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7
Region 1
Side
Side
Side
Side
1
2
3
4
A surface (type 5).
On the axis (type 1).
An interface with side 1 of region 4 (type 7).
An interface with side 2 of region 3 (type 7).
Region 2
Side
Side
Side
Side
1
2
3
4
On the axis (type 1).
A surface (type 5).
An interface with side 1 of region 3 (type 7).
A stream boundary (type 3)*.
Region 3
Side
Side
Side
Side
1
2
3
4
An interface with side 3 of region 2 (type 7).
An interface with side 4 of region 1 (type 7).
An interface with side 1 of region 4 (type 7).
A stream boundary (type 3)*.
Region 4
Side 1
An interface with side 3 of region 1 and side
3 of region 3 (type 7).
Side 2 On the axis (type 1).
Side 3 A stream boundary (type 3).
Side 4 A stream boundary (type 3)*.
* For high Mach numbers, type 8 boundaries would be preferable.
Side 3 of region 4 should be upstream of the disturbance. The boundary at the
base is almost exact in the outer part of the flow as long as the x component of the
velocity is well supersonic. Unless this boundary is very far downstream, there will
be subsonic flow in the wake and some error in the flow. The magnitude of this
could be determined by placing the downstream boundary at different locations.
This system of flow boundaries has proved to be sufficiently flexible to cope with
almost all flow problems that have been encountered.
When an interface between regions lies along curved sides, the cell elements will
match exactly only if they are equal in number and identically distributed along
the interface. Any mismatch will result in small "gaps" or "overlaps" at the
interface. The program procedures are designed to cope with this eventuality, but
it greatly increases the normally very small probability of simulated molecules
going "astray". It is strongly recommended that the cell divisions be chosen such
that curved interfaces are exactly matched. There are no problems with cell size
discontinuities across straight interfaces as far as the flow calculations are
concerned. However, if contour output is chosen, the contours will be continuous
across the region boundaries only if the cells match exactly.
If the Knudsen number for the flow shown in Fig 2 was sufficiently small for the
flow to be near-continuum, very thin cells would be necessary in the region of high
vorticity near the surface. Should the desirable cell size lead to an excessively
small number of simulated molecules in the cell, the problem can be overcome in
a steady flow by calculating the boundary layer on a shorter time-scale. The
number of molecules in the cell is increased by reducing the number of real
molecules that are represented by each simulated molecule. If the time step is
reduced by exactly the same fraction, the flux of molecules across the interfaces
with the outer flow are exactly matched. This simultaneous change in DTM and
FNUM is ideal for flows in the stagnation region where FNUM is reduced in order
to increase the number of molecules in very thin cells near the surface. The
reduction is DTM is also desirable because of the thin cells. However, for problems