Re: [Anuga-user] Modeled discharge doesn't match input discharge?

[Gareth D. <gar...@gm...>]

Hi Kyle,

There are 2 issues to consider: How to force the boundary, and how to 
back-calculate the fluxes.

## Forcing the boundary ##

Can you explain this a bit more?:
**For physical reasons, I would prefer to prescribe this discharge using 
a Dirichlet boundary condition (rather than an inlet + reflective BC).**

Without some more context, I'd think the best approach would be "inlet + 
reflective". This has the advantage of ensuring the mass inflow is 
exactly as desired.

In ANUGA, it is hard to control the boundary fluxes using boundary 
conditions, because the boundary condition is used to compute the 
"boundary edge flow state as viewed from outside the domain". The latter 
is combined with the interior flow state to compute the flux (with the 
approximate Riemann solver). Thus with boundary conditions, the flux 
depends on the flow inside the model, as well as the boundary condition, 
and so is hard to control.


## Back-calculate fluxes ##

A discharge measurement based on the raster (like in your snippet below) 
will be inaccurate to some extent. ANUGA outputs flow quantities at 
centroids, but it is difficult to directly access the fluxes. The 
variables like "uh/vh" at centroids will not be the same as the mass 
fluxes at edges, even at steady state, because the edge fluxes are 
computed with the approximate Riemann solver. This is separate to any 
"raster interpolation error", which might also be substantial if the 
channel is small.

To directly measure the flux when debugging the model, one approach is 
to cut a "pit" somewhere in your domain just downstream of the channel, 
to catch all the flow. Then check how quickly the pit fills.

Cheers,
Gareth.


On 2/4/19 9:39 am, Kyle A Wright wrote:
> Hi,
>
> I am currently using Anuga to model a river delta, and need a 
> discharge inflow at the upstream boundary. For physical reasons, I 
> would prefer to prescribe this discharge using a Dirichlet boundary 
> condition (rather than an inlet + reflective BC). I have tried 
> multiple boundary conditions for this input, including: the default 
> Dirichlet, the Dirichlet_discharge_boundary, the Inflow_boundary, and 
> one additional BC module I wrote that uses discharge and stage as 
> inputs. I have tested all of these on a simplified case, and with 
> minor differences, all appear to work fine.
>
> Here is my problem: when I use these BCs on my full domain, the 
> discharge I am measuring across the upstream channel (~780 m3/s) is 
> much lower than the discharge I am prescribing at the boundary (1620 
> m3/s). I do not know if this discrepancy is due to the BC, to the 
> model evolution, or the data post-processing. Has anybody else 
> encountered this problem, and does anybody know what the issue is?
>
> For context, I have even tried multiplying the inflow by the 
> fractional difference in the model results (2.09x), and the resulting 
> discharge was still too low (~1300 m3/s). Aside from the discharge, 
> everything about the model evolution appears normal.
>
> A simplified version of the code/workflow, if needed:
>
> ### Compute inflow:
> Q = 1620# [m3/s]
> upstream_stage = 0.74 # [m]
> z = pd.read_csv('channel_profile.csv', names=['elev']) # reads in 
> 1-meter-res csv of elevations along the boundary
> z = np.array(z['elev'])
> profile = -z[z <= upstream_stage] + upstream_stage # to find channel area
> mean_depth = np.mean(profile)
> channel_area = np.trapz(profile)
> U = Q / channel_area
> momentum_in = mean_depth*U
>
> ### [establish domain, mesh, topography, etc. Manning's is n=0.03 in 
> channel]
>
> ### Inflow BC is one of the following:
> Bin = 
> anuga.shallow_water.boundaries.Dirichlet_discharge_boundary(domain, 
> stage0 = upstream_stage, wh0 = momentum_in)# my default choice
> Bin = anuga.Dirichlet_boundary([upstream_stage, x_momentum_in, 
> y_momentum_in]) # equivalent to above, requires computing x,y components
> Bin = anuga.shallow_water.boundaries.Inflow_boundary(domain, rate = Q) 
> # requires changing the mesh boundary & gives unrealistic depths, but 
> still results in a discharge
> Bin = 
> anuga.shallow_water.boundaries.Dirichlet_Q_stage_boundary(domain, rate 
> = Q, stage = upstream_stage) # I wrote this to work like an 
> Inflow_boundary, but uses a prescribed stage instead of a calculated 
> one, and only applies it over BC edges with elevation < upstream_stage
>
> domain.set_boundary({'upstream: Bin, 'bay': Bout, 'sides': Br})
>
> ### [run model, save SWW]
>
> ### Post-processing:
> anuga.utilities.plot_utils.Make_Geotif(
>      swwFile = swwname,
>      output_quantities = ['depth', 'velocity', 
> 'depthIntegratedVelocity'],
>      myTimeStep = 100,
>      CellSize = 10.0,# cell size of raster in meters
>      proj4string = '+proj=utm +zone=15 +datum=NAVD88 +units=m +no_defs',
>      k_nearest_neighbours = 3) # number of nearest neighbors for 
> interpolation (I've tried = 1)
>
> ### [load in raster, sum depthIntegratedVelocity across transects of 
> the upstream channel, multiply by cell size. Resulting Q is too low]
>
> Any help or insight would be greatly appreciated.
> -- Kyle
>
> *----------------------------------------------------------------------------------------*
> *Kyle Wright*
> The University of Texas at Austin
> Department of Environmental & Water Resources Engineering
>
>
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