Coupled systems

Mechanics

Oct 24, 2013 (4 years and 8 months ago)

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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

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

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
.

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

are

not

cost

free
.

The

partitioned

approach

requires

careful

formulation

and

implementation

to

avoid

in

stability

and

accuracy
.

Parallel

implementations

are

particularly

delicate
.