2D ADI Solver

Model fluvial, overland, estuarine and coastal applications

The 2D ADI solver can be applied to fluvial, overland, estuarine and coastal modelling problems. It has been developed to be accurate, robust and fast for a wide range of applications. It is widely used for surface water modelling, local and catchment scale assessments, flood mapping, embankment and asset failure and other flood risk management studies.

Model fluvial, overland, estuarine and coastal applications

Develop a detailed understanding of the causes of flood risk in urban areas

Dynamically link the 2D ADI solver to Flood Modeller's 1D river and 1D urban solvers for a fully integrated and more accurate approach

Key facts

Calculates water depths, velocity and flow paths

Provides greater flexibility in producing an integrated catchment model

Deliver your 2D modelling projects using the Flood Cloud service

The 2D ADI solver calculates both water depth and velocity and can be linked dynamically to Flood Modeller's 1D river and 1D urban solvers to enable integrated catchment modelling to be undertaken. Models can be linked by water level or by flow and can represent lateral floodplains, a 1D channel running into a 2D estuary, spill over defences, and other river, coastal or floodplain systems.

The ADI solver works by representing the model domain as a grid of square cells. Water levels are calculated at each cell centre, and the two components of velocity at cell edges. This allows the model to use the velocity components to calculate flow across cell edges and between cells.

ADI stands for Alternating Direct Implicit, which is the mathematical solution method used by the solver. The 2D ADI solver calculates the discretised shallow water equations by sub-dividing the computation at each time step into x- and y-directions. On the first half time step the water depth and the unit width discharge qx are solved implicitly in the x-direction, whilst the other variables are represented explicitly. Similarly, for the second half time step, the water depth and the unit width discharge qy are solved implicitly in the y-direction, with other variables being represented explicitly. This solution technique is efficient, both in terms of processor time and memory.

Explore 2D results in the core map interface, overlaid on the built-in background mapping and any other contextual layers. The built-in animation functions enable you to view and record a complete picture of your model results.

Multiple 2D domains, with different cell sizes, time-steps and simulation times can be coupled to a single 1D model to represent different areas of a floodplain at different resolutions.


Flood Modeller's user-friendly interface provides an intuitive environment for building, running, and analysing 2D models. You can harness the power of cloud computing and run your simulations at lightning speed using Flood Cloud or export your flood extents for viewing in Flood Viewer, Google Earth or Navisworks to create immersive visualisations and engineering design models. 

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