and is fully automated. If needed user can defined their own areas for grid refinement.

Subgrid versus depth averaging

To show what subgrid does for the modeller we have built a model with and without subgrid.

The calculation cells and all simulation settings are the same in this example.

In the image on the left the result of a flood simulation without subgrid. For each cell there is only 1 elevation available, giving a coarse result and affection the flow and timing of the flood. On the image on the right we use subgrid, here the calculation cells are the same size but for every calculation cell the high resolution elevation data that is available is used.

The difference is clear:

with subgrid we get a better result, and the computational time is the same!

Nested Newton

To solve for closed pipe systems we have implement a nested newton approach. This means we can handle closed profiles without the need for articifial artefacts as a Preissman slot. It has the following benefits:

  • Perfectly suitable for pressurized systems.
  • Calculations are more accurate
  • Small mass balance error



A breach is a predefined point in a levee where the 1D-2D interaction is set by the Modeller. By identifying it as a breach the Verheij en Van der Knaap formula for breach growth is used. Flow through the breach is calculated using our weir formula.

breach growth

Longitudinal cross-section of breach showing the breach growth parameters.

In the breach formulation it is expected that the material of the levee (sand or clay), an initial breach width, the maximum breach depth and the period that is needed to reach this depth are known.


This formulation splits the growth of the breach into two phases; in the first phase the breach deepens and in the second phase the breach widens.

It is an experimental formula, widely regarded as the best available in the field of hydrodynamics.

How we capture reality

Within 3Di we make a distinguishment between:

  • schematisation
  • threedimodel
  • simulation templates

A schematisation is a depiction of reality, e.g. rasters, spatialite database, and settings to set the 3Di calculation grid and tables

A threedimodel is a converted schematisation with which 3Di can calculate.

A simulation template contains all information for a simulation with a 3Di model:

  • initial water
  • events, e.g. dike breach, dem edit, control structure
  • forcings, e.g. rain, laterals, boundary conditions
  • simulation settings

The way this is set up:

Once you have a threedimodel you can perform any simulation and store the information that was behind this simulation as a template. This makes it easy for yourself or colleagues to redo the exact same simulation or look back on historical simulation and see what settings were used in a certain simulation



Every new feature added to the computational core is also added into our testbank. The testbank evaluates the new computational core against analytic outcomes. This ensures that with every update or potential bugfix the outcome of the computational core is guaranteed.

Benchmark Studies On Modelling Instruments

On a regular basis benchmark studies analyze the reliability of instruments that model inundation. 3Di has been benchmarked in two studies, one carried out by STOWA and another one carried out by the Environment Agency.


STOWA is the foundation for applied water research in the Netherlands, it’s mission is to develop knowledge that supports Dutch Water Mangers. The hydraulic benchmark study shows 3Di is the only modelling package that could correctly execute all test cases. As 3Di provides accurate results for any case test, it is a recommendable hydraulic modelling solution for any water manager. The modelling instruments tested by STOWA include: 3Di, D-HYDRO, InfoWorks ICM, HEC-RAS, SOBEK 2, TELEMAC, SIMGRO, WOLK and TYGRON

Environment Agency

The Environment Agency is the public body that protects and improves the environment in England. In August 2013 they published the report ‘Benchmarking the latest generation of 2D hydraulic modelling packages‘. After passing the STOWA benchmark, the 3Di team recreated the environment agency benchmark test and published the outcomes in this report. Since then 3Di has been approved for use in the UK.

The science behind 3Di

We care a lot about the math and physics at the heart of 3Di’s hydrodynamic simulations. We work closely with Prof. dr. Guus Stelling and use the latest mathematical insights to solve the full St. Venant equations with conservation of mass and momentum. The science behind 3Di is well documented:

Scientific publications

Ready to start?

Are you interested in how 3Di works and how you can use it? Please use this form to request a demonstration. We will contact you to give an online demonstration and will answer all your questions.