International Journal for Numerical Methods in Fluids,
Год журнала:
2025,
Номер
unknown
Опубликована: Янв. 15, 2025
ABSTRACT
This
paper
investigates
the
accuracy
of
U‐Net++
networks
in
predicting
Reynolds‐Averaged
Navier‐Stokes
(RANS)
solutions.
The
study
employs
symbolic
distance
function
(SDF)
to
represent
geometry
and
flow
conditions,
utilizing
parameterized
airfoil
data
from
UIUC
(University
Illinois
at
Urbana‐Champaign)
datasets.
research
assesses
performance
multiple
trained
neural
pressure
velocity
distributions.
Specifically,
examines
influence
varying
network
weights
on
solution
accuracy.
Through
optimization
model,
demonstrates
that
mean
relative
error
is
below
1.72%
for
a
range
previously
unseen
wing
shapes,
with
computational
speedup
factor
up
1,000×
certain
scenarios.
achieved
by
this
model
underscores
significant
potential
deep
learning‐based
approaches
as
reliable
tools
aerodynamic
design
optimization.
Long-term
predictions
of
nonlinear
dynamics
three-dimensional
(3D)
turbulence
are
very
challenging
for
machine
learning
approaches.
In
this
paper,
we
propose
an
implicit
U-Net
enhanced
Fourier
neural
operator
(IU-FNO)
stable
and
efficient
on
the
long-term
large-scale
turbulence.
The
IU-FNO
model
employs
recurrent
layers
deeper
network
extension
incorporates
U-net
accurate
prediction
small-scale
flow
structures.
is
systematically
tested
in
large-eddy
simulations
three
types
3D
turbulence,
including
forced
homogeneous
isotropic
(HIT),
temporally
evolving
turbulent
mixing
layer,
decaying
numerical
demonstrate
that
more
than
other
FNO-based
models
vanilla
FNO,
FNO
(IFNO)
(U-FNO),
dynamic
Smagorinsky
(DSM)
predicting
a
variety
statistics
velocity
spectrum,
probability
density
functions
(PDFs)
vorticity
increments,
instantaneous
spatial
structures
field.
Moreover,
improves
predictions,
which
has
not
been
achieved
by
previous
versions
FNO.
Besides,
proposed
much
faster
traditional
LES
with
DSM
model,
can
be
well
generalized
to
situations
higher
Taylor-Reynolds
numbers
unseen
regime
Traditional
fluid–structure
interaction
(FSI)
simulation
is
computationally
demanding,
especially
for
bi-directional
FSI
problems.
To
address
this,
a
masked
deep
neural
network
(MDNN)
developed
to
quickly
and
accurately
predict
the
unsteady
flow
field.
By
integrating
MDNN
with
structural
dynamic
solver,
an
system
proposed
perform
of
flexible
vertical
plate
oscillation
in
fluid
large
deformation.
The
results
show
that
both
field
prediction
structure
response
are
consistent
traditional
system.
Furthermore,
method
highly
effective
mitigating
error
accumulation
during
temporal
predictions,
making
it
applicable
various
deformation
Notably,
model
reduces
computational
time
millisecond
scale
each
step
regarding
part,
resulting
increase
nearly
two
orders
magnitude
speed,
which
greatly
enhances
speed
Conducting
large-scale
numerical
computations
to
obtain
flow
field
during
the
hypersonic
vehicle
engineering
design
phase
can
be
excessively
costly.
Although
deep
learning
algorithms
enable
rapid
prediction
with
high-precision,
they
require
a
significant
investment
in
training
samples,
contradicting
motivation
of
reducing
cost
acquiring
field.
The
combination
feature
extraction
and
regression
also
achieve
high-precision
fields,
which
is
more
suitable
tackle
three-dimensional
small
dataset.
In
this
study,
we
propose
reduced-order
model
(ROM)
for
utilizing
proper
orthogonal
decomposition
extract
representative
features
Gaussian
process
improved
automatic
kernel
construction
(AKC-GPR)
perform
nonlinear
mapping
physical
prediction.
selection
variables
based
on
sensitivity
analysis
modal
assurance
criterion.
underlying
relationship
unveiled
between
inflow
conditions.
ROM
exhibits
high
predictive
accuracy,
mean
absolute
percentage
error
(MAPE)
total
less
than
3.5%,
when
varying
altitudes
Mach
numbers.
During
angle
attack
variations,
only
effectively
reconstructs
distribution
by
interpolation
MAPE
7.02%.
excellent
small-sample
fitting
capability
our
AKC-GPR
algorithm
demonstrated
comparing
original
AKC-GPRs
maximum
reduction
35.28%.
These
promising
findings
suggest
that
proposed
serve
as
an
effective
approach
accurate
predicting,
enabling
its
application
analysis.
Machine
learning
has
great
potential
for
efficient
reconstruction
and
prediction
of
flow
fields.
However,
existing
datasets
may
have
highly
diversified
labels
different
scenarios,
which
are
not
applicable
training
a
model.
To
this
end,
we
make
first
attempt
to
apply
the
self-supervised
(SSL)
technique
fluid
dynamics,
disregards
data
pre-training
The
SSL
embraces
large
amount
(8000
snapshots)
at
Reynolds
numbers
Re
=
200,
300,
400,
500
without
discriminating
between
them,
improves
generalization
Transformer
model
is
pre-trained
via
specially
designed
pretext
task,
where
it
reconstructs
complete
fields
after
randomly
masking
20%
points
in
each
snapshot.
For
downstream
task
reconstruction,
fine-tuned
separately
with
256
snapshots
number.
models
accurately
reconstruct
based
on
less
than
5%
random
within
limited
window
even
250
600,
whose
were
seen
phase.
other
prediction,
128
consecutive
snapshot
pairs
corresponding
then
correctly
predict
evolution
over
many
periods
cycles.
We
compare
all
results
generated
by
trained
supervised
learning,
former
unequivocally
superior
performance.
expect
that
methodology
presented
here
will
wider
applications
mechanics.
The
Reynolds-averaged
Navier-Stokes
equation
for
compressible
flow
over
supercritical
airfoils
under
various
conditions
must
be
rapidly
and
accurately
solved
to
shorten
design
cycles
such
airfoils.
Although
deep-learning
methods
can
effectively
predict
fields,
the
accuracy
of
these
predictions
near
sensitive
regions
their
generalizability
large-scale
datasets
in
engineering
applications
enhanced.
In
this
study,
a
modified
vision
transformer-based
encoder-decoder
network
is
designed
prediction
transonic
addition,
four
are
encode
geometric
input
with
information
points
performances
compared.
statistical
results
show
that
generate
accurate
complete
field,
mean
absolute
error
on
order
1e-4.
To
increase
shock
area,
multilevel
wavelet
transformation
gradient
distribution
losses
introduced
into
loss
function.
This
maximum
typically
observed
area
decreasing
by
50%.
Furthermore,
models
pretrained
through
transfer
learning
finetuned
small
improve
applications.
generated
demonstrate
yields
comparable
from
reduced
training
time.
In
marine
applications,
estimating
velocity
fields
or
other
states
from
limited
data
are
important
as
it
provides
a
reference
for
active
control.
this
work,
we
propose
PVNet
(Pressure-Velocity
Network),
an
improved
U-shaped
neural
network
(UNet)
combined
with
Transformer
Modules
and
Multi-scale
Fusion
Modules,
to
predict
pressure
on
the
hydrofoil
surface.
To
improve
prediction
accuracy,
position
encodings
have
been
incorporated
into
input
features.
Tests
cavitation
dataset
of
NACA66
(National
Advisory
Committee
Aeronautics)
demonstrate
that
outperforms
traditional
models
such
shallow
networks
UNet.
addition,
conducted
quantitative
analysis
impact
features
performance,
providing
guidance
practical
arrangement
sampling
points.
Furthermore,
by
comparing
different
positional
encodings,
found
reasonable
can
significantly
accuracy.
Traditional
numerical
simulation
methods
for
airfoil
flowfields
are
complex
and
time-consuming,
deep
learning-based
inference
Reynolds-averaged
Navier–Stokes
equations
(RANS)
solutions
of
transonic
airfoils
have
limitations
in
terms
their
robustness
generalization.
A
novel
data-driven
method
named
as
attention
UNet
(AU)-RANS
is
proposed
efficient
accurate
prediction
around
with
strong
compressibility
large-scale
turbulent
separation.
First,
to
enhance
the
learning
boundary
flow
information
entire
flowfield
solution,
an
innovative
data
preprocessing
convert
physical
quantities
coordinate
RANS
into
neural
network
spatial
information.
Second,
mechanism
introduced
suppress
feature
responses
irrelevant
background
regions
sensitivity
geometrical
features
input
varying
inflow
conditions.
The
quantitative
qualitative
analyses
AU-RANS
results
demonstrate
that
well-trained
model
can
effectively
infer
accurately
predict
shock
waves
separation
phenomena
under
high
Mach
number
conditions
a
large
angle
attack.