Flow over a bump: Difference between revisions

From CIRPwiki
Jump to navigation Jump to search
 
(5 intermediate revisions by one other user not shown)
Line 3: Line 3:
<font color=red>'''UNDER  CONSTRUCTION'''</font>
<font color=red>'''UNDER  CONSTRUCTION'''</font>
== Setup ==
== Setup ==
The spatial domain consists of a rectangular  
The spatial domain consists of a rectangular domain with the bed elevation <math>z_b</math> given by
  {{Equation| <math> z_b =  
\begin{equation} \tag{1}
\begin{cases}  
  z_b =  
0, & \mbox{if } x<8  \\  
  \begin{cases}  
0.2-0.05(x-10)^2, & \mbox{if } 8 \leq x \leq 12 \\
    0, & \mbox{if } x<8  \\  
0, & \mbox{if } x>8  \\  
    0.2-0.05(x-10)^2, & \mbox{if } 8 \leq x \leq 12 \\
\end{cases} </math> |2=1}}
    0, & \mbox{if } x>8  \\  
  \end{cases}
\end{equation}


where <math>z_b</math> is the bed elevation and <math>x</math> is the horizontal distance.
where <math>x</math> is the horizontal distance.


Table 1. General Settings for Flow over a Bump
'''Table 1. General Settings for Flow over a Bump'''
{|border="1"
{|border="1"
|'''Parameter'''
|'''Parameter'''
Line 30: Line 32:
== Model Setup ==
== Model Setup ==
[[Image:Bump_Grid.png|thumb|right|600px| Figure 1. Computational grid.]]
[[Image:Bump_Grid.png|thumb|right|600px| 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 x min.  
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.  


<br style="clear:both" />
<br style="clear:both" />
Line 41: Line 43:
Table 2. Goodness of fit statistics for the water elevation
Table 2. Goodness of fit statistics for the water elevation
{|border="1"
{|border="1"
|'''Statistic'''
|'''Statistic''' ||'''Value'''
|'''Value'''
|-
|-
|RMSE  
|RMSE || 0.0074 m
| 0.0074 m
|-
|-
|RMAE
|NMAE || 0.0068
| 0.0068
|-
|-
|R^2  
|R^2 || 0.991
| 0.991
|-
|-
|Bias  
|Bias || 0.0017 m
| 0.0017 m
|}
|}
* For a definition of the goodness of fit statistics see [[Statistics |  Goodness of fit statistics]].


<br style="clear:both" />
<br style="clear:both" />


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


----
----

Latest revision as of 14:36, 16 July 2012

UNDER CONSTRUCTION

Setup

The spatial domain consists of a rectangular domain with the bed elevation 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 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


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.

Test Cases

Documentation Portal