In many simulations, fluid must flow out one or more boundaries of the computational region. But what constitutes a good boundary condition at such “outflow” boundaries?

In compressible flows, when the flow speed at the outflow boundary is supersonic, it makes little difference how the boundary conditions are specified since flow disturbances can’t propagate upstream. However, in low speed and incompressible flows disturbances introduced at an outflow boundary can affect the entire computational region.

Continuative Approximation

The simplest and most commonly used outflow condition is that of a “continuative” boundary. Continuative boundary conditions consist of zero normal derivatives at the boundary for all quantities. The zero-derivative condition is intended to represent a smooth continuation of the flow through the boundary.

It must be stressed that the continuative boundary condition has no physical basis; it is a mathematical statement that may or may not provide the desired flow behavior. In particular, if flow enters the computational region across such a boundary, then the computations may be wrong because nothing has been specified about flow conditions existing outside the boundary.

Improved Continuative Approximation

FLOW-3D uses a special enhancement to continuative boundaries to improve their behavior. If flow attempts to enter the computational region across this type of boundary it must do so by starting from a condition of rest. This practice helps to reduce inflow and often results in a reasonable approximation of a smooth outflow condition. Nevertheless, a continuative boundary condition must always be viewed with suspicion.

Other Approximations

For limited classes of problems, better outflow boundary conditions do exist. For example, special boundary treatments have been devised for wave propagation problems that try to determine the speed and direction of waves approaching the boundary and then set boundary conditions so that they continue through the boundary with a minimum of reflection. A useful example of this type of treatment, sometimes called a radiation boundary condition, is described by I. Orlanski, Jour. Comp. Phys. 21, 251 (1976).

As a general rule, a physically meaningful boundary condition, such as a specified pressure condition, should be used at outflow boundaries whenever possible. When a continuative condition must be used it should be placed as far from the main flow region as is practical so that any adverse influence on the main flow will be minimal.