ASEN5519 Topics in Multiphysics ModelingLecture01: IntroductionClass of Coupled-Field ProblemsCoupling/Interface ClassificationSome Challenging ProblemsModeling and Analysis ChallengesWhy do we want to study coupled-field problems?• Single-discipline oriented traditional science and engi-neering education curricula are proving to be less effec-tive (exceptions do exist!), because adequate solutions ofmodern science and engineering problems do require in-terdisciplinary approaches.• Coupled-field problems is just one approach to addressinterdisciplinary challenges.• Mechanical, aerospace and civil engineering systems in-volve judicious integrations of: structural/solid mechan-ics, fluid/gas/air dynamics, control, acoustics, electrody-namics, thermal fields, material processing, etc.Why do we want to study coupled-field problems? – cont’d•Most important of all, we do want to utilize all the existingdesign, modeling and analysis software modules that havebeen developed for single field problems (structural analysis soft-ware, fluid flow software, electrodynamics software, thermal analysis softwaremodules) to tackle coupled-field problems without having toreinvent new design and analysis software for interactionproblems!• Hence, the modeling and analysis paradigm has to bepartitioned modeling and analysis on which much of thiscourse is focused.Class of Coupled-Field ProblemsStructure-structure interaction:beam-plate, solid-plate, solid-bar, nano-micro-meso-continuum, fuselage-wing-stabilizer, body-floor-engine blocks, etc.Structure-fluid interaction:(wing, propeller, rotor blade)-fluid, vane-blood flow, heart-hemodynamics,(surface ship, submerged vehicle, ocean drilling platform, underwater tele-phone cable)-ocean waves and currents, . . .Structure-thermal interaction:satellite structure-solar radiation, turbine blade-hot wter/gas flow, metalforming.Structure-control/acoustic interaction:vibration mitigation, noise mitigation, sound generation, acoustic sensors,pressure sensors, etc.Class of Coupled-Field Problems – cont’dStructure-electrodynamic interaction:MEMS devices such as resonators, gyroscope, sensors of all categories, mag-netically levitated vehicle, motor rotors, ...Multi-scale interaction:molecule-molecules, nano-micro, micro-continuum, . . .Fluid-thermal interaction:large circulation of ocean currents, upper-lower atmospheric dynamics, geo-physics of several length scales, . . .Coupling/Interface ClassificationIntegration of field variables at the interfacesnon-overlapping interfacing.overlapping interfacing.Classical (or global) Lagranges multiplier methodLocalized Lagranges multiplier methodMatched impedance interfaceReduced (or filtered) interface modelsSome Challenging Problems•Structural mechanics problems consisting of subsystems that exhibit fromdiscontinuity, rapidly varying spatial and temporal characteristics, medium fre-quencies, and slowly varying subsystems.•Multiphysics problems that utilize single-field simulation capabilities of differingtime and spatial resolution requirements.•Multiscale problems that needs model refinements whose grid sizes vary severalorders of magnitude from finer grids to coarse grid zones.Modeling and Analysis Challenges•How to construct interactions• How best to preserve software modularity of single-field analyzers• How to capture the interaction phenomena without overburdening the task ofmodeling of the interfaces•How to capture the essential physical insight with a minimum of model ordersLet’s get down to the business, that is, formulating the coupled-field problems viapartitioned formulation.What is partitioned formulation?It is a divide-and-conquer strategy in modeling complex systems by the followingprocedure:•Construct the total energy of completely free system for each of the constituentsingle-field systems. Here, the term ’energy’ is broadly used to encompass thetotal energy, the total Lagrangian, the total Hamiltonian, etc.• Construct the interface mechanisms in terms of constraints and obtain theconstraint functional via the method of Lagrange multipliers.•Add the all the energy of the constituent single fields to form the total systemenergy.What is partitioned formulation? - - cont’d•Append the constraint functional to the total system energy.• Perform discretization while adhering to the single field-specific discretizationfor each field.•Perform the variational process when applicable, or perform a weak-form least-squares discretization.•Develop solution procedures or design optimization procedures that preservessingle-field analysis and design software modules.• Acquire physical insight through the analysis of coupled-field problems andapply it for improved and/or new
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