Implement Inflow Boundary Condition

[ole]

Create boundary object that can apply a hydrograph to a boundary segment. The units are cubic meters per second and it should be time varying.

The challenge is to estimate the depth along the boundary segment based on Manning's formula and the slope into the domain.

Q = V*A
V = R^{2/3} * S^{1/2}/n

Where 
Q is the inflow [m^3/s]
A is the area of the boundary cross section
V is the estimated velocity
R is the perimeter width ~ estimated depth
S is the slope of the energy line ~ inward bedslope

the estimated quantities may be the result of an iterative process. Please comment on this everyone.

[ole]

Ted Rigby sent the following description through on 15th April 2009:

Along an inflow boundary depth and velocity will vary (faster where deeper). Averaging momentum would not be realistic. I attach a rather quick python like (I hope) outline of how the inflow boundary elevation is traditionally estimated in fortran. assume boundary flow is normal - imposes need on user to make boundary reasonably sensible for each triangle on bdry ! (w is triangle base width along bdry -- as in Q= r^{5/3 *(w/n*sqrt(S))}

calculate the triangles slope normal to the bounadary (impose min of say 1/1000) ensure flow calculate q(i) = w/n *sqrt(S)

for elevation of water surface in range (lowest plus a bit to heaps, inc by reasonable small amount)

compute Q=sum(r(i)^{5/3 * q(i)) ! this is Q for that elevation assuming normal depth flow at the bdry if Q > Qtarget gone past use linear interp to obtain elev at Q compute momentum associated with each triangle on bdry for that elev and Q apply to model}

some cleverer code uses a crude estimate of elev made along the lines you suggested and the algorithm coded to converge on the correct elev within a tolerance All use iteration though -- I know of no direct solution for computing the elevation for a Q Some funnies to watch

it is critical that Q is accurately transfered into the model (mass balance) - does not matter if v and d are individually a bit out. at low flow will not engage all triangles along inflow bdry at high flow elev may be above nodes at end bdry string at any flow elev may intersect part way between nodes triangles may quickly alter in slope downstream of the bdry (for real or because of user alteration) so above is not a realistic solution. Elevation will in reality be controlled by downstream water levels in subcritical flow and by upstream conditions if super. As noted not a problem as long as Q is accurate.