HPC Turbulence FAQ

Why are you changing the default turbulence representation in the 2020-01 TUFLOW HPC release as this means there will be some change in results from the 2018-03 release?

Turbulence is pronounced in areas of highly transient flow (high velocities, bends, ledges, flow contraction/expansion). Where the flow is more benign and/or bed roughness is high, turbulence is not so important as it only applies where there are strong spatial velocity gradients (for example, for uniform flow in a straight rectangular channel the turbulence term is zero as there is no spatial velocity gradient). The problem with the Smagorinsky form of turbulence closure (which is a large scale eddy turbulence model originally developed for coastal modelling) is that it is cell size dependent (is proportional to cell surface area) and tends to zero as the cell size tends to zero – this has historically not been a major issue as cell sizes have typically been greater than the depth, however, the general recommendation in the TUFLOW Manual is to be careful of using cell sizes significantly smaller than the depth based on research and knowledge at the time (see Section 1.4 of the Manual). However, as cells have been becoming finer and finer with the advent of GPU models this issue has increasingly emerged and is has become particularly pertinent if using a Quadtree or flexible mesh and very small cells relative to their depths are being used. TUFLOW, many years ago, changed from purely Constant or purely Smagorinsky to Smagorinsky plus (a small amount of) Constant. This improved absorption of eddies into the streamlines behind a bluff body (see Section 3.4 in this paper) and helped by varying degrees the modelling at finer cell sizes. However, an improved turbulence representation is needed for 2D schemes with fine-scale cells, preferably with parameter(s) that are valid across a wide range of hydraulic scales from flume model to large river systems. This need is especially the case for our new Quadtree mesh option and for flexible meshes as these meshes often incorporate fine-scale cells in areas of high flows.

Does this mean the Smagorinsky plus Constant turbulence model (pre TUFLOW 2020-01 default) is wrong?

The Smagorinsky/Constant turbulence combination has served the industry well and can continue to be used where the cell sizes are not significantly smaller than the depth where highly transient flows are occurring. If the model is well calibrated (using conventional parameters), continuing to use the Smagorinsky/Constant turbulence option is certainly an acceptable approach provided the model cell size is not reduced. If the model cell size is reduced in part or all of the model, it will be important to demonstrate consistent results occur compared with the coarser cell size(s). If the model is uncalibrated, the same principle applies, but the lack of calibration will imply greater uncertainty in the results.

What was the objective of the new turbulence approach?

Our aim was to have a turbulence scheme that, with the same parameter(s) produces accurate results across a wide range of scales from flume tests to large rivers, i.e. there is no or little need to calibrate the turbulence parameters like there is at the moment. The Wu turbulence seems to achieve this which is a major step forward for the industry. We’re not aware of any 2D modelling research or other software that has addressed the issue of turbulence at fine cell sizes and that can demonstrate the same parameter(s) apply to a wide range of hydraulic scales from flume to river. 2D schemes, as far as we’re aware, either omit the turbulence scheme or offer it using either the Constant or Smagorinsky approach (we believe TUFLOW is the only one that allows a combination of Constant and Smagorinsky, and now Wu).

What is numerical dispersion and why is it a problem?

1^st order spatial schemes are known to be numerically dispersive, which means that the solution stepping forward each timestep is less accurate than a higher order solution (an analogy would be fitting a line through three points is less accurate than a polynomial). The problem with numerical dispersion is that it has a similar effect to turbulence in that it diffuses (smooths out) the numerical solution, but it is, of course, totally unrelated to the physics of turbulence. Unfortunately, though, it may give the false impression of being an alternative or substitute for representing turbulence. 1^st order schemes will artificially create a steeper gradient due to the additional effects of numerical dispersion (this was observed with the first incarnation of HPC – called TUFLOW GPU – which was a 1^st order spatial solution and for early calibration of the Brisbane River modelling required lower Manning’s n values to calibrate compared with 2^nd order schemes). Numerical dispersion also helps stabilise a model, but for the wrong reasons. A 2^nd order scheme will have little or no measurable numerical dispersion, and typically becomes unstable or “bouncy” if the turbulence scheme is turned off. So, a 1^st order scheme can exhibit turbulence like effects and good stability but is not physics based and will not be as accurate as 2^nd order schemes. And 2^nd order schemes generally need turbulence to be stable, but the simplification of turbulence (which is extremely complex) down to a solution that is valid across a wide range of hydraulic scales has always been a challenge for 2D schemes. Of note is that 1D schemes cannot represent turbulence as they have no knowledge of flow in the 2^nd direction.

Is the best approach of currently available methods prior to the 2020-01 release to use a ‘Constant’ viscosity value with no Smagorinsky with calibration/validation/sensitivity testing being required to select an appropriate value for the particular system & grid size being modelled?

Constant may be able to be used provided a good calibration can be demonstrated across a wide range of flows. Prior to implementation and testing of the turbulence methods for 2020-01 release, Smagorinsky plus Constant would be the recommendation. For example, the very heavily calibrated Brisbane River model, which uses a cell size of 30 m (which is indicative of the maximum depth for major floods, so is about as fine as we’d like to go before the cell size is less than the depth effect kicks in), calibrates very well using the same combination of (conventional) Manning’s n values, minor additional energy losses on sharp bends (to cater for 3D secondary currents) and standard Smagorinsky/Constant eddy viscosity coefficients (TUFLOW defaults) across a wide range of hydraulic flows from tidal to five floods varying in magnitude from the 1 in 10 to the 1 in 100.

Up
Back to HPC Modelling Guidance