Dam Reservoir Boundary Condition

At the surface of fluid-structure, it is clear that there must be no flow across the interface. This is based on the fact that face of the concrete dams are impermeable. This results into the condition that at the normal to the boundary there is no relative velocity or another word we can write it mathematically:

< = vn in which n is the unit normal vector to the boundary at the dam-reservoir interface and vn and vn are the velocity of the structure (dam) and fluid along the n respectively (figure 2.16). The above equation can be rewritten as following:

Differentiating the above equation with respect to time will give:

dvss dv

It must be noted that n is normal to the surface and it direction is constant as well as its value at a point. From the Euler equation and knowing that ^Vf is normal acceleration of the dam at the interface we can write:

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