356
11. Efficiency and Accuracy Improvement
Fig. 11.10. A non-refined
CV at the refinement interface: it has six faces (cl,
. . . ,cg) in common with six
neighbor CVs (N1, . . . , Ng)
small part of the domain, the total number of grid points is relatively small
so both the cost of computation and the memory requirements are reduced
enormously. Furthermore, it can be designed so that the user need not be an
expert grid designer. Especially for flows around bluff bodies such as cars,
airplanes, and ships, in which very fine grids are needed near the body and
in the wake but coarse grids can be used elsewhere, local grid refinement is
essential for accurate and efficient simulation.
Finally, these methods combine very well with the multigrid method. The
nested grids can be regarded as the ones used in multigrid; the only important
difference is that, because the coarse grids provide enough accuracy where
refinement was not necessary, the finest grids do not cover the entire domain.
In the non-refined region, equations to be solved remain the same for both
levels. Since the largest cost of the multigrid method is due to iterations on
the finest grid, the savings can be very large, especially in 3D. For further
details, see Thompson and Ferziger (1989) and Muzaferija (1994).
In Fig. 11.9 an example of the use of locally refined grids to solve a
complex flow problem is presented. Fluid is injected into a large combustion
chamber through holes of different size. Uniform grid refinement would soon
exhaust the computer memory. For example, refining the first grid which has
342 CV uniformly four times yields a grid with 1.4 million CVs; the locally
refined grid shown in the figure has the same number of refinements and
about 0.25 million CVs, about one sixth as many. The uniformly refined grid
thus requires about six times as much memory, an even larger increase in
computing time, and yields only slightly higher accuracy. In compressible
flows, local grid refinement is necessary to resolve shocks efficiently.
11.5 Parallel Computing in CFD
The rapid growth in capability of single-processor computers has slowed in
recent years. It now appears that further increases in speed will require mul-
11. Efficiency and Accuracy Improvement
Fig. 11.10. A non-refined
CV at the refinement interface: it has six faces (cl,
. . . ,cg) in common with six
neighbor CVs (N1, . . . , Ng)
small part of the domain, the total number of grid points is relatively small
so both the cost of computation and the memory requirements are reduced
enormously. Furthermore, it can be designed so that the user need not be an
expert grid designer. Especially for flows around bluff bodies such as cars,
airplanes, and ships, in which very fine grids are needed near the body and
in the wake but coarse grids can be used elsewhere, local grid refinement is
essential for accurate and efficient simulation.
Finally, these methods combine very well with the multigrid method. The
nested grids can be regarded as the ones used in multigrid; the only important
difference is that, because the coarse grids provide enough accuracy where
refinement was not necessary, the finest grids do not cover the entire domain.
In the non-refined region, equations to be solved remain the same for both
levels. Since the largest cost of the multigrid method is due to iterations on
the finest grid, the savings can be very large, especially in 3D. For further
details, see Thompson and Ferziger (1989) and Muzaferija (1994).
In Fig. 11.9 an example of the use of locally refined grids to solve a
complex flow problem is presented. Fluid is injected into a large combustion
chamber through holes of different size. Uniform grid refinement would soon
exhaust the computer memory. For example, refining the first grid which has
342 CV uniformly four times yields a grid with 1.4 million CVs; the locally
refined grid shown in the figure has the same number of refinements and
about 0.25 million CVs, about one sixth as many. The uniformly refined grid
thus requires about six times as much memory, an even larger increase in
computing time, and yields only slightly higher accuracy. In compressible
flows, local grid refinement is necessary to resolve shocks efficiently.
11.5 Parallel Computing in CFD
The rapid growth in capability of single-processor computers has slowed in
recent years. It now appears that further increases in speed will require mul-