1.4 Limitations and Recommendations

TUFLOW is designed to model free-surface flow in coastal waters, estuaries, rivers, creeks, floodplains and urban drainage systems using the 1D St Venant Equations (all physical terms) and the 2D form of the free surface Navier-Stokes equations (all physical terms) often referred to as the Shallow Water Equations (SWE). Flow regimes through structures are handled using standard structure equations covering all flow regimes, and supercritical upstream controlled flow is supported in the 1D and 2D solvers. The 2^nd order spatial solutions produce negligible numerical diffusion. TUFLOW HPC also supports non-Newtonian flow and mixed flow (Newtonian and non-Newtonian).

However, all solutions are approximations to reality. Whilst TUFLOW’s solvers have industry leading accuracy and have been comprehensively benchmarked to known solutions or measurements, they have their limitations, with the key ones discussed below.

• All models, irrespective of the software, require a sufficiently fine computational resolution to not limit the model’s accuracy. Demonstrating results convergence, that is that the results do not demonstrably change when the computational interval (timestep) or 2D cell size is reduced, is an important quality control test. TUFLOW’s solvers have been extensively benchmarked for results convergence and new features such as TUFLOW HPC’s Sub-Grid Sampling (SGS) can greatly assist with improving results convergence. However, no matter the solution or software, results convergence testing during the model design phase should be a standard test.

• Where super-critical flow occurs the results should be treated with caution, particularly if they are in key areas of interest. Hydraulic jumps and surcharging against obstructions are complex 3D flow phenomena. For example, for hydraulic jumps, 1D solutions simply show a change from supercritical to subcritical flow from one computational point to the next. Both TUFLOW Classic and TUFLOW HPC 2D solvers will handle the transition and provide higher resolution output than 1D. However, TUFLOW HPC will produce a more accurate solution due to its shock capturing formulation. Where vertical acceleration is important, such as flow down a dam spillway face, both the 1D and 2D equations are not suited to modelling the flow in detail, however, the quantity of flow passing through such a structure can be well represented by using a spillway structure in 1D or for TUFLOW HPC varying the weir flow parameters introduced for the 2023‑03 release.

• The TUFLOW HPC Wu turbulence model, as of the 2020‑01 release, is recommended over the Smagorinsky eddy viscosity formulation, which in turn is preferred over the constant viscosity formulation to model sub-cell turbulence (Barton, 2001; Collecutt et al., 2020). As of the 2020-01 release, the default approach for TUFLOW HPC is the Wu turbulence model and for TUFLOW Classic the Smagorinsky approach (as the Wu model has not yet been built into the Classic solver). It is always good practice to carry out sensitivity tests to ascertain the importance of the sub-cell turbulence coefficient(s) and formulation, which will be most influential where the bed friction is low (e.g. in tidal reaches and coastal waters) and where there are significant changes in velocity direction and magnitude, causing sub-grid shear effects (e.g. downstream of a constriction).
  
  If using the Smagorinsky formulation, caution is needed when using 2D cell sizes where the flow depth is larger than the cell width (Barton, 2001; Collecutt et al., 2020). Modelling on a fine resolution where water depths are greater than the cell size will likely not produce converging results with decreasing cell size. For this reason, the default in TUFLOW Classic since the 2000s is the combination of the Smagorinsky formulation with a constant eddy viscosity. This is because the Smagorinsky formulation tends to a no turbulence state with reducing cell size, with the small addition of constant eddy viscosity offsetting this trend.
  
  Collecutt et al. (2020) demonstrates that the constant coefficient is heavily dependent on the 2D cell size and needs to be calibrated. The default Smagorinsky and constant coefficients in TUFLOW Classic can be considered suitable for most real-world applications where the cell size is similar or greater than the depths in the main flowpaths.
  
  The Wu turbulence model (default setting in TUFLOW HPC from the 2020‑01 release) resolves the above issues with benchmarking demonstrating 2D models can confidently be constructed and utilised across a wide range of cell sizes (flume scale to major rivers), even when much less than the depth (Collecutt et al., 2020).

• Modelling of hydraulic structures should always be cross-checked with desktop calculations or other software, especially if calibration data is unavailable and/or the structures are located in key areas. All 1D and 2D schemes are only an approximation of the complex 3D flows that can occur through a structure, and regardless of the software used, the modeller should check model performance (Syme et al., 1998; Syme, 2001a).

• There is no momentum transfer between 1D and 2D connections when using the sink/source connection approach (SX link). The HX link does preserve momentum in the sense that the velocity field is assumed to be undisturbed across the link, but the velocity direction is not influenced by the direction of the linked 1D channel. In most situations these assumptions are not of significant concern, however, they may influence results where a large structure (relative to the 2D cell size) is modelled as a 1D element. Under such circumstances, TUFLOW has a range of options for modelling large structures in the 2D solution scheme. Modelling fully in 2D will preserve the momentum transfer.