4.1 Boundary mesh

Sec. 3.2 describes the computational mesh used by the finite volume method. It identifies a domain boundary by faces which are connected only to one cell. The boundary faces are grouped into patches, each under a unique name, corresponding to different regions of the boundary. Boundary conditions are then applied to each patch to provide a representative solution to the case of interest.

PICT\relax \special {t4ht=

In the example of flow in a pipe, it would be logical to split the boundary into 3 patches in order to specify inflow, outflow and solid walls; and, inlet, outlet and wall would be logical names for these patches.

Patch geometric data

The geometry of a patch is described using face data described in Sec. 3.3 , including:

  • the face area vector eqn, with area magnitude and direction eqn;
  • the face unit normal vector eqn;
  • the face centre eqn.

The cell connected to each patch face is denoted by the subscript “P”, e.g. the cell centre is denoted eqn.

PICT\relax \special {t4ht=

Patch deltas

Sec. 3.8 describes the “delta” eqn for each face as the vector connecting the centres of its owner and neighbour cells. eqn is defined differently for a patch face since it has no neighbour cell.

PICT\relax \special {t4ht=

The delta is defined as the component of eqn in the face normal direction. The surface gradient eqn is orthogonal to the face, which eliminates the error associated with non-orthogonality, at the expense of introducing a skewness error. Taking the inner product with eqn gives the magnitude which is then multiplied by eqn to assign the direction, i.e.

d = nf(nf (Cf CP)) \relax \special {t4ht=
The delta coefficients are eqn, as defined in Sec. 3.8 . The delta coefficient eqn, representing “inverse distance”, is a critical parameter in the discretisation of boundary conditions.
Notes on CFD: General Principles - 4.1 Boundary mesh