2D TVD Solver

Achieve accurate and stable results for complex two-dimensional hydraulics

The 2D TVD solver has specifically been developed to provide an accurate representation of two-dimensional 'shocks' (rapid changes in water surface profile) which address the limitations of the 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.

Key facts

  • Provides quick, accurate and robust model simulations

  • Dynamic linking to Flood Modeller's 1D river and 1D urban solvers to enable an integrated modelling approach

  • TVD scheme can be run using a GPU to accelerate run times

  • Allows complex hydraulics to be calculated more accurately – particularly useful with dam breaks and breaches in defences

  • Multiple 2D domains can be used to represent different areas of a floodplain at different resolutions.

  • Provides a range of analysis and visualisation tools 

  • Run your simulations using the Flood Cloud service

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.

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. Additionally, you can seamlessly load flood extents, as well as other shapefiles and images, to Flood Viewer to easily share model results with others. 

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.

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.