Flow by shallow water equation

Update: June 1, 2017

OpenFOAM 4.x

Case directory

$FOAM_TUTORIALS/incompressible/shallowWaterFoam/squareBump

Summary

The shallow water equation is used to calculate the flow in a system where the velocity distribution in the depth direction can be ignored. The equations to be solved are as follows.

${\partial\over\partial t}(h \vec{u})+\nabla\cdot(h \vec{u}^T \vec{u})+f\times h\vec{u} = - \left \vert \vec{g} \right \vert h \nabla(h + h_0) + \tau^\omega - \tau^b$

${\partial\over\partial t}(h + h_0)+\nabla\cdot(h \vec{u}) = 0$

where h and u are the fluid depth (fluid surface height) and velocity vector, respectively. The f is the Coriolis force, g is the acceleration of gravity, h₀ is the deviation from the mean fluid depth, and τ^ω and τ^b are the stresses from the fluid surface and bottom, respectively.

Fluid flows in from the region "inlet" (red part) at a velocity of (0.1, 0, 0) m/s and out from the region "outlet" (green part). The walls of the channel (blue part) are set to slip wall conditions, and the calculation is performed as a 2-dimensional problem with a single mesh in the Z direction. The fluid depth is set to 0.009 m only in the center of the channel and 0.01 m in the other areas.