Program OUTBOUND Description:
Introduction:
OUTBOUND applies a choice of methods for tailoring a hypersonic flow grid.
Tailoring refers mainly to aligning the outer boundary with the shock.
Techniques demonstrated here are expected to be incorporated in the DPLR
flow solver for periodic adaptation of the grid as the solution converges.
Adjusting the radial grid point distributions is an implied requirement.
Again, several options are provided.
SAGE performs these functions along with further solution adaptations, and
the LAURA flow solver is able to tailor the grid during the flow solution.
The intent here is to implement ideas from SAGE and LAURA and elsewhere in
a form that lends itself to installation in DPLR.
One-Block-at-a-Time Strategy:
Initially, it is hoped that adaptations can be performed on grid blocks
in succession, independently of other grid blocks. Even if grid blocks
are split at DPLR run time, DPLR possesses the mechanism needed to gather
each block, operate on it, and scatter the results back to the relevant
processors.
[LATER REALIZATION: Actually, DPLR cannot afford to process more than
one split block on one processor (for memory reasons). Thus, the only
parts of the tailoring scheme that must treat a whole block at a time are
the smoothing of the outer boundary changes in radial arc length, and the
smoothing of the cell-Reynolds-number-based wall increments. Both of
these exceptions involve surface data only.
In this stand-alone driver for the tailoring scheme, block splitting is
not in the picture, so all steps operate on one whole block at a time.
The implementation in DPLR will perform everything in parallel on the
split blocks except for the smoothing of surface data.]
Thus, the grid block is considered the natural unit for processing here.
Common boundaries must therefore be treated exactly the same way. This
is not possible if blocks don't necessarily have entire faces in common.
Therefore, it is highly recommended that OUTBOUND be applied only to grids
that are split anywhere a neighboring block has a corner (NO "SUBFACING").
Preserving smoothness in the outer boundary is one of the challenges.
The one-block-at-a-time strategy means block corner points must be omitted
from any smoothing: interior edge points can be smoothed with edge data
(only), then interior surface points can be smoothed, but no guarantee of
smoothness across block boundaries is possible with this strategy.
Smoothing Strategy:
Rather than smoothing (x,y,z) directly, the tailored outer boundary arc
lengths were initially smoothed as functions of two variables - the arc
lengths in the two surface index directions of the untailored boundary.
Use of normalized arc lengths loses information from outer patches that
are far from square. Instead, the bidirectional smoothing uses real
space arc-length-based weighting of the contributions from the two
directions, combined with decay of those weights towards the edges.
Smoothing radial arc lengths, though, is always affected by geometric
features of the inner boundary. Therefore:
Better idea: smooth the distances of the adjusted boundary from the
original boundary. With repeated tailoring, this smoothing should
approach a steady state, assuming the initial boundary is reasonably
smooth and stays that way.
Note that smoothing full arc lengths (a la SAGE) would not leave a
perfectly tailored grid as is, whereas smoothing CHANGES in arc length
(ideally all zero at convergence) would.
Nevertheless, for situations where the initial outer boundary is not
smooth, this version of OUTBOUND has an option to perform such smoothing.
Rather than attempting to interpolate the solution and proceed with
tailoring, the program terminates after such smoothing. [DPLR can now
perform either or BOTH types of smoothing. Most recently, DPLR can now
smooth surface data across block boundaries, thanks to Matt Bartkowicz's
work that has not been incorporated in OUTBOUND. (It would conflict with
the straightforward processing of one block at a time.) Matt's smoothing
is index-based rather than surface-arc-length based, but this appears to
be a non-issue. Note that after several alignments, the initial estimate
of the shock location before any smoothing should be good, with little
noise, so fewer smoothing iterations are recommended - e.g., 10-15 for the
final pass, depending on grid resolution.]
Other stipulations:
> Adaptations are strictly along the radial grid lines of the original
grid except that any extrapolation via added_margin is strictly linear.
> If the grid contains more than a single layer of blocks, only the outer
layer of blocks is normally adapted (i.e., the blocks with a freestream
boundary are tailored to the shock, or possibly left alone in places
determined to be in the wake). However, the retrofitted option to fix
a block outer boundary and apply the basic tailoring method to k planes
1 : mk < nk does allow an outer block layer to remain untouched. This
requires the retrofitted block-blanking option.
> The DPLR boundary condition control data are employed to treat grids
with arbitrary indexing. For instance, a face with a BC of 1 means it
is at the free-stream boundary, while its opposite face may or may not
be at a solid boundary.
> All files are PLOT3D-type grid and functions files, multiblock, 3-D,
(or 2-D now), formatted or not.
> The function file is vertex-centered with one or more functions. The
function to be used for shock detection - say Mach number - may be in
any specified location, but if cell-Reynolds-number-based spacing is
specified, the first three functions should be DENSITY, SPEED OF SOUND,
and VISCOSITY in that order.
> Output of an interpolated flow solution is not attempted here. To be
of any use to DPLR, the function file would need to contain the state
variables at the cell centers, and these would not include the Mach
number. [Michael Wright points out that an approximation to Mach
number could be made, but standard practice would not be to use an
interpolated solution. Halo cell issues are best avoided for now.]
> Initial coding employs conventional (i,j,k) indexing for compatibility
with the XYZQ_IO package. DPLR works with (k,j,i) ordering. This
conflict is handled by swapping conventions within OUTBOUND, not DPLR.
> The argument-driven routine that tailors one grid block cannot change
the size of that block because it updates the block in-place for the
convenience of DPLR. This does not preclude the stand-alone driver
from imposing new grid point counts in a routine that will not be used
by DPLR.
Option to Compress an Initial Hyperbolic Volume Grid:
Shock edge method = -1 (along with a fudge factor at the bottom of the
control file that's not required for an optional free stream value) is
available in this version as an attempt to reduce the need for double
smoothing when DPLR is started on a hyperbolic volume grid commonly used
for capsule forebodies. (Cases with aft bodies may also be compressed,
although the wake region may grow in length as a consequence of allowing
a margin for the shock, and there is no way at present to shorten wake
regions.)
Ancillary program COMPRESSION_DATA can determine the transformation from
an initial grid to an existing aligned grid. The transformation consists
of scale factors applied to the radial grid line arc lengths, saved as a
multiblock 3-space (r, theta, z - zu) dataset, where r is the distance of
the initial outer boundary point U from the point furthest upstream (not
its perpendicular distance to the line through that point parallel to the
X axis, which would require a steady increase of the initial grid's outer
radius). An input fudge factor is applied to the scale factors.
Running OUTBOUND with fudge factor = 1.0 and the initial grid used when
the compression dataset was generated would reconstruct the associated
compressed grid. With fudge factor > 1.0, the radial lines of the output
grid will be longer than for the original compressed grid. The compression
can be varied this way - use trial and error. Preserving convexity in the
resulting outer boundary is not guaranteed, but the hope is that some
compression will be preferable to none when a new geometry is tackled.
Compression data from a related geometry should be applicable initially.
The geometry dimensions can change, as can the surface grid topology,
because the compression dataset (compression_data.g and .f) is adjusted by
OUTBOUND for the maximum radius of the input grid, and it is searched
efficiently for scale factors in (r, theta, dz) space using the structured
surface form of an Alternating Digital Tree search package. As with DPLR,
the effects of non-zero angle of attack need to be kept in mind. Best
results should be obtained using compression data from a similar angle of
attack case, particularly the same Alpha for similar/related geometries.
The standard ds1 >= 0 options for radial distribution method 2 are
provided (existing wall spacing or specified spacing, one- or two-sided
stretching).
Option to Scale the Volume Grid (SAGE-like, two variations):
Shock edge method = -2 (along with a scale factor at the bottom of the
control file that's not required for an optional free stream value) is
available for growing or shrinking the outer boundary in a way that
differs from all other methods: it does not retain the existing radial
lines unless they happen to be perfectly straight. Scale factors close
to 1 (smaller or larger) are recommended, although the added_margin
capability is likely to be a better choice. Two variations are offered:
scale_factor > 0 (constant everywhere):
x(k) <-- x(1) + scale_factor * (x(k) - x(1))
y(k) <-- y(1) + scale_factor * (y(k) - y(1))
z(k) <-- z(1) + scale_factor * (z(k) - z(1))
scale_factor < 0 (adjusted scaling as follows):
dx = x(k) - x(1) [and likewise for dy, dz]
dstraight = sqrt (dx^2 + dy^2 + dz^2)
factor = -scale_factor * (dstraight / sold(k))
xnew(k) = x(1) + factor * dx [and likewise for ynew, znew]
The second variation slightly improves the effect of curving radial lines,
but not enough to help much if |scale_factor| is large.
OUTBOUND Outline:
> Open and read the control file (standard input - format shown below)
> Open and read the DPLR-type file of control data including BCs
> For each block of the input grid:
> Read the grid block and the corresponding function file block
> Determine outer boundary face indices; do nothing if no BC = 1
> For each outer boundary point:
> Locate the preliminary new outer boundary (shock detection)
> Smooth all 4 edges of the new locations (1-D method, corners fixed)
> Smooth interior points of the new outer boundary (2-D surf. method)
> If cell Reynolds number is being used to define radial increments
at the wall, generate them all for this block and smooth them.
> For each radial line:
> Redistribute the radial line along the original arc
> Update the original block in-place.
> If specified, adjust the point counts [not applicable to DPLR]
> Output the tailored grid block
Control File Format (Standard Input)
OUTBOUND controls for case xxx
---------------------- INPUT VOLUME GRID ---------------------------------
baseline.g Initial grid
T Formatted? [T|F]
--------------------- INPUT FUNCTION FILE --------------------------------
baseline.f Flow quantity(s), vertex-centered: [rho, a, mu,] M|p|rho
T Formatted? [T|F]
1 Index of function to be used for tailoring
--------------- INPUT DPLR CONTROL FILE WITH BCS -------------------------
dplr.inputs For ibc(6,nblocks)
--------------------- TAILORED VOLUME GRID -------------------------------
tailored.g Output volume grid
T Formatted? [T|F]
--------------- OUTER BOUNDARY TAILORING CONTROLS ------------------------
1 Shock edge method|0; 1|4: Mach; 2: p,rho,T; 3: flow grad.
0 # smoothing iters. applied to flow var. [method 3 only?]
0.95 Freestrm. multiplier or tolerance; depends on edge method
4 Multiple of local grid spacing for outer margin
1.50 Multiple of local spacing to limit smoothing changes
30 # smoothing iterations applied to outer boundary
2. Additional margin (times outer spacing, possibly < 0)
0 nk_margin >= 0; plane nk - nk_margin is treated as for 0
--------------- RADIAL DISTRIBUTION CONTROLS -----------------------------
1 1: Re_cell; 2: given ds1; 3 (method_edge = 0): use |dT/ds|
0 nradial > 0 allows changing the no. of radial grid points
............... Radial method 1 controls: Re-cell-based ds1 ..............
1. Nominal cell Reynolds # to impose at the wall
0.000005 Minimum wall spacing (before smoothing); < 0 => % arc
0.000015 Maximum " " " " " "
10 ng where pts. 1:ng are geometric; ng <= 2 => pure Vinokur
1.05 Geometric growth rate if ng > 2
0.25 Factor applied to 1-sided ds2 to give 2-sided ds2
............... Radial method 2 controls: ds1 specified ..................
0. ds1 > 0 => const.; 0 => existing; < 0 => % arc; 999. => du
10 ng where pts. 1:ng are geometric; ng <= 2 => pure Vinokur
1.05 Geometric growth rate if ng > 2
0.25 Factor applied to 1-sided ds2 to give 2-sided ds2
............... Radial method 3: recluster outer pts; use edge method = 0)
0.5 0.1 0.5 Outer and blend fractions of nk, and shape fn. exponent
--------------- PLOTTABLE PROFILE CONTROLS + OPTIONAL INPUTS -------------
8 Block number to extract radial profiles from
1 17 1 1 Indices defining surface patch row(s)|column(s) to extract
17.88 Optional free-stream; < 0 => local peak; absent => block 1
(also used as a scale factor if shock edge method = -1|-2,
or as a constant outer margin (+ve or -ve) if present,
nonzero, and shock edge method = 0)
Ancillary Control File ('outbound.inp.2'):
This optional file can be used to blank blocks (suppress all changes).
Enter any reasonable list of blocks on the first line. E.g.,
11:16 or 11-16 would both expand to 11, 12, 13, 14, 15, 16
10 12 14:20 or any other such intelligible list, in any order
This first line can be empty, meaning no blocks are suppressed.
If the file is not present, no blocks are suppressed.
Further Notes:
(1) Shock edge detection methods (method_edge):
-2 => Scaling options - see description above
-1 => Compression option - see description above
0 => a: if method_radial /= 3:
smooth radial arcs directly (no further tailoring):
if a function file is present, it may still be used with
method_radial = 1 (cell Re # option); otherwise, only the
file header will be read; use file name 'none' if no such
file is available.
b: if method_radial == 3:
no edge detection -- only redistribution of the outer
portion of each radial line so as to cluster towards the
shock (and possibly other high-temperature-gradient flow
features) without touching the boundary layer region;
the function file is assumed to have translational T as
the first (and probably only) function.
1 => Mach number: some fraction of freestream (or of local peak).
2 => LAURA-type significant increase in pressure, density or T.
3 => SAGE-type relative flow gradient change.
4 => As for 1 but search outwards, not inwards, & omit wake test.
Corresponding fs_scale:
1 => fraction < 1 such as 0.95 applied to the freestream value.
2 => multiplier applied to the freestream value as in LAURA.
3 => fraction applied to peak flow gradient as in SAGE.
4 => as for 1.
(2) Safety margin (ds_local_multiple, added_margin, and constant_margin):
ds_local_multiple = multiple of local spacing at estimated edge;
e.g., 4.*local_ds, added to edge location
before smoothing.
smoothing_limiter * local_ds provides upper & lower bounds on how
much smoothing of delta arcs can change them,
given that the initial edge estimate should
be in the right neighborhood.
smoothing_limiter * outer ds bounds direct smoothing of the
outer boundary similarly.
added_margin = multiple of outermost spacing (possibly < 0)
constant_margin = constant absolute margin entered (with
shock edge method = 0) in place of the
optional input for free-stream Mach number
used when shock edge method /= 0.
(3) ds1 input (method_radial == 2):
> 0. => apply this constant spacing at the wall everywhere.
= 0. => retain the existing wall spacing everywhere.
< 0. => apply this percentage of total arc length at the wall.
= 999. => apply uniform spacing along all radial lines.
(4) Gradient-based clustering towards the shock (method_radial = 3):
Use method_edge = 0 for this option. Some outer portion (say
half the number of radial points) is redistributed to resolve the
shock better as is desirable for uncoupled radiative heating
calculations. The outer boundary location is not changed; nor
is the boundary layer portion (innermost ~half of the points).
Inputs outer_fraction and blend_fraction are applied to nk to
control what fraction of radial points are changed (leaving the
boundary-layer points undisturbed) and what fraction either side
of that split is used to blend the spacing (2-sided Vinokur).
0.5 and 0.1 should be reasonable inputs.
No other redistribution options are permitted at the same time.
The outer margin should be somewhat larger than normal so that
there will still be at least 2 points at free-stream conditions
after the redistribution.
(5) nk_margin > 0 and method_radial /= 3:
Any unblanked block will have its outer boundary left intact,
presumably for compatibility with another block layer such as
the nozzle block(s) in an arc-jet simulation. The normal align-
ment algorithm will be applied to k planes 1 : nk - nk_margin.
The points between mk = nk - nk_margin and nk will be blended at
k = mk and reuse the original spacing for k = nk - 1 : nk.
Sponsor:
Reacting Flow Environments Branch, NASA Ames Research Center,
in particular, Michael Wright, main author of DPLR.
History:
05/27/05 DAS/MJW/SSY Initial design (one whole block at a time).
06/06/05 DAS/SSY Initial testing (Mach number profiles; retaining
relative radial distributions suffices for now).
06/10/05 " " Pressure and density-based shock detection seems
too difficult, at least for the Shuttle, in spite
of heuristics to try and cope with unpredictable
flow profiles.
06/24/05 " " (After a hiatus:) higher fractions of Mach number
look promising for Shuttle Mach 9 case (0.90+).
06/28/05 " " 0.90 x Minf + 0.20 x arc margin still tends to
underestimate the lee-side boundary and over-
estimate most of the wind-side boundary.
Try backing up a specified multiple of the local
grid spacing rather than of total arc length.
Use a fraction of total length as a cap.
07/10/05 " " Added Vinokur-type radial redistribution options.
Smooth distances to the old outer boundary, not
radial distances from the OML.
07/14/05 " " Handle more than one flow quantity in the function
file, to allow for cell-Reynolds-number-based
spacing at the wall.
08/09/05 " " Reorganization to drive a remodularized form of
the original TAILOR_BLOCK in which the smoothing
steps are separated for use by DPLR on surface
data for a whole block while the remaining steps
are suited to parallel operation on split blocks.
08/17/05 " " Accommodated DPLR's (k,j,i) indexing but left the
(i,j,k) convention alone at the higher level for
compatibility with the I/O utilities.
11/23/05 " " Added "added_margin" at Mike Wright's request;
added an option to smooth a wiggly outer boundary
(only - no other tailoring until the solution has
been reconverged) - use method_edge = 0.
11/28/05 " " Disallowing the cell Re # option if method_edge = 0
was misguided. Allow for that and also for not
having any relevant function file.
12/22/05 DAS Ensure linear extrapolation if the outer boundary
expands - parametric cubics can't be trusted.
01/31/06 " 10 smoothing iterations for cell-Reynolds # based
increments may be too few. It should be an input,
but bump it up to 30 for now.
02/04/06 " The added_margin input should be more useful if it
is applied as a multiple of the outermost spacing.
04/24/06 " Added option to change the number of radial points.
This is not appropriate for the DPLR installation,
and is appropriate here for standard grids only
(where the k direction is off the wall for all
blocks).
05/05/06 " Added option to impose % arc length increments
at the wall (possible alternative to cell Reynolds
number for difficult cases).
05/06/06 " The limits on the cell-Re-based wall increments
may now be relative to arc length (-% inputs).
Both inputs should have the same sign. Smoothing
occurs AFTER the limits are imposed.
12/17/06 " Option to constrain the smoothing, which has been
observed (in DPLR) to cause the shock to be hit
by the boundary in front of the wing leading edge.
12/18/06 " Refinement to ds_local in shock location routine.
Long-time bug: method 2 radial controls were
clobbering the values read for method 1!
01/13/07 " Chun Tang had trouble with a Mach 2.5 case: the
outflow boundary Mach number can exceed the free
stream value. Therefore, treat boundary points not
at (essentially) free-stream as for those already
considered in the wake, where Minf * 0.97 (or
whatever) cannot be found: leave the boundary
location alone.
Optional final control input allows for overriding
the free-stream value to use if the first point
from block 1 is not in the free stream.
02/22/07 " No-outer-boundary blocks were not being transcribed
to the output file. Safeguarded EXPDIS4 from an
initial "smallest" increment that is on the wrong
side of the uniform increment.
09/05/07 Todd White Edge method 4 introduced to search from the wall
and use local peaks instead of a single f.s. Mach.
The test for being in the wake is also by-passed.
10/04/07 DAS/TRW Made Todd's option permanent, with the added option
to enter a negative free-stream value to invoke use
of the local peak for either edge method 1 or 4.
Method 4 now differs from 1 both in its search
direction and in its lack of test for wake blocks
where the outermost flow value is at the specified
free stream. [Unplanned-for application of OUTBOUND
to nozzle flows is what prompted Todd's experiment-
ation. It may be that no iso-surface behaves well
everywhere in such flows, but use of local peak
Mach numbers is now an option anyway. Note that the
distinction from edge method 2 is a bit fuzzy now.]
10/05/07 DAS Added the block-blanking and nk_margin options with
an optional outbound.inp.2 file.
12/17/07 " Allow nsmoothg < 0, which means entire edges are
not touched during smoothing (not just corners).
10/15/09 " Replaced EXPDIS4 with EXPDIS5 (which switches to
geometric distributions if trouble arises). The
safeguarding of EXPDIS4 is no longer needed.
12/24/09 " For method_radial = 2, ds1 = 999. means apply
uniform distributions along all radial lines, as
may be helpful for elliptic smoothing purposes.
03/24/11- D. Saunders Compression option (shock edge method = -1 along
03/29/11 ERC, Inc./ with fudge factor on the existling last line of
NASA ARC the control file) implemented as an attempt to
improve widely used initial hyperbolic volume
grids. See description above.
Also: SAGE-like scaling option (shock edge method
= -2, two variations) - see description above.
04/11/11 " " Fudge factor = 1.0 now corresponds to reproducing
the compressed grid from the initial grid used to
generate the compression data. Fudge factor > 1.0
=> longer radial lines/less compression.
04/12/11 " " The compression transformation is now stored as a
3-space (r, theta, dz) dataset, not the original
2-space (r, theta) form, which suffered from rare
aft-body anomalies because of extreme skewness.
08/06/13 " " All ADT variants are now in a single module with
generic build_adt and search_adt interfaces.
12/12/13 " " 2-D grids are now an option, in anticipation of
a T-gradient redistribution option intended for
better shock resolution, with uncoupled radiative
heating calculations by NEQAIR in mind.
12/18/13 " " Installed GRADDIS[3D]2 for the shock-clustering
option (method_edge = 0 + method_radial = 3) as
described above.
03/13/15 " " A case where the shock was too close to the
forebody prompted a way of growing the forebody
outer boundary without also extending the wake
too much (as gmargin applied to local outer ds
tends to): use method_edge = 0 along with a
constant/absolute margin in place of the optional
input for Mach (free) used when method_edge /= 0.
04/11/16 " " Dinesh needed a way of changing wall spacing for
some inner blocks while preserving the outer
spacing. (The inner blocks had to be extracted
to be operated on with OUTBOUND.) Use radial
method 2 with ds2_fraction = 0. and fixed d1.
Authors:
David Saunders, ELORET Corp./NASA Ames Research Center, Moffett Field, CA
Then ERC, Inc. at NASA ARC; now AMA, Inc. at NASA ARC.
Seokkwan Yoon, Applications Branch, NAS Division, NASA ARC.
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