Theory for the Wall Boundary Condition
See Wall for the node settings. Note that some modules have additional theory sections describing options available with that module.
Slip
The No Slip condition assumes that there are no viscous effects at the slip wall and hence, no boundary layer develops. From a modeling point of view, this is a reasonable approximation if the important effect of the wall is to prevent fluid from leaving the domain. Mathematically, the constraint can be formulated as:
The no-penetration term takes precedence over the Neumann part of the condition and the above expression is therefore equivalent to
expressing that there is no flow across the boundary and no viscous stress in the tangential direction.
For a moving wall with translational velocity utr, u in the above equations is replaced by the relative velocity urel = uutr.
Sliding Wall
The sliding wall option is appropriate if the wall behaves like a conveyor belt; that is, the surface is sliding in its tangential direction. The wall does not have to actually move in the coordinate system.
where t = (ny , nx) for 2D and t = (nz, −nr) for axial symmetry.
The normalization makes u have the same magnitude as uw even if uw is not exactly parallel to the wall.
Constraint Settings
The wall feature uses three different techniques to constraint the velocity field:
The main advantage of pointwise constraints is that they enforce the constraint exactly pointwise. This means that they do not introduce any leakage of the velocity across the wall, unless specified. The main disadvantage of pointwise constraints is that they introduce locking effects when trying to impose a no penetration condition for the velocity, u · n = 0, on curved walls or walls with sharp corners.
Using Weak constraints is an alternative method to prescribe the velocity. It consists on enforcing the boundary condition for the velocity via Lagrange multipliers. Their main advantage is that the Lagrange multiplier can provide an accurate representation of the reaction flux at the wall. Their main disadvantage is that they introduce extra unknowns, and are usually difficult to combine with other constraint methods on adjacent boundaries. Moreover, they may require extra constraints for the Lagrange multipliers. For more information, see Weak Constraints in the COMSOL Multiphysics Reference Manual.
The following combination of Constraint techniques can be selected in the Constraint Setting sections of Wall boundary conditions:
Use default settings. The default settings use different constraint methods depending on whether only the normal component of the velocity is prescribed, such as in the no penetration condition, u · n = 0, imposed for example in Slip walls or No Slip walls using Wall Functions or Automatic Wall Treatment, or both tangential and normal components are prescribed, as is the case of No Slip walls in laminar flow.
DG constraints are used to impose the no penetration condition for Slip walls. When a No Slip condition is prescribed, pointwise constraints are used except for moving walls where DG constraints are used.