Simulation of Aortic Valve, see ADINA News, Apr. 15, 2003

ADINA offers fluid-structure interaction capabilities in one single program for the solution of problems where the fluids are fully coupled to general structures that can undergo highly nonlinear response due to large deformations, inelasticity, contact and temperature-dependency. A fully coupled fluid-structure interaction means that the response of the solid is strongly affected by the response of the fluid, and vice versa.

From the fluid point of view, the Navier-Stokes flow can be incompressible, slightly compressible, low-speed or high-speed compressible. From the structural point of view, all available element types can be used (i.e. shell, 2-D and 3-D solid, beam, iso-beam, contact surfaces, etc.) as well as all available material models.

Additionally, ADINA offers very efficient fully coupled fluid-structure interaction capabilities in which the fluid is assumed to be an acoustic medium.

How ADINA FSI Works

ADINA combines in one single program state-of-the-art computational solid and fluid dynamics schemes. For fluid flow analysis the user can choose between a nodal-based FCBI (Flow-Condition-Based Interpolation) scheme and a cell-based FCBI-C scheme.

• FCBI finite element scheme: A flow-condition-based interpolation of the velocities is used to provide stability. The finite element equations are assembled calculating consistent Jacobian matrices in the Newton-Raphson iterations. Hence, consistent stiffness matrices can be established for the complete fluid-structure system which makes it possible to solve very complex practical problems with highly nonlinear response.
  
  
• FCBI-C finite element scheme: All solution variables are defined in the center of the element and the coupling between the velocity and the pressure is handled iteratively. Therefore, in FSI analysis the coupling between the solid and fluid models is also handled iteratively. This scheme allows the solution of very large practical problems.

Theses schemes are applicable to any Reynolds number flow, from low to high Reynolds numbers.

Once any part of the computational domain deforms, the Eulerian description of the fluid flow is no longer applicable. Therefore, ADINA solves the governing equations of fluid flow using an Arbitrary-Lagrangian-Eulerian (ALE) formulation.

ADINA FSI is unique because it offers two different methods, DIRECT FSI COUPLING and ITERATIVE FSI COUPLING, to solve the coupling between the fluid and the structural models. In both cases, the conditions of displacement compatibility and traction equilibrium along the structure-fluid interfaces are satisfied:

Displacement compatibility,            d_f = d_s

Traction equilibrium,                      f_f = f_s

where d and f are displacements and tractions, and the subscripts f and s stand for fluid and solid respectively. In transient analyses, like for the flow-induced cantilever vibration response shown above, a second-order time integration scheme can be used.

DIRECT FSI COUPLING

In the Direct FSI Coupling solution method the fluid and solid equations are combined and treated in one system (one stiffness matrix), linearized and solved using an iterative algorithm such as the Newton-Raphson method. The Direct FSI Coupling algorithm offers great robustness when solving very difficult FSI problems, for example, large deformations with "soft" structures or highly compressible flows abating very stiff structures. These types of problems are difficult to solve using the Iterative FSI Coupling.

ITERATIVE FSI COUPLING

The fluid and solid equations are solved individually, in succession, always using the latest information provided by the other part of the coupled system. The Iterative FSI Coupling solution method requires less memory than the Direct FSI Coupling method and therefore may be more adequate to solve very large problems.

The unique offering of the two procedures, Iterative and Direct FSI Coupling, provided by ADINA is essential to successfully solve a wide range of problems in the most efficient way.

             ·   Direct and Iterative FSI Coupling Example

Some Features of ADINA Fluid-Structure Interactions

1. The FCBI scheme provides great stability, and is applicable to problems with both very high and very low Reynolds numbers.
   • New FCBI Elements for Fluid Flow
   
   
   
2. FSI analysis can be carried out with all flow types, namely incompressible, slightly compressible, low-speed compressible, and high-speed compressible flow. In addition, all fluid material models including non-Newtonian fluids, turbulence models and the VOF method are available for FSI analyses.
   • FSI Analysis of a Deformable Container using VOF
   • FSI Analysis of a Breaking Pipe
   
   
   
3. Potential-based fluid elements are available for efficient FSI analysis with acoustic flows. The potential-based fluid elements may also be used to perform frequency analysis of structures interacting with acoustic flows.

   • Analysis of Liquid Storage Tanks Using Potential-Based Fluid Elements
   • Frequency Analysis of Structures Coupled with Inviscid Fluids
   
   
   
4. ADINA allows the use of arbitrary meshes in the fluid and solid models. Furthermore, the fluid and solid meshes do not have to match perfectly at the fluid-structure interface.
   
   
   
   • Patch Test Using Arbitrary Incompatible Fluid and Solid Meshes on the FSI Boundary
   
   
   
5. Thermal and porous coupling is available between the fluid and the structural models.

   • Thermal Fluid-Structure Interaction including Shell Elements
   
   
   
6. All structural elements, the contact capabilities and the solid material models (i.e., elastic, viscoelastic, rubber, plasticity, etc.) are available for FSI solutions.
   
   
   
7. Gap boundary conditions can be respresented in the fluid models. The gap boundary condition, combined with the contact capabilities in ADINA have been used successfully to model the opening and closing of valves in automotive and biomedical applications.
   • Simulation of Aortic Valve
   
   
   
8. FSI analysis with sliding-mesh capability is available. Combining sliding meshes with FSI capabilities is particularly useful to analyze rotating equipment and turbomachinery.
   • FSI Analysis of a Turbine Using a Sliding Mesh
   
   
   
9. An efficient option can be the automatic one-way-coupled FSI analysis. This type of analysis is very useful when deformations in the solid are small and their influence on the fluid response is negligible. Therefore, no iteration between the fluid and the solid models is needed.
   • One-Way Coupled Fluid-Structure Interactions

ADINA FSI Applications in Industry

• Automotive Systems
• Biomedical Applications
• Nuclear Power and Pipe Systems
• Compressors, Pumps and Pipe Systems
• Micro-Electro-Mechanical Systems (MEMS)

Some Articles Using ADINA CFD

Doyle MG, Tavoularis S, Bourgault Y, "Simulation of close-loop flow in a ventricular assist device coupled with a circulatory system model," Third MIT Conference on Computational Fluid and Solid Mechanics, Elsevier, 1: 972-974 JUNE 2005.

Tang DL, Yang C, Zheng J, Woodard PK, Sicard GA, Saffitz JE, Yuan C, "3D MRI-based multicomponent FSI models for atherosclerotic plaques," Annals of Biomedical Engineering, 32 (7): 947-960 JUL 2004.

Tang DL, Yang C, Kobayashi S, Ku DN, "Effect of a lipid pool on stress/strain distributions in stenotic arteries: 3-D fluid-structure interactions (FSI) models," Journal of Biomechanical Engineering-Transactions of the ASME, 126 (3): 363-370 JUN 2004.

Shangguan WB, Lu ZH, "Modeling of a hydraulic engine mount with fluid-structure interaction finite element analysis," Journal of Sound and Vibration, 275 (1-2): 193-221 AUG 6 2004.

Shangguan WB, Lu ZH, "Experimental study and simulation of a hydraulic engine mount with fully coupled fluid-structure interaction finite element analysis model," Computers & Structures, 82 (22): 1751-1771 SEP 2004.

Chatila J, Tabbara M, "Computational modeling of flow over an ogee spillway," Computers & Structures, 82 (22): 1805-1812 SEP 2004.

Bathe KJ, Zhang H, "Finite element developments for general fluid flows with structural interactions," International Journal for Numerical Methods in Engineering, 60 (1): 213-232 MAY 7 2004.

Kroyer R, "FSI analysis in supersonic fluid flow," Computers & Structures, 81 (8-11): 755-764 MAY 2003.

Kaazempur-Mofrad MR, Bathe M, Karcher H, Younis HF, Seong HC, Shim EB, Chan RC, Hinton DP, Isasi AG, Upadhyaya A, Powers MJ, Griffith LG, Kamm RD, "Role of simulation in understanding biological systems," Computers & Structures, 81 (8-11): 715-726 MAY 2003.

Zhang H, Zhang XL, Ji SH, Guo YH, Ledezma G, Elabbasi N, deCougny H, "Recent development of fluid-structure interaction capabilities in the ADINA system," Computers & Structures, 81 (8-11): 1071-1085 MAY 2003.

Andersson L, Andersson P, Lundwall J, Sundqvist J, Nilsson K, Veber P, "On the validation and application of fluid-structure interaction analysis of reactor vessel internals at loss of coolants accidents," Computers & Structures, 81 (8-11): 469-476 MAY 2003.

Deserranno D, Popovic ZB, Greenberg NL, Kassemi M, Thomas JD, "Axisymmetric fluid-structure interaction model of the left ventricle," Second MIT Conference on Computational Fluid and Solid Mechanics, Elsevier, 2: 1669-1672 JUNE 2003.

Younis HF, Kaazempur-Mofrad MR, Chung C, Chan RC, Kamm RD, "Computational analysis of the effects of exercise on hemodynamics in the carotid bifurcation," Annals of Biomedical Engineering, 31 (8): 995-1006 SEP 2003.

Sussman T, Sundqvist J, "Fluid-structure interaction analysis with a subsonic potential-based fluid formulation," Computers & Structures, 81 (8-11): 949-962 MAY 2003.

Kurihara R, "Thermofluid analysis of free surface liquid divertor in Tokamak fusion reactor," Fusion Engineering and Design, 61-2: 209-216 NOV 2002.

Guo YH, Bathe KJ, "A numerical study of a natural convection flow in a cavity," International Journal for Numerical Methods in Fluids, 40 (8): 1045-1057 NOV 20 2002.

Younis HF, Chung CI, Kamm RD, "Challenges in developing an accurate model for carotid bifurcation blood flow and wall mechanics," First MIT Conference on Computational Fluid and Solid Mechanics, Elsevier, 2: 1434-1439 JUNE 2001.

Tang DL, Yang C, Huang Y, Ku DN, "Wall stress and strain analysis using a three-dimensional thick-wall model with fluid-structure interactions for blood flow in carotid arteries with stenoses," Computers & Structures, 72 (1-3): 341-356 JUL-AUG 1999.

Wang, XD, "Analytical and computational approaches for some fluid-structure interaction analyses," Computers & Structures, 72 (1-3): 423-433 JUL-AUG 1999.

Wang, XD, "Simulation of a deformable ball passing through a step diffuser," Computers & Structures, 72 (1-3): 435-456 JUL-AUG 1999.

Moore WI, Donovan ES, Powers CR, "Thermal Analysis of automotive lamps using ADINA-F coupled specular radiation and natural convection model," Computers & Structures, 72 (1-3): 17-30 JUL-AUG 1999.

Wang XD, Feng ZF, Forney LJ, "Computational simulation of turbulent mixing with mass transfer," Computers & Structures, 70 (4): 447-465 FEB 1999.

Andersson L, Andersson P, "Some experiences in the use of ADINA in the Swedish nuclear industry," Computers & Structures, 64 (5-6): 893-907 SEP 1997.