28
2. Introduction to Numerical Methods
Fig. 2.2. Example of a 2D block-structured grid which matches at interfaces, used
to calculate flow around a cylinder in a channel
In Fig. 2.3 a block-structured grid with non-matching interfaces is shown;
it was used to calculate the flow around a submerged hydrofoil. It consists
of five blocks of grids of different fineness. This kind of grid is more flexible
than the previous ones, as it allows use of finer grids in regions, where
greater resolution is required. The non-matching interface can be treated
in a fully conservative manner, as will be discussed in Chap. 8. The programming is more difficult than for grid types described above. Solvers for
structured grids can be applied block-wise, and complex flow domains can
be treated with these grids. Local refinement is possible block-wise (i.e.,
the grid may be refined in some blocks).
Fig. 2.3. Example of a 2D block-structured grid which does not match at interfaces,
designed for calculation of flow around a hydrofoil under a water surface
Block-structured grids with overlapping blocks are sometimes called composite or Chimera grids. One such grid is shown in Fig. 2.4. In the overlap
region, boundary conditions for one block are obtained by interpolating
the solution from the other (overlapped) block. The disadvantage of these
grids is that conservation is not easily enforced at block boundaries. The
advantages of this approach are that complex domains are dealt with more
easily and it can be used to follow moving bodies: one block is attached to
the body and moves with it, while a stagnant grid covers the surroundings.
This type of grid is not very often used, although it has strong supporters
(Tu and Fuchs, 1992; Perng and Street, 1991; Hinatsu and Ferziger, 1991;
Zang and Street, 1995; Hubbard and Chen, 1994, 1995).
2. Introduction to Numerical Methods
Fig. 2.2. Example of a 2D block-structured grid which matches at interfaces, used
to calculate flow around a cylinder in a channel
In Fig. 2.3 a block-structured grid with non-matching interfaces is shown;
it was used to calculate the flow around a submerged hydrofoil. It consists
of five blocks of grids of different fineness. This kind of grid is more flexible
than the previous ones, as it allows use of finer grids in regions, where
greater resolution is required. The non-matching interface can be treated
in a fully conservative manner, as will be discussed in Chap. 8. The programming is more difficult than for grid types described above. Solvers for
structured grids can be applied block-wise, and complex flow domains can
be treated with these grids. Local refinement is possible block-wise (i.e.,
the grid may be refined in some blocks).
Fig. 2.3. Example of a 2D block-structured grid which does not match at interfaces,
designed for calculation of flow around a hydrofoil under a water surface
Block-structured grids with overlapping blocks are sometimes called composite or Chimera grids. One such grid is shown in Fig. 2.4. In the overlap
region, boundary conditions for one block are obtained by interpolating
the solution from the other (overlapped) block. The disadvantage of these
grids is that conservation is not easily enforced at block boundaries. The
advantages of this approach are that complex domains are dealt with more
easily and it can be used to follow moving bodies: one block is attached to
the body and moves with it, while a stagnant grid covers the surroundings.
This type of grid is not very often used, although it has strong supporters
(Tu and Fuchs, 1992; Perng and Street, 1991; Hinatsu and Ferziger, 1991;
Zang and Street, 1995; Hubbard and Chen, 1994, 1995).