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Not all solvers are the same | How to choose the right 2D solver

Flood Modeller provides three 2D solvers as standard, allowing you to select the most appropriate solution method for each project. However, it can be difficult to know how to choose the right 2D solver. In this article, we provide some useful information to help you decide which one to use – in some cases you may wish to use more than one!

What 2D solvers are available?

2D ADI solver

The 2D ADI (Alternating Direct Implicit) solver can be applied to fluvial, overland, estuarine and coastal modelling problems, and in many cases, is the ‘go to’ solver for 2D modelling. It is the preferred solution for various flood modelling packages due to it being an accurate, robust and fast method which can be applied to a wide range of flood risk management studies, including surface water modelling, local and catchment scale assessments, and flood and hazard mapping.

The 2D ADI solver represents the 2D 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.

Multiple 2D domains, with different cell sizes and time-steps, can be incorporated into your model to represent different areas of a floodplain. This allows you to model areas of interest in greater detail, without compromising simulation run times.

The solver can be linked dynamically to Flood Modeller's 1D river and 1D urban solvers to enable integrated catchment modelling of surface and sub-surface flows. 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.

2D TVD solver

​​The 2D TVD (Total Variation Diminishing) solver has been specifically developed to provide an accurate representation of two-dimensional 'shocks' (rapid changes in water surface profile) and addresses the limitations of solvers found in other software packages. It enables flood risk and flood hazards to be confidently understood and the impacts on people, property and the environment to be assessed, and mitigation options to be tested.

The 2D TVD solver is capable of modelling trans-critical flow and is widely used for modelling dam breach, very steep catchments or flow down spillways. For rapidly varying flow, where hydraulic jumps may occur, the TVD solver generates more stable and smoother solutions as it’s particularly suited to modelling steep changes in velocity and water level.

The solver uses predictor and corrector steps to compute depth and flow at the new timestep. A TVD term is then applied to the mean of the predictor and corrector steps to remove numerical oscillations near sharp gradients – providing accurate, stable results.

The TVD solver discretises the shallow water equations in a slightly different way to the ADI scheme, as flows are represented at the cell centres, rather than at the edges. Since the TVD scheme uses explicit time stepping, the maximum stable Courant number is around 1. This means a much smaller time step must be used with the TVD scheme to ensure stability.

2D FAST solver

The 2D FAST solver is an innovative flood inundation modelling tool designed to allow quick assessment of flooding using simplified hydraulics. It provides results in seconds or minutes, as opposed to hours or days, which are up to 1,000 times faster than traditional 2D models.

The 2D FAST solver allows modellers to rapidly estimate flood extents and depths from multiple sources of water, including tide, surge and fluvial overtopping or breaching of defences, surface water and sewer flooding. Applications include near real-time flood inundation prediction on the Tidal Thames in London, England, through to prediction of areas susceptible to pluvial flooding for the whole of Scotland to mapping flood risk scenarios for the Philippines.

The speed with which the solver calculates water depths gives modellers the flexibility to rapidly test “what if” scenarios, explore uncertainty and probabilistic analysis, and evaluate the interactions and dependency between flood sources.

The 2D FAST solver works by identifying depressions on the floodplain then routing water through these depressions. Water depths in the depressions are determined by the volume of water flowing into each one and the water level in the neighbouring depressions. The solver is able to do this by adopting new ways of resolving the detailed hydraulics.

The solver is often used in conjunction with the ADI and TVD solvers on large-scale projects. The FAST solver is first used to quickly identify flood ‘hot spots’, allowing these areas to be modelling in more detail using the ADI or TVD solvers.

2D GPU solver

Coming in Flood Modeller 5.1 (September 2021), the new 2D GPU solver harnesses the power of modern graphics processing unit (GPU) hardware to provide 2D modelling results fast. It is compatible with NVIDIA GPU hardware and delivers significant speed increases, whilst retaining similar levels of detail and accuracy, when compared to the standard 2D ADI and TVD solvers. It allows you to improve your modelling capabilities, by incorporating higher cell resolution and larger extents into your models, enabling more accurate and detailed results.

How do the solvers compare?

Below is a comparison table to show you the main features of the three 2D solvers in a snapshot.

For further information detailing how Flood Modeller’s 2D solvers can be applied, visit our case study page or contact our technical support team.

Register for our introduction to 2D modelling training course to learn how to use all three 2D solvers as well as to be introduced to 1D-2D modelling.


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