8.2 Grid Generation
219
Grids of this kind are called Chimera grids in the literature (the Chimera
is a mythological creature with lion's head, goat's body, and snake's tail).
Examples of the use of overlapping grids are found in papers by Hinatsu and
Ferziger (1991), Perng and Street (1991), Tu and Fuchs (1992), and Hubbard
and Chen (1994,1995), among others.
8.1.3 Boundary-Fitted Non-Orthogonal Grids
Boundary-fitted non-orthogonal grids are most often used to calculate flows
in complex geometries (most commercial codes use such grids). They can be
structured, block-structured, or unstructured. The advantage of such grids is
that they can be adapted to any geometry, and that optimum properties are
easier t o achieve than with orthogonal curvilinear grids. Since the grid lines
follow the boundaries, the boundary conditions are more easily implemented
than with stepwise approximation of curved boundaries. The grid can also
be adapted to the flow, i.e. one set of grid lines can be chosen t o follow
the streamlines (which enhances the accuracy) and the spacing can be made
smaller in regions of strong variable variation, especially if block-structured
or unstructured grids are used.
Non-orthogonal grids have also several disadvantages. The transformed
equations contain more terms thereby increasing both the difficulty of programming and the cost of solving the equations, the grid non-orthogonality
may cause unphysical solutions and the arrangement of variables on the grid
affects the accuracy and efficiency of the algorithm. These issues are discussed
further below.
In the remainder of this book we shall assume that the grid is nonorthogonal. The principles of discretization and solution methods which we
shall present are valid for orthogonal grids as well, since they can be viewed
as a special case of a non-orthogonal grid. We shall also discuss the treatment
of block-structured grids.
8.2 Grid Generation
The generation of grids for complex geometries is an issue which requires too
much space to be dealt with in great detail here. We shall present only some
basic ideas and the properties that a grid should have. More details about
various methods of grid generation can be found in books and conference
proceedings devoted t o this topic, e.g. Thompson et al. (1985) and Arcilla et
al. (1991).
Even though necessity demands that the grid be non-orthogonal, it is important to make it as nearly orthogonal as possible. In FV methods orthogonality of grid lines a t CV vertices is unimportant - it is the angle between
the cell face surface normal vector and the line connecting the CV centers on
219
Grids of this kind are called Chimera grids in the literature (the Chimera
is a mythological creature with lion's head, goat's body, and snake's tail).
Examples of the use of overlapping grids are found in papers by Hinatsu and
Ferziger (1991), Perng and Street (1991), Tu and Fuchs (1992), and Hubbard
and Chen (1994,1995), among others.
8.1.3 Boundary-Fitted Non-Orthogonal Grids
Boundary-fitted non-orthogonal grids are most often used to calculate flows
in complex geometries (most commercial codes use such grids). They can be
structured, block-structured, or unstructured. The advantage of such grids is
that they can be adapted to any geometry, and that optimum properties are
easier t o achieve than with orthogonal curvilinear grids. Since the grid lines
follow the boundaries, the boundary conditions are more easily implemented
than with stepwise approximation of curved boundaries. The grid can also
be adapted to the flow, i.e. one set of grid lines can be chosen t o follow
the streamlines (which enhances the accuracy) and the spacing can be made
smaller in regions of strong variable variation, especially if block-structured
or unstructured grids are used.
Non-orthogonal grids have also several disadvantages. The transformed
equations contain more terms thereby increasing both the difficulty of programming and the cost of solving the equations, the grid non-orthogonality
may cause unphysical solutions and the arrangement of variables on the grid
affects the accuracy and efficiency of the algorithm. These issues are discussed
further below.
In the remainder of this book we shall assume that the grid is nonorthogonal. The principles of discretization and solution methods which we
shall present are valid for orthogonal grids as well, since they can be viewed
as a special case of a non-orthogonal grid. We shall also discuss the treatment
of block-structured grids.
8.2 Grid Generation
The generation of grids for complex geometries is an issue which requires too
much space to be dealt with in great detail here. We shall present only some
basic ideas and the properties that a grid should have. More details about
various methods of grid generation can be found in books and conference
proceedings devoted t o this topic, e.g. Thompson et al. (1985) and Arcilla et
al. (1991).
Even though necessity demands that the grid be non-orthogonal, it is important to make it as nearly orthogonal as possible. In FV methods orthogonality of grid lines a t CV vertices is unimportant - it is the angle between
the cell face surface normal vector and the line connecting the CV centers on