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 twoway. 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
Fluid structure interaction domain
One way: fluid motion imposed by moving
structure
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)
Turbine Gas Ceramic
Wigley hull
Examples
Industrial applications
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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.