Coupled systems
Coupled systems
•
A
coupled
system
is
one
in
which
physically
or
computationally
heterogeneous
mechanical
components
interact
dynamically
.
•
The
coupled
system
is
called
one

way
,
if
there
is
no
feedback
between
the
subsystems
and
two
way
,
if
there
is
feedback
between
the
subsystems
.
•
The
concept
of
coupled
systems
can
be
generalized
to
multi

coupled
systems
,
for
example
fluid

structure

fluid
(e
.
g
.
water

boat

air)
.
•
In
most
problems
it
cannot
be
decided
if
the
problem
is
one

way
or
two

way
.
Regarding
the
interaction
of
a
very
slow
driving
car
with
the
surrounding
air,
the
influence
of
the
air
on
the
car
can
be
neglected
.
At
a
certain
speed
however,
the
aerodynamic
resistance
plays
an
important
role
.
One way and two way
One
way
: fluid
motion
imposed
by
moving
structure
Fluid
structure
interaction
domain
Two
way
:
flow
will
act
on
the
surface
of
the
elastic
structure
and
will
cause
a
deformation
.
This
deformation
changes
the
flow
domain
.
Three Hot Areas in Computational Mechanics
COUPLED SYSTEMS
are modeled
and
simulated by three “
multis
”
•
MULTIPHYSICS
: divide problem into partitions
as per physics (as in structures and fluids)
at similar
space/time
scales.
•
MULTISCALE
: model physical partitions
as per represented scales. Material models spanning a range of
physical scales.
•
MULTIPROCESSING
: distribute representations
as per computational resources. It refers to
computational methods that use system.
Hierarchy: (1) physics, (2) scales, (3)
resources
Decomposition of a complex coupled system
Types of Partitions
•
Physical Partitions
: physical
fields with mathematical
models.
–
1. Structure
–
2. Fluid
•
Artificial Partition
–
3. Dynamic (ALE) Mesh
Decomposition of a complex coupled system
Types of Partitions
For computational treatment of a
dynamical coupled system, fields
are discretized in space and time:
•
PARTITION
:
a
subdivision
of
a
coupled
system
in
space,
usually
based
on
physics
(fields)
.
Partitioning
may
be
algebraic
(matching
meshes)
and
differential
(
Nonmatched
meshes)
SPLITTING:
a separation of a partition in
time or pseudo

time of a field
.
Examples
•
Fluid Structure interaction (2)
•
Control structure interaction(2)
•
Electro

thermo

mechanical
interaction(3)
•
Control fluid structure interaction
(3)
•
Fluid structure combustion thermal
interaction (4)
Wigley
hull
Turbine Gas
Ceramic
Examples
Industrial
applications
•
Automotive
—
shock
absorbers
,
hydraulic
engine
mounts
,
valves
,
pumps
,
compressors
, tire
hydroplaning
, airbag
deployment
,
exhaust
systems
, car
door
seals
,
etc
•
Fluid
containers
—
oil
tanks
subject
to
earthquake
, fuel
tank
sloshing
, etc.
•
Biomechanics
—
cardiovascular
mechanics
,
cerebrospinal
mechanics
,
implant
/
prosthetic
design
,
cell
/
tissue
mechanics
, artificial
lung
,
drug
delivery
,
eye
disease
, ventricular
assist
devices
,
carpal
tunnel
, vocal
fold
/
upper
airway
, artificial
heart
valves
,
aneurysms
,
bile
flow
,
bioreactors
, etc.
•
Turbomachinery
—
impellers
, gas turbines,
wind
turbines, etc.
•
Nuclear
power
plants
—
control
rod
drop
,
blowdown
condition
, etc.
•
Aeroelasticity
—
flutter
of
airplane
wings
•
Wind
engineering
—
effect
of
wind
on
tall
buildings
, cable
stayed
bridges, etc.
•
Compressors
,
Pumps
,
Valves
and Pipe
Systems
—
gear
pumps
,
impedance
pumps
,
check
valves
,
membrane
valves
, etc.
•
Seals
—
hydrodynamic
seals
,
face
seals
,
brush
seals
, etc.
•
Micro

Electro

Mechanical
Systems
(MEMS)
•
Dam

reservoir
Interaction
—
dynamic
analysis of
different
types
of
dams
(Concrete, Rock

fill
,
etc.)
Control

structure
interaction
Interaction diagram
The
fluid, structure and mesh models in
the
diagram
have similar space and time scales
Interaction diagram:
Equations
Underwater Shock (UWS)

Early 70s
Interaction Diagram for Underwater Shock
Solution Strategies
ODE Elimination Methods
special, numerically dangerous
Monolithic Methods
general, “top

down flavor”
Partitioned Methods
general, “bottom

up flavor”
Solution Strategies
Monolitic
approach
:
•
The
equations
governing
the
flow
and
the
displacement
of
the
structure
are
solved
simultaneously,
with
a
single
solver
.
Both
subproblems
(fluid

structure)
must
be
formulated
as
one
combined
.
•
In
cases
where
the
flow
and
the
solid
physics
are
inseparable
linked
together,
the
governing
equations
of
the
physics
of
the
fluid
and
the
solid
must
be
solved
simultaneously
.
This
approach
seems
to
be
ideal
when
the
physical
interactions
are
strongly
non

linear
.
At
present
,
this
method
is
practicable
only
for
elementary
examples
.
Solution Strategies
•
Partitioned
approach
:
the
equations
governing
the
flow
and
the
displacement
of
the
structure
are
solved
separately,
with
two
distinct
solvers
.
An
advantage
of
the
partitioned
approach
is
that
differents
solvers
can
be
used
for
the
different
subproblems
.
•
Field
elimination
:
the
elimination
of
field
variables
at
the
level
of
differential
equations
is
limited
to
elementary
linear
problems
.
For
this
method
the
equations
must
be
inserted
one
into
the
other
.
Partitioning: advantages and disadvantages
•
Simplifies reuse of software, methods & models
–
Different software & methods for different partitions
–
New methods and models may be introduced in a modular fashion
according to project needs. For example, it may be necessary to include
local nonlinear effects in an individual field while keeping everything else
the same.
•
Facilitates individual research on components.
Separate models
can be prepared by different design teams
•
These
advantages
are
not
cost
free
.
The
partitioned
approach
requires
careful
formulation
and
implementation
to
avoid
degradation
in
stability
and
accuracy
.
Parallel
implementations
are
particularly
delicate
.
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