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Coupled systems

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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.

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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.

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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

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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

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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.

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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

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Examples

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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.)

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Control-structure interaction

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Interaction diagram The fluid, structure and mesh models in the diagram have similar space and time scales

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Interaction diagram: Equations

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Underwater Shock (UWS)- Early 70s

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Interaction Diagram for Underwater Shock

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Solution Strategies ODE Elimination Methods special, numerically dangerous Monolithic Methods general, “top-down flavor” Partitioned Methods general, “bottom-up flavor”

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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.

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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.

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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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