Boundary conditions

**periodic boundary conditions**

These conditions hold for , , and on opposite faces of .**Dirichlet boundary conditions**

On subsets Dirichlet conditions may be defined. The same b.c. hold for , i.e. . These b.c. lead to homogeneous Neumann conditions for the pressure on . If or is calculated, Dirichlet b.c. for these quantities have to be specified on .**Slip conditions**

Here, homogeneous Dirichlet conditions hold for the normal velocity component and homogeneous Neumann conditions for the tangential velocity components. The same b.c. hold for . These b.c. lead to homogeneous Neumann conditions for the pressure .**Outflow boundary condition I**

On faces of homogeneous Neumann b.c. for the velocity may be defined as**Outflow boundary condition II**

Alternatively a boundary condition of convective type can be applied at outflow boundaries, i.e. it consists of a discretization of- If no Dirichlet or periodic boundary conditions are specified, then homogeneous Neumann conditions are assumed for and .