Notes on Computational Fluid Dynamics: General Principles

4.18 Recommended boundary conditions

This chapter covers a range of boundary conditions and their implementations. It first describes a specification of the basic conditions at inlet, outlet and wall boundaries for subsonic flow with fixed value and zero gradient.

The conditions, based on the propagation of disturbances, are described in Sec. 4.3 :

• zero gradient on at an inlet, fixed value on other variables;
• fixed value on at an outlet, zero gradient on other variables.

The conditions at a wall are similar to an inlet for and , but generally are represented more directly by physical models, e.g. the condition for heat flux for .

Supersonic conditions

The basic conditions for supersonic flow are discussed in Sec. 4.5 . If the flow speed is supersonic at an inlet, the basic condition is fixed value for ; it is zero gradient for if the flow is supersonic at an outlet.

Robust, practical conditions

Section 4.6 introduced a free boundary that cannot be defined as an inlet or outlet, but instead often uses the following conditions:

• total pressure for , see Sec. 4.7 ;
• inlet-outlet-velocity for , see Sec. 4.15 ;
• inlet-outlet for , see Sec. 4.10.

These conditions also respond well at an outlet, in the event that some inflow occurs at startup, a rotating structure passes through the boundary etc., see Sec. 4.10 .

The freestream conditions, Sec. 4.16, are effective for cases with known and at a free, far-field boundary.

The symmetry and wedge conditions enable suitable cases to be simplified as symmetric and axisymmetric, respectively.

In the presence of a body force , the zero gradient condition for at inlets and walls should be replaced by a fixed gradient condition , see Sec. 4.4 .