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:

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