4.14 Direction mixed condition

In some cases, a boundary condition is sometimes needed which applies a different underlying type — fixed value or gradient — to different components of a non-scalar field.

PICT\relax \special {t4ht=

The condition is most readily applied to velocity eqn, where different conditions are applied to its normal and tangential components to the patch, eqn and eqn respectively.

The direction mixed condition combines the mixed condition from Sec. 4.9 with the transform conditions of Sec. 4.11 . The mixed condition can be first expressed in the form of a general transform condition Eq. (4.13 ) as

 rn---b- f = v b + (1 v) C + P : \relax \special {t4ht=
In the direction mixed condition the value fraction eqn is replaced by a transformation tensor eqn, whose components are value fractions in the range 0 to 1, by
 rn b f = G(Y; b)+ G [I Y] ; ------+ P : C \relax \special {t4ht=
The value fraction tensor eqn is set according to the requirements of the boundary condition which is derived from this direction mixed framework.

PICT\relax \special {t4ht=

Imagine an example of eqn at a face oriented with normal vector eqn, for which the eqn condition is fixed gradient and eqn is fixed value. The value fraction must be 1 in the tangential direction and 0 in the normal direction, which gives:

 0 1 B 0 0 0 C Y = I nfnf = @ 0 1 0 A : 0 0 1 \relax \special {t4ht=
The boundary condition is then implemented similarly to the symmetry and wedge conditions of Sec. 4.12 and Sec. 4.13 . First, eqn is the calculated eqn using current eqn by Eq. (4.23 ) and the explicit gradient eqn is calculated from Eq. (4.17 ).

The factor eqn corresponds to eqn. For a vector field, it is calculated, as in the symmetry condition in Eq. (4.19 ), by

 p -- = diag( Y): \relax \special {t4ht=
For a tensor eqn, the factor is eqn, where eqn are the coeffcients for a vector, as described for the symmetry condition in Sec. 4.12 .

The condition is implemented using value and gradient factors according to the transform condition, summarised in the table on page 284 . Any boundary condition which is based on this direction mixed condition then only requires a description of the eqn, eqn and eqn parameters.

Notes on CFD: General Principles - 4.14 Direction mixed condition