Radial Basis Functions Vector Fields Interpolation for Complex Fluid Structure Interaction Problems
Abstract
:1. Introduction
2. Materials and Methods
2.1. RBF Background Theory
2.2. Parametric Mesh Formulation
2.3. Background to Modal Analysis and Modal Superposition
2.4. Modal Superposition for Static Analysis
2.5. Unsteady Analysis Modal Approach
2.6. Setup of Modal FSI Analysis
- Transient FSI in which structural displacements are known in advance and, therefore, imposed to the structure. It is the case of flapping devices experiencing complex motion, which was computed using FEA, multi-body, or observed in experimental tests. Acceleration of structural modes can be used to prepare ROM for non-linear flutter analysis;
- Steady FSI in which structural displacements are evaluated on the CFD mesh. It can be applied in aeronautical and motorsport applications, and can also be used to perform optimization considering coupled response. In some cases structural deflection can influence in a strong way the CFD mesh around wetted surfaces;
- Full coupled transient FSI in which the interaction between fluid flow and structure is captured by a time marching solution.
2.7. Setup of Non-Linear Imposed Wall Motion
3. Industrial Applications of FSI Modal Approach
3.1. Transient FSI with Prescribed Displacement Field Examples
3.2. Steady FSI Examples
3.3. Transient FSI Examples
3.4. Advanced Approaches for Limiting Mesh Distortion
4. Conclusions
Author Contributions
Funding
- RBF4AERO: Innovative benchmark technology for aircraft engineering design and efficient design phase optimisation, funded by the EU Seventh Framework Programme (FP7/2007-2013) under grant agreement 605396—https://cordis.europa.eu/project/id/605396;
- RIBES: Radial basis functions at fluid Interface Boundaries to Envelope flow results for advanced Structural analysis, funded by the EU Seventh Framework Programme (FP7/2007-2013) under grant agreement 632556—http://ribes-project.eu/;
- FORTISSIMO: Enabling Manufacturing SMEs to benefit from High Performance, Computerbased Simulations, funded by the EU Seventh Framework Programme (FP7/2007-2013) under grant agreement 609029—https://www.fortissimo-project.eu/;
- MEDITATE: the Medical Digital Twin for Aneurysm Prevention and Treatment, funded by EU’s Horizon 2020 research and innovation programme under the Marie Skłodowska-Curie grant agreement No 859836—https://meditate-project.eu/.
Institutional Review Board Statement
Informed Consent Statement
Data Availability Statement
Conflicts of Interest
Symbols
Weights of the polynomial corrector vector | |
RBF coefficients vector | |
Vector of modal coordinates | |
Damping factor | |
Radial function | |
Natural frequency | |
Vector of nodal forces | |
Known values of displacement | |
h | RBF correction polynomial |
Structural stiffness matrix | |
Position of a 3d point | |
Vector of source points | |
Structural mass matrix | |
Constraint matrix used for RBF fit | |
r | Euclidean distance between two points |
q | Generic polynomial |
Q | Nodal loads |
s | RBF interpolant |
Matrix of eigenvectors | |
Vector of structural displacements | |
Interpolation matrix used for RBF fit | |
Mesh nodes position | |
Mesh nodes in the undeformed position |
Definitions, Acronyms and Abbreviations
AePW | Aeroelastic prediction workshop |
CAE | Computer-aided engineering |
CFD | Computational fluid dynamics |
CSM | Computational structural mechanics |
DLM | Doublet lattice method |
FFD | Free-form deformation |
FEM | Finite element model |
FRF | Frequency response functions |
FSI | Fluid-structure interaction |
GAF | Generalized aerodynamic force |
RBF | Radial basis functions |
ROM | Reduced order model |
SMM | Standard mortar method |
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RBF with Global Support | |
---|---|
Spline type (Rn) | |
Thin plate spline | |
Multiquadric (MQ) | |
Inverse multiquadric (IMQ) | |
Inverse quadric (IQ) | |
Gaussian (GS) | |
RBF with Compact Support | |
Wendland C0 (C0) | |
Wendland C2 (C2) | |
Wendland C4 (C4) |
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Groth, C.; Porziani, S.; Biancolini, M.E. Radial Basis Functions Vector Fields Interpolation for Complex Fluid Structure Interaction Problems. Fluids 2021, 6, 314. https://doi.org/10.3390/fluids6090314
Groth C, Porziani S, Biancolini ME. Radial Basis Functions Vector Fields Interpolation for Complex Fluid Structure Interaction Problems. Fluids. 2021; 6(9):314. https://doi.org/10.3390/fluids6090314
Chicago/Turabian StyleGroth, Corrado, Stefano Porziani, and Marco Evangelos Biancolini. 2021. "Radial Basis Functions Vector Fields Interpolation for Complex Fluid Structure Interaction Problems" Fluids 6, no. 9: 314. https://doi.org/10.3390/fluids6090314