[saumavadey]

Hello!

I am developing a multi-region solver for coupling water flow over the overland surface and through stream networks using the diffusive model of Saint Venant equations. My simulation region consists of two regions: overland and channel. At the interface of the overland region, I need to exchange a flux with the channel region. The flux is one-way (overland to channel) or two-way (overland to channel and vice versa) based on a parameter Zb (bank elevation).

The flux calculations are as follows:

if (Zb > hc)
Qoc = Cd*(ho - Zb)^1.5
Qco = 0

else
Qoc = Qco = Cd*((ho - hc)^0.5)*(ho - Zb)

ho = flow depth in the overland region
hc = flow depth in the channel
Cd = a constant
Qoc = flux from overland to channel
Qco = flux from channel to overland

I seek help in how to implement it as a boundary condition on the coupled interface.

I desperately need some help as my whole work has got stuck for some time due to this.