Free-Stream

Velocity

For supersonic inflow, the velocity is taken to be the free-stream velocity, computed from the specified Mach number and temperature.

For supersonic outflow, the boundary face velocity is extrapolated from the cell value using reconstruction gradients.

For subsonic inflow, the tangential component of the free-stream velocity is combined with the boundary normal velocity computed from characteristics as follows:

(127)

where is the component of free-stream velocity normal to the boundary and is the boundary normal velocity obtained from characteristics:

(128)

In this expression, is the normal component of the boundary velocity extrapolated from the cell. is the speed of sound obtained from the free-stream temperature. is the speed of sound obtained from , the boundary temperature extrapolated from the cell, that is:

(129)

For subsonic outflow, the tangential component of the boundary velocity, extrapolated from the cell using the reconstruction gradient , is combined with the boundary normal velocity computed from characteristics. The result is:

(130)

where is again computed using Eqn. 128.

Pressure

For supersonic inflow, the pressure is taken to be the free-stream pressure.

For supersonic outflow, the boundary face pressure is extrapolated from the adjacent cell value using reconstruction gradients.

For subsonic inflow, the pressure is computed from the free-stream pressure using the following isentropic relation:

(131)

For subsonic outflow, the pressure is computed from the adjacent cell value using the following isentropic relation:

(132)

Temperature

For supersonic inflow, the boundary face temperature is taken to be the free-stream temperature.

For supersonic outflow, the boundary face temperature is extrapolated from the adjacent cell value using reconstruction gradients.

For subsonic flow, the boundary face temperature is computed as:

(133)

where:

(134)