Flow over a bump

UNDER CONSTRUCTION

Setup

The spatial domain consists of a rectangular domain with the bed elevation $z_{b}$ given by \begin{equation} \tag{1}

 z_b = 
 \begin{cases} 
    0, & \mbox{if } x<8  \\ 
    0.2-0.05(x-10)^2, & \mbox{if } 8 \leq x \leq 12 \\
    0, & \mbox{if } x>8  \\ 
 \end{cases}

\end{equation}

where $x$ is the horizontal distance.

Table 1. General Settings for Flow over a Bump

Parameter	Value
Discharge	0.18 m^3/s
Downstream water level	0.33 m
Bottom friction	None

Model Setup

Figure 1. Computational grid.

The computational domain is 25 m long and has a constant grid resolution of 0.1 m. A flux boundary condition is specified at the inflow boundary and a constant water level boundary condition is applied to the downstream boundary. An adaptive time between 0.1-1 s is applied. The computational time on a single processor is approximately 1 min.

Results

Figure 2. Comparison of analytical and calculated water surface elevations and bed elevations.

A comparison between the analytical solution for water levels is compared to the calculated water levels in Figure 2. As shown in the goodness of fit statistics, the model results agree well with the analytical solution. The minimum water level is captured well, however there is a small shift in the location of the water level drop over the bump toward the downstream direction.

Table 2. Goodness of fit statistics for the water elevation

Statistic	Value
RMSE	0.0074 m
NMAE	0.0068
R^2	0.991
Bias	0.0017 m

• For a definition of the goodness of fit statistics see Goodness of fit statistics.

References

• Caleffi, V., Valiani, A., and Zanni, A. (2003). "Finite volume method for simulating extreme flood events in natural channels," Journal of Hydraulic Research, 41(2), 167-177.

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