88
4. Finite Volume Methods
Fig. 4.7. Geometry and boundary conditions for convection of
a step profile in a uniform flow
oblique to grid lines
improvement is found in the solution on the refined grid. On the other hand,
CDS produces a profile with the proper steepness, but it oscillates. Local grid
refinement would help localize and, perhaps even remove, the oscillations as
will be discussed in Chap. 11. The oscillations could also be removed by
locally introducing numerical diffusion (e.g. by blending CDS with UDS).
This is sometimes done in compressible flows near shocks.
Fig. 4.8. Profile of 4 at x = 0.45, calculated on a 10 x 10 CV grid (left), and at
x = 0.475, calculated on a 20 x 20 CV grid (right)
One can show that the UDS method embodied in Eq. (4.41) is more nearly
solving the convection-diffusion problem:
4. Finite Volume Methods
Fig. 4.7. Geometry and boundary conditions for convection of
a step profile in a uniform flow
oblique to grid lines
improvement is found in the solution on the refined grid. On the other hand,
CDS produces a profile with the proper steepness, but it oscillates. Local grid
refinement would help localize and, perhaps even remove, the oscillations as
will be discussed in Chap. 11. The oscillations could also be removed by
locally introducing numerical diffusion (e.g. by blending CDS with UDS).
This is sometimes done in compressible flows near shocks.
Fig. 4.8. Profile of 4 at x = 0.45, calculated on a 10 x 10 CV grid (left), and at
x = 0.475, calculated on a 20 x 20 CV grid (right)
One can show that the UDS method embodied in Eq. (4.41) is more nearly
solving the convection-diffusion problem: