Boundary Conditions for the Momentum Equation
Categorizing Boundary Conditions
Physics Dirichlet Neumann Robin
Solid Mechanics Displacement Traction (stress) Spring
Heat Transfer Temperature Heat flux Convection
Pressure Acoustics Acoustic pressure Normal acceleration Impedance
Electric Currents Fixed potential Fixed current Impedance
Computers have enabled us to solve the Navier–Stokes equations numerically for much more complicated flows using computational fluid dynamics (CFD)

The Periodic or Cyclic boundary condition defines a cyclic/repeating situation of the flow across the boundary surface. Tt is mandatory to select two boundary faces that will be treated as if they are physically connected. The flow exiting/entering from one face then enters/exits the other face (ocean!)

\(\text{No-Slip Wall Boundary} \left(p_b = ?;\, \dot{m}_b = 0;\, \mathbf{v}_b = \mathbf{v}_{\text{wall}}\right)\)

NoSlipWallBoundary

\(\text{Slip Wall Boundary} \left(p_b = ?;\, \dot{m}_b = 0;\, \mathbf{F}_b = 0\right)\)

SlipWallBoundary

1 Henrik Sönnerlind. (2016). How to Make Boundary Conditions Conditional in Your Simulation. COMSOL Blog

2 F. Moukalled, L. Mangani, M. Darwish. (2015). The Finite Volume Method in Computational Fluid Dynamics: An Advanced Introduction with OpenFOAM® and Matlab. Springer Cham.