Convective outflow

The convective outflow boundary condition models flow exiting the fluid domain without specifying the pressure. It lets the flow field exit and enter the flow domain on each element of the boundary as necessary conserving the mass.

At the centroids of each face element lying on the convective outflow boundary, the dependent variable fields, φ, are computed from a discretized form of the advection equation:

For the purposes of the above boundary condition equation, the advecting velocity field is taken as uniform, in the direction normal to the boundary. The solver computes the magnitude of the velocity, U, from the average velocity of all other flow boundaries to conserve mass of the flow domain.

To compute the diffusive and advective fluxes, the solver derives an expression for the values of the dependent variables at the boundary face elements as a function of the values at the nodes of the adjacent solid element, and imposes them implicitly.

For the mass equation on the convective outflow boundary, the flow solver computes the outflow velocity field explicitly based upon the current nodal field. It is then scaled to conserve mass, accounting for density variation with time.

Transient initialization

Because the temporal derivative is often dominant in the boundary value equation, a reasonable initial condition is crucial. Therefore, a small number of initializing steps are performed in which the outflow boundary is treated as an opening, to obtain a reasonable and conservative starting point for the solution of the evolution of the boundary field.

Steady state assumption

For better stability, in steady state runs, the flow solver computes the advected values from a zero-normal-derivative condition, with temporal derivative explicitly neglected. This assumption is true in the converged steady state solution. It removes the need for the initializing iterations and improves convergence and robustness. Because the conservation of mass is explicitly enforced over the entire domain, the pressure field at the outflow boundary can evolve naturally, so that the upstream flow features are not strongly influenced by nearness of the boundary.