University of Colorado - Dept of Aerospace Engineering Sci.ences & Center for Aerospace Structures CISM Lectures on Computational Aspects of Structural Acoustics and Vibration Udine, June 19-23, 2006

University of Colorado - Dept of Aerospace Engineering Sci.ences & Center for Aerospace Structures Presenter: Carlos A. Felippa Department of Aerospace Engineering Sciences and Center for Aerospace Structures University of Colorado at Boulder Boulder, CO 80309, USA

University of Colorado - Dept of Aerospace Engineering Sci.ences & Center for Aerospace Structures Topics Partitioned Analysis of Coupled Systems: Overview 1. Partitioned Analysis of Coupled Systems: Overview 2. Synthesis of Partitioned Methods 3. Mesh Coupling and Interface Treatment 4. Partitioned FSI by Localized Lagrange Multipliers spread over 5 lectures

University of Colorado - Dept of Aerospace Engineering Sci.ences & Center for Aerospace Structures Lecture Sources Parts 1 and 2: Material of recent FSI course (Spr 2003) posted at contains posted student projects and references to journal papers, including those in CISM brochure: (Felippa-Park-Farhat - CMAME 2001) (Park-Ohayon-Felippa - CMAME 2002) Will add these slides sets on return to Boulder Part 3: a potpourri of bits and pieces, mostly unpublished Part 4: two CMAME papers under preparation (Ross’ Thesis)

University of Colorado - Dept of Aerospace Engineering Sci.ences & Center for Aerospace Structures Carlos A. Felippa Partitioned Analysis of Coupled Systems: Overview Partitioned Analysis of Coupled Systems: Overview Computational Aspects of Structural Acoustics and Vibration - Part 1 Udine, June 19-23, 2006

University of Colorado - Dept of Aerospace Engineering Sci.ences & Center for Aerospace Structures General Comment on Lectures Note that in an FSI simulation (say) I won’t talk on how to do the structure how to do the fluid I assume you know how to do each piece by itself, or to get existing software that do them. My focus is how you may couple the pieces and solve the coupled system.

University of Colorado - Dept of Aerospace Engineering Sci.ences & Center for Aerospace Structures Lecture Topics Partitioned Analysis of Coupled Systems: Overview  1. Partitioned Analysis of Coupled Systems: Overview 2. Synthesis of Partitioned Methods 3. Mesh Coupling and Interface Treatment 4. Partitioned FSI by Localized Lagrange Multipliers

University of Colorado - Dept of Aerospace Engineering Sci.ences & Center for Aerospace Structures Part 1A + 1A. Coupled Systems Overview

University of Colorado - Dept of Aerospace Engineering Sci.ences & Center for Aerospace Structures Three Hot Areas in Computational Mechanics  COUPLED SYSTEMS are modeled and simulated by three “multis”  Multiphysics  Multiscale  Multiprocessing

University of Colorado - Dept of Aerospace Engineering Sci.ences & Center for Aerospace Structures The “Multis” are Hierarchical MULTIPHYSICS: divide problem into partitions as per physics MULTISCALE: model physical partitions as per represented scales MULTIPROCESSING: distribute representations as per computational resources Hierarchy: (1) physics, (2) scales, (3) resources (for engineers; material & computer scientists have different views)

University of Colorado - Dept of Aerospace Engineering Sci.ences & Center for Aerospace Structures Multiphysics MULTIPHYSICS : the interaction of physically heterogeneous components modeled at similar space/time scales  Heterogeneous means: benefits from custom treatment

University of Colorado - Dept of Aerospace Engineering Sci.ences & Center for Aerospace Structures Aeroelasticity

University of Colorado - Dept of Aerospace Engineering Sci.ences & Center for Aerospace Structures Dynamic Mesh Modeled by Elastic Frame

University of Colorado - Dept of Aerospace Engineering Sci.ences & Center for Aerospace Structures Multiphysics Example (cont’d) This is an Interaction Diagram The fluid, structure and mesh models in the diagram have similar space and time scales

University of Colorado - Dept of Aerospace Engineering Sci.ences & Center for Aerospace Structures Multiscale Effect Example

University of Colorado - Dept of Aerospace Engineering Sci.ences & Center for Aerospace Structures How Local Turbulence Adds Multiscale

University of Colorado - Dept of Aerospace Engineering Sci.ences & Center for Aerospace Structures Lecture Scope Limitation These lectures will cover only two-way multiphysics problems, one of which components is a structure. The other may be fluid, control, etc.

University of Colorado - Dept of Aerospace Engineering Sci.ences & Center for Aerospace Structures Main Message For Students Coupled systems can explode in complexity. Don’t worry. Give the “weapons of math destruction’’ to computer algebra systems

University of Colorado - Dept of Aerospace Engineering Sci.ences & Center for Aerospace Structures Coupled Problems: One-Way vs. Two- Way Two-way is more difficult to simulate because the overall state has to be simultaneously updated over interacting subsystems

University of Colorado - Dept of Aerospace Engineering Sci.ences & Center for Aerospace Structures More 1-Way vs Multiway Examples Car,trains, etc the same

University of Colorado - Dept of Aerospace Engineering Sci.ences & Center for Aerospace Structures Partition vs. Splitting (1) In these lectures: PARTITION: a subdivision of a coupled system in space, usually based on physics SPLITTING: a separation of a partition in time or pseudo-time [Other investigators have different definitions]

University of Colorado - Dept of Aerospace Engineering Sci.ences & Center for Aerospace Structures Partition vs. Splitting (2)

University of Colorado - Dept of Aerospace Engineering Sci.ences & Center for Aerospace Structures Typical Coupled Problems + Early (1973) FSI Example: Underwater Shock Has historical value as motivator of partitioned methods

University of Colorado - Dept of Aerospace Engineering Sci.ences & Center for Aerospace Structures Early 1970’s Source Problem in FSI N-torpedo

University of Colorado - Dept of Aerospace Engineering Sci.ences & Center for Aerospace Structures Related Problem: Cavitation Shock (late 1980s)

University of Colorado - Dept of Aerospace Engineering Sci.ences & Center for Aerospace Structures Underwater Shock (UWS)- Early 70s

University of Colorado - Dept of Aerospace Engineering Sci.ences & Center for Aerospace Structures Interaction Diagram for Underwater Shock

University of Colorado - Dept of Aerospace Engineering Sci.ences & Center for Aerospace Structures Partitioned Method Software

University of Colorado - Dept of Aerospace Engineering Sci.ences & Center for Aerospace Structures More Typical of Current Technology  Full Flight Simulation: Flying a flexible aircraft on the computer (Farhat et al, 1990s)  Important as source for several advances in methodology & parallel implementation: FETI Geometric Conservation Laws for moving meshes Staggered Parallel Methods Non-matching meshes Turbulence as multiscale feature

University of Colorado - Dept of Aerospace Engineering Sci.ences & Center for Aerospace Structures DD10 Poster Engineering Center

University of Colorado - Dept of Aerospace Engineering Sci.ences & Center for Aerospace Structures Aeroelasticity in More Detail

University of Colorado - Dept of Aerospace Engineering Sci.ences & Center for Aerospace Structures This Example Illustrates 2 Types of Partitions ( Physical Partitions  1. Structure  2. Fluid ( Artificial Partition  3. Dynamic (ALE) Mesh

University of Colorado - Dept of Aerospace Engineering Sci.ences & Center for Aerospace Structures Aeroelasticity: Interaction Diagram

University of Colorado - Dept of Aerospace Engineering Sci.ences & Center for Aerospace Structures NonMatching Meshes Treated in more detail in Parts 3 and 4

University of Colorado - Dept of Aerospace Engineering Sci.ences & Center for Aerospace Structures Flight Simulation: Equations

University of Colorado - Dept of Aerospace Engineering Sci.ences & Center for Aerospace Structures Degrees of Freedom in Full Flight Simulation Structure : 0.1-1M DOFs (corotational FEM) Fluid: M DOFs –For DNS Turbulence, need over 1000B! Control: “wet modes” (wet modes)  Simulation in real time still impossible: 10 sec simulation takes hrs on supercomputer

University of Colorado - Dept of Aerospace Engineering Sci.ences & Center for Aerospace Structures Ambitious Simulations + Ongoing: sea-moored wind turbine + Future(?): ceramic gas turbine

University of Colorado - Dept of Aerospace Engineering Sci.ences & Center for Aerospace Structures Courtesy Jason Jonkman, NREL, Golden, Colorado

University of Colorado - Dept of Aerospace Engineering Sci.ences & Center for Aerospace Structures Prototypes at NREL Courtesy Jason Jonkman, NREL, Golden, Colorado

University of Colorado - Dept of Aerospace Engineering Sci.ences & Center for Aerospace Structures Ceramic Gas Turbines

University of Colorado - Dept of Aerospace Engineering Sci.ences & Center for Aerospace Structures Gas Turbine Interaction Diagrams

University of Colorado - Dept of Aerospace Engineering Sci.ences & Center for Aerospace Structures Symbiosis Value Inequalities of Hermann Matthies:

University of Colorado - Dept of Aerospace Engineering Sci.ences & Center for Aerospace Structures Part B  1B. Partitioned Analysis Overview

University of Colorado - Dept of Aerospace Engineering Sci.ences & Center for Aerospace Structures Solution Strategies ODE Elimination Methods  special, numerically dangerous Monolithic Methods  general, “top-down flavor” Partitioned Methods  general, “bottom-up flavor”

University of Colorado - Dept of Aerospace Engineering Sci.ences & Center for Aerospace Structures Two General Strategies Monolithic Methods Complete system advanced as a whole Partitioned Methods Subsystems advanced separately while exchanging interaction data

University of Colorado - Dept of Aerospace Engineering Sci.ences & Center for Aerospace Structures Coupled ODE Example

University of Colorado - Dept of Aerospace Engineering Sci.ences & Center for Aerospace Structures Time Discretization

University of Colorado - Dept of Aerospace Engineering Sci.ences & Center for Aerospace Structures Monolithic Solution

University of Colorado - Dept of Aerospace Engineering Sci.ences & Center for Aerospace Structures Partitioned Solution

University of Colorado - Dept of Aerospace Engineering Sci.ences & Center for Aerospace Structures Solving Partitioned Equations The equations can be now solved in tandem

University of Colorado - Dept of Aerospace Engineering Sci.ences & Center for Aerospace Structures Staggered Partition Graphical representation of steps:

University of Colorado - Dept of Aerospace Engineering Sci.ences & Center for Aerospace Structures Staggered Partition Drawing only the data interchange between programs that simulate X and Y: Picture suggested name staggered solution procedure (Park, Felippa, DeRuntz 1977)

University of Colorado - Dept of Aerospace Engineering Sci.ences & Center for Aerospace Structures Staggered Partition: Advantages Simplifies reuse of software, methods & models Different software & methods for different partitions Modules may be improved & replaced by plug-ins Models may be prepared independently Facilitates individual research on components Important in university thesis and lab projects Higher numerical efficiency per timestep Component equation systems are smaller, less coupled; Solution times grow superlinearly in unknowns

University of Colorado - Dept of Aerospace Engineering Sci.ences & Center for Aerospace Structures Staggered Partition: Disadvantages  Stability and accuracy may suffer Example (I): uncoupled X and Y integrator A-stable, but conditionally stable or unstable if staggered Example (II): uncoupled X and Y integrators 2nd order accurate, but accuracy drops to 1st order if staggered  Not parallelizable at partition level Not important in the 1970s These difficulties can be addressed by the Tools of Partitioned Analysis that have evolved since 1977

University of Colorado - Dept of Aerospace Engineering Sci.ences & Center for Aerospace Structures Tools of Partitioned Analysis (1)

University of Colorado - Dept of Aerospace Engineering Sci.ences & Center for Aerospace Structures Tools of Partitioned Analysis (2) As important as all these time-advancing tools, is the customized treatment of interfaces in space. One instance (LLM) covered in Part 4.

University of Colorado - Dept of Aerospace Engineering Sci.ences & Center for Aerospace Structures Example of Current Practice We see use of half-station integration, selective corrections, and full parallelization (Lesoinne & Farhat, Vol 190, CMAME, 2002) From Charbel Farhat’s aeroelastic staggered codes:

University of Colorado - Dept of Aerospace Engineering Sci.ences & Center for Aerospace Structures Subcycling and Distributed-CPU Parallelization

University of Colorado - Dept of Aerospace Engineering Sci.ences & Center for Aerospace Structures Stop  End of Part 1