Test cases and benchmarks

We have used a wide range of test cases to assess 2D Solver's performance during development and before release.These cases have results from laboratory experiments, analytical solutions or other models can to evaluate 2D Solver's results. A selection are described below.

Flow up a planar beach

This case models flow with a uniform velocity on a planar beach with slope of 10^-3. For a rectangular model domain, the flow is one dimensional in nature and the water depth can be described by the following equation:

S₀ is the beach slope, h the water depth, n Manning's roughness and u the velocity. This is solved with Euler's method to give the water surface profile, which is than used to evaluate the 2D Solver model of the same scenario. More details of this solution can be found in Horritt (2002) (Evaluating wetting and drying algorithms for finite element models of shallow water flow , Int. J. Numer. Meth. Engng., 55: 835–851. doi: 10.1002/nme.529).

Water levels predicted by ADI solver models, with cell size 5 m, for velocities 0.1, 0.5 and 1.0ms^-1, are compared with the analytical solutions in the figure below. Root-mean-square errors between the 2D Solver and the surface profile derived from the analytical solution are <1 mm.

Water level profile for flow up a planar beach for three velocities.

Flow along a flat floodplain

This test case is similar to the flow up a planar beach, but with S₀ set to zero. The equation can then be integrated analytically, typically giving steeper water surface slopes than in the planar beach case.

Figure below compares water levels predicted by an ADI solver model, with cell size 5 m, with the analytical solution. Root-mean-square errors are ~10 mm.

Water level profile for flow along a flat floodplain.

Hydraulic jump

This case models uniform, supercritical flow down three different slopes, with a hydraulic jump at the transition to deeper, subcritical flow. The TVD solver is used to represent these transcritical flows. Uniform flow depths down the slope (y₁) and the ratio of sequent to initial depth (y₂/y₁) have also been calculated according to Manning's equation and the equation describing depths associated with a hydraulic jump:

The Manning's roughness n for this test is 0.03 and the specific discharge q is 2m²s-1. Model cell size is 2 m.

The results (see figure below) show that TVD solver performs well in representing uniform flow conditions down the slope (depth errors<10mm), and that the ratio of sequent to initial depths in the jump is also well predicted.

Water level profiles of slope and hydraulic jump for three slopes. Comparison between initial depths and sequent/initial depth ratio are shown on the right.

Dam Break in Laboratory Flume

This tests the TVD solver's ability to represent moving shocks and waves in a laboratory investigation of dam break flow round a solitary object. The experimental setup up is shown in the Figure below. Water depths were measured at 6 points over a period of 30s, recording the dynamics of waves and jumps as the wave is released from behind the gate and impinges on the obstacle.

The 2D solver model uses a cell size of 0.1m, with initial conditions a water depth of 0.4m in the flume to the left of the gate, and dry to the right. The results in Figure below show that 2D solver is predicting well both the peak water depths and the time of arrival of the waves in the flume, for both sub- and supercritical regions.

Experimental set up for dam break validation data (top, with the six measurement locations G1 - G6), and results of 2D solver modelling (blue lines) and laboratory measurements (black lines).