CFD-FVM-12: Implementation of boundary conditions

Introduction

The most common boundary conditions:

• inlet
• outlet
• wall
• prescribed pressure
• symmetry
• periodicity (or cyclic boundary condition)

Note that additional nodes outside the boundary are required to store values that correlate with the boundary conditions, as shown in the figure below:

In this chapter, we make the following assumptions:

• the flow is always subsonic (M < 1),
• turbulence modelling is used,
• the hybrid differencing method is used for discretisation and
• the SIMPLE solution algorithm is applied

Inlet boundary conditions

Figures 9.2 to 9.5 show the grid arrangement in the immediate vicinity of an inlet for - and -momentum, scalar and pressure correction equation cells.

The figures indicate that all links to neighbouring nodes remain active for the first -, - and -cell, so to accommodate the inlet boundary condition for these variables it is unnecessary to make any modifications to their discretised equations

Figure 9.4 shows that the link with the boundary side is cut in the discretised pressure correction equation by setting the boundary side (west) coefficient equal to zero. Since the velocity is known at inlet, it is also not necessary to make a velocity correction here and hence we have

Outlet boundary conditions

If the location of the outlet is selected far away from geometrical disturbances the flow eventually reaches a fully developed state where no change occurs in the flow direction. In such a region we can place an outlet surface and state that the gradients of all variables (except pressure) are zero in the flow direction.

Before the relevant equations are solved the values of flow variables at the next node (NI), just outside the domain, are determined by extrapolation from the interior on the assumption of zero gradient at the outlet plane.

To make the mass flux out equal to the mass flux coming into the domain all the outlet velocity components are multiplied by the ratio . Thus the outlet plane velocities with the continuity correction are given by

Wall boundary conditions

See original book for how to deal with Laminar flow / linear sub-layer and Turbulent flow near wall.

The constant pressure boundary condition

Typical problems where this boundary condition is appropriate include external flows around objects, free surface flows, buoyancy-driven flows such as natural ventilation and fires, and also internal flows with multiple outlets.

A convenient way of dealing with a constant pressure boundary condition is to fix pressure at the nodes just inside the physical boundary, as indicated in the diagrams by solid squares.

Symmetry boundary condition

The conditions at a symmetry boundary are:

• no flow across the boundary
• no scalar flux across the boundary.

Periodic or cyclic boundary condition

Easy to understand, see original book for details.