$FOAM_TUTORIALS/incompressible/shallowWaterFoam/squareBump

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.

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, h_{0} 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.

Model geometry

Definition of fluid depth

The meshes are as follows.

Meshes

To visualize the fluid depth, Check "h" in the "Properties" tab on ParaView.

Check h

The calculation result is as follows.

Depth distribution of fluid (h)

Depth distribution of fluid at 0 second (h)

Depth distribution of fluid at 1 second (h)

Depth distribution of fluid at 100 seconds (h)

We can see how the wave is generated at the central projection and then approaches the steady state.

cp -r $FOAM_TUTORIALS/incompressible/shallowWaterFoam/squareBump squareBump

cd squareBump

blockMesh

shallowWaterFoam

paraFoam

cd squareBump

blockMesh

shallowWaterFoam

paraFoam

4.87 seconds *Single, Inter(R) Core(TM) i7-2600 CPU @ 3.40GHz 3.40GHz