# Transport equation based wall distance calculation

(Difference between revisions)
 Revision as of 00:33, 27 September 2005 (view source)Zxaar (Talk | contribs)← Older edit Revision as of 06:28, 3 October 2005 (view source)Zxaar (Talk | contribs) Newer edit → Line 18: Line 18: Where as the wall distance vector could be written as:
Where as the wall distance vector could be written as:
:$\vec d = d{{\nabla \phi } \over {\left| {\nabla \phi } \right|}}$ :$\vec d = d{{\nabla \phi } \over {\left| {\nabla \phi } \right|}}$ + + + + ---- + Return to [[Numerical methods | Numerical Methods]]

## Revision as of 06:28, 3 October 2005

### Wall-distance variable

Wall distance are required for the implementation of various turbulence models. The approaximate values of wall distance could be obtained by solving a transport equation for a variable called wall-distance variable or $\phi$.
The transport equation for the wall distance variable could be written as:

$\int\limits_A {\nabla \phi \bullet d\vec A} = - \int\limits_\Omega {dV}$

with the boundary conditions of Dirichlet at the walls as $\phi = 0$ and Neumann at other boundaries as ${{\partial \phi } \over {\partial n}} = 0$

This transport equation could be solved with any of the approaches similar to that of Poisson's equation.

### Wall distance calculation

Wall distance from the solution of this transport equation could be easily obtained as:

$d = \sqrt {\nabla \phi \bullet \nabla \phi + 2\phi } - \left| {\nabla \phi } \right|$

Where as the wall distance vector could be written as:

$\vec d = d{{\nabla \phi } \over {\left| {\nabla \phi } \right|}}$