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A solver to simulate a channel water flow with Saint-Venant equation

Hi everyone

I need to simulate a channel water flow in an inclined slope. Saint-Venant equations are mostly used to model surface flow. So I programmed a solver with Saint-Venant equation and Manning's equation.

The continuity equation was:
$\frac{h}{t}$ + $\frac{\partial u}{\partial x}$ + $\frac{\partial v}{\partial y}$ + $\frac{\partial w}{\partial y}$ =Qrain

The Manning–Strickler formula is used for relating velocity to friction slopes
u= $\frac{h^{2/3}}{n_{man}}$ $\sqrt{S_{x}}$
v= $\frac{h^{2/3}}{n_{man}}$ $\sqrt{S_{y}}$
w= $\frac{h^{2/3}}{n_{man}}$ $\sqrt{S_{z}}$

Test case:
Rainfall continues for 30 min over a 183 m long parking lot (of Manning's
roughness 0.025) at an intensity of 1.4E-5 m/s, and then no rainfall for 30 min. The slope of the parking lot is 0.0016, just like the figure 1 shows.

The boundary of h(water depth) and U (velocity), are all set for zeroGradient.
I calculate the outflow rate at the end of the parking lot. Simulated water depth and outflow rate are increased for the first 30 min and then no change for the next 30 min, just like figure 2 shows.

However, compared with the analytical solution and other software's results, outflow rate are first increased and then reached steady status for the first 30 min rainfall time and then decreased for the next 30 min no rainfall time, just like figure 3 shows.

What could I do to change to adjust my results? the boundary condition for outflow? Or I should add the slope's elevation to the governing equation? Or the solver?

Can anyone please give me any advice?

Thank you very much for your attention!:):)

Hello!

I am trying to develop a solver similar to yours for simulating overland and channel flow. I am having difficulty in developing the critical depth boundary condition at the channel outlet.

Have you been able to solve your problem?

I need tips for solving the issue.

Hi All,

I also used the saint-vernant equations in openfoam. I found 3 nice project which helped me out:

- avalanche, which solves the equations in the coordinate along the slope and adds a centrifugal force for when the slope changes (https://develop.openfoam.com/Community/avalanche). Note the wrong implementation of the gravity in the shear stress formulations. It should only include the part normal to the bed.

- shallowFoam, which is only suitable for low slope angles. It does include depth averaged turbulence, which the previous one lacked (https://github.com/mintgen/shallowFoam). Described in his dissertation: Mintgen, F.: Coupling of Shallow and Non-Shallow Flow Solvers - An Open Source Framework. 2018. PhD dissertation. Technical University of Munich.

- Paper by Y Ni, Z Cao, Q Liu called: "mathematical modeling of shallow water on steep slopes" (https://scholar.google.com/scholar?q...n+steep+slopes)