CISM Lectures on Computational Aspects of Structural Acoustics and Vibration Udine, June 19-23, 2006

1. CISM Lectures on Computational Aspects of Structural Acoustics and Vibration Udine, June 19-23, 2006

2. Presenter: Carlos A. Felippa Department of Aerospace Engineering Sciences and Center for Aerospace StructuresUniversity of Colorado at Boulder Boulder, CO 80309, USA

3. Topics 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

4. Lecture Sources Parts 1 and 2: Material of recent FSI course (Spr 2003) posted at http://caswww.colorado.edu/courses.d/FSI.d/Home.html 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- CMAME 2002) Will add these slides sets on return to Boulder Part 3: a potpourri of bits and pieces, mostly unpublished Part 4: two CMAME papers under preparation (Ross’ Thesis)

5. Partitioned Analysis of Coupled Systems: Overview Carlos A. Felippa Computational Aspects of Structural Acoustics and Vibration - Part 1Udine, June 19-23, 2006

6. 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.

7. Lecture Topics • 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

8. Part 1A • 1A. Coupled Systems Overview

9. Three Hot Areas in Computational Mechanics • COUPLED SYSTEMSare modeled and simulated by three “multis” • Multiphysics • Multiscale • Multiprocessing

10. 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)

11. Multiphysics MULTIPHYSICS: the interaction of physicallyheterogeneous components modeled atsimilar space/time scales jk Heterogeneousmeans: benefits from custom treatment

12. Aeroelasticity

13. Dynamic Mesh Modeled by Elastic Frame

14. Multiphysics Example (cont’d) This is an Interaction Diagram The fluid, structure and mesh models in thediagram have similar space and time scales

15. Multiscale Effect Example

16. How Local Turbulence Adds Multiscale

17. Lecture Scope Limitation These lectures will cover only two-waymultiphysics problems, one ofwhich components is a structure. The other may be fluid, control, etc.

18. Main Message For Students Coupled systems can explode in complexity. Don’t worry. Give the “weapons of math destruction’’ tocomputer algebra systems

19. Coupled Problems: One-Way vs. Two-Way Two-way is more difficult to simulate because the overall state has to be simultaneously updatedover interacting subsystems

20. More 1-Way vs Multiway Examples Car,trains, etc the same

21. 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]

22. Partition vs. Splitting (2)

23. Typical Coupled Problems • Early (1973) FSI Example: Underwater Shock Has historical value as motivator of partitioned methods

24. Early 1970’s Source Problem in FSI N-torpedo

25. Related Problem: Cavitation Shock (late 1980s)

26. Underwater Shock (UWS)- Early 70s

27. Interaction Diagram for Underwater Shock

28. Partitioned Method Software

29. 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

30. DD10 Poster Engineering Center

31. Aeroelasticity in More Detail

32. This Example Illustrates 2 Types of Partitions • Physical Partitions • 1. Structure • 2. Fluid • Artificial Partition • 3. Dynamic (ALE) Mesh

33. Aeroelasticity: Interaction Diagram

34. NonMatching Meshes Treated in more detail in Parts 3 and 4

35. Flight Simulation: Equations

36. Degrees of Freedom in Full Flight Simulation • Structure : 0.1-1M DOFs (corotational FEM) • Fluid: 10-100M DOFs • For DNS Turbulence, need over 1000B! • Control: 20-50 “wet modes” (wet modes) • Simulation in real time still impossible: 10 sec simulation takes hrs on supercomputer

37. Ambitious Simulations • Ongoing: sea-moored wind turbine • Future(?): ceramic gas turbine

38. Courtesy Jason Jonkman, NREL, Golden, Colorado

39. Prototypes at NREL Courtesy Jason Jonkman, NREL, Golden, Colorado

40. Ceramic Gas Turbines

41. Gas Turbine Interaction Diagrams

42. Symbiosis Value Inequalities of Hermann Matthies:

43. Part B • 1B. Partitioned Analysis Overview

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

45. Two General Strategies • Monolithic Methods Complete system advanced as a whole • Partitioned Methods Subsystems advanced separately while exchanging interaction data

46. Coupled ODE Example

47. Time Discretization

48. Monolithic Solution

49. Partitioned Solution

50. Solving Partitioned Equations The equations can be now solved in tandem