Computational grid and spatial discretization

Velocity components and pressure values are defined on the nodes:

defined on | ||

`` | ||

`` | ||

`` | ||

`` |

and

The values
,
,
,
are defined analogously.
To preserve the second order accuracy of the stencils a smooth distribution of
the grid spaces
,.. is required. To obtain such smooth grids use the
The other diffusive terms are discretized in a similar fashion. Stencils similar to the one for are used for , and , where is either or .

Five different discretizations of the convective terms are possible:

- Donor-Cell (hybrid-scheme) (1st/2nd order)
- Quadratic upwind interpolation for convective kinematics (QUICK) (2nd-Order)
- Hybrid-Linear Parabolic Arppoximation (HLPA) (2nd-Order)
- Sharp and Monotonic Algorithm for Realistic Transport (SMART) (2nd-Order)
- Variable-Order Non-Oscillatory Scheme (VONOS) (2nd/3rd-Order) (default)

**Second order convective terms:**

Stencils similar to the one for are used for the discretization of the convective terms in () and (), e.g. we have

where | |||

and | |||

where | |||

and | |||

Stencils similar to the one for are used for the upwind discretization of the convective terms in () and (). First and second order terms can be blended using a parameter by, e.g.

first ordersecond order

The blending parameter is user definable (see chapter ) and may be chosen
different for the equations of momentum and energy or transport of a scalar.
We employ a conservative discretization which is simply the nested application of the centered difference for the pressure gradient and the centered difference for the natural discretization of the divergence, e.g.

For the solution of the linear equation arising from discretization of the pressure poisson equation, the following numerical methods are implemented:

- Successive Overrelaxation (SOR)
- Symmetric SOR (forward/backward)
- Red-Black scheme
- 8-Color SOR
- 8-Color Symmetric SOR (fw/bw)
- BiCGStab

To select a method, select the corresponding option in the scene description file(see section on how to do this). By default, the Poisson-equation is solved using the BiCGStab-method.