alinik
۱۴ مهر ۱۳۸۸, ۰۰:۰۸
When the geometry is regular (e.g. rectangular or circular), choosing the
grid is simple: the grid lines usually follow the coordinate directions. In complicated
geometries, the choice is not at all trivial. The grid is subject to
constraints imposed by the discretization method. If the algorithm is designed
for curvilinear orthogonal grids, non-orthogonal grids cannot be used;
if the CVs are required to be quadrilaterals or hexahedra, grids consisting of
triangles and tetrahedra cannot be used, etc. When the geometry is complex
and the constraints cannot be fulfilled, compromises have to be made.
8.1.1 Stepwise Approximation Using Regular Grids
The simplest approach uses orthogonal grids (Cartesian or polar-cylindrical).
In order to apply such a grid to solution domains with inclined or curved
boundaries, the boundaries have to be approximated by staircase-like steps.
This approach has been used, but it raises two kinds of problems:
0 The number of grid points (or CVs) per grid line is not constant, as it is
in a fully regular grid. This requires either indirect addressing, or special
arrays have to be created that limit the index range on each line. The
computer code may need to be changed for each new problem.
0 The steps at the boundary introduce errors into the solution, especially
when the grid is coarse. The treatment of the boundary conditions at stepwise
walls also requires special attention.
218 8. Complex Geometries
An example of such a grid is shown in Fig. 8.1. This approach is a last resort,
to be used when an existing solution method cannot be quickly adapted to
a grid that fits boundary better. It is not recommended, except when the
solution algorithm allows local grid refinement near the wall (see Chap. 11
for details of local grid refinement methods). An example is the large eddy
simulation of flow over a wall-mounted hemisphere by Manhart and Wengle
(1994).
Fig. 8.1. An example of a grid using stepwise approximation of an inclined boundary
grid is simple: the grid lines usually follow the coordinate directions. In complicated
geometries, the choice is not at all trivial. The grid is subject to
constraints imposed by the discretization method. If the algorithm is designed
for curvilinear orthogonal grids, non-orthogonal grids cannot be used;
if the CVs are required to be quadrilaterals or hexahedra, grids consisting of
triangles and tetrahedra cannot be used, etc. When the geometry is complex
and the constraints cannot be fulfilled, compromises have to be made.
8.1.1 Stepwise Approximation Using Regular Grids
The simplest approach uses orthogonal grids (Cartesian or polar-cylindrical).
In order to apply such a grid to solution domains with inclined or curved
boundaries, the boundaries have to be approximated by staircase-like steps.
This approach has been used, but it raises two kinds of problems:
0 The number of grid points (or CVs) per grid line is not constant, as it is
in a fully regular grid. This requires either indirect addressing, or special
arrays have to be created that limit the index range on each line. The
computer code may need to be changed for each new problem.
0 The steps at the boundary introduce errors into the solution, especially
when the grid is coarse. The treatment of the boundary conditions at stepwise
walls also requires special attention.
218 8. Complex Geometries
An example of such a grid is shown in Fig. 8.1. This approach is a last resort,
to be used when an existing solution method cannot be quickly adapted to
a grid that fits boundary better. It is not recommended, except when the
solution algorithm allows local grid refinement near the wall (see Chap. 11
for details of local grid refinement methods). An example is the large eddy
simulation of flow over a wall-mounted hemisphere by Manhart and Wengle
(1994).
Fig. 8.1. An example of a grid using stepwise approximation of an inclined boundary