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oai:recercat.cat:2117/4080052026-01-30T08:55:24Zcom_2072_1033col_2072_452950

Spectral Properties of Mimetic Operators for Robust Fluid–Structure Interaction in the Design of Aircraft Wings Curtò i Díaz, Joaquim de Zarzà i Cubero, Irene de Barcelona Supercomputing Center Àrees temàtiques de la UPC::Informàtica::Aplicacions de la informàtica::Aplicacions informàtiques a la física i l‘enginyeria Fluid dynamics Mimetic finite-difference Operators Spectral analysis Stochastic analysis Aircraft wing Simulació per ordinador This paper presents a comprehensive study on the spectral properties of mimetic finite-difference operators and their application in the robust fluid–structure interaction (FSI) analysis of aircraft wings under uncertain operating conditions. By delving into the eigenvalue behavior of mimetic Laplacian operators and extending the analysis to stochastic settings, we develop a novel stochastic mimetic framework tailored for addressing uncertainties inherent in the fluid dynamics and structural mechanics of aircraft wings. The framework integrates random matrix theory with mimetic discretization methods, enabling the incorporation of uncertainties in fluid properties, structural parameters, and coupling conditions at the fluid–structure interface. Through spectral and localization analysis of the coupled stochastic mimetic operator, we assess the system’s stability, sensitivity to perturbations, and computational efficiency. Our results highlight the potential of the stochastic mimetic approach for enhancing reliability and robustness in the design of aircraft wings, paving the way for optimization algorithms that integrate uncertainties directly into the design process. Our findings reveal a significant impact of stochastic perturbations on the spectral radius and eigenfunction localization, indicating heightened system sensitivity. The introduction of randomized singular value decomposition (RSVD) within our framework not only enhances computational efficiency but also preserves accuracy in low-rank approximations, which is critical for handling large-scale systems. Moreover, Monte Carlo simulations validate the robustness of our stochastic mimetic framework, showcasing its efficacy in capturing the nuanced dynamics of FSI under uncertainty. This study contributes to the fields of numerical methods and aerospace engineering by offering a rigorous and scalable approach for conducting uncertainty-aware FSI analysis, which is crucial for the development of safer and more efficient aircraft. The work is developed under the following projects at BARCELONA Supercomputing Center: ‘TIFON’ and ‘NEXTBAT’. This work has also received funding from the EUROPEAN High-Performance Computing Joint Undertaking (EuroHPC-JU) under grant agreement no. 101093393 (CEEC). The work is also developed under UFV R&D pre-competitive project ‘OpenMaas: Open Manufacturing as a Service’. Peer Reviewed Postprint (author's final draft) 2024 Article Curtó, J. de; Zarzà i Cubero, I. de. Spectral Properties of Mimetic Operators for Robust Fluid–Structure Interaction in the Design of Aircraft Wings. "Mathematics", 2024, vol. 12, núm. 8, 1217. 2227-7390 https://hdl.handle.net/2117/408005 10.3390/math12081217 eng https://www.mdpi.com/2227-7390/12/8/1217 info:eu-repo/grantAgreement/EC/HE/101093393/EU/Center of Excellence for Exascale CFD/CEEC info:eu-repo/grantAgreement/EC/HE/101103983/EU/Next generation technologies for battery systems in transport electrification based on novel design approach to increase performance and reduce carbon footprint/NEXTBAT info:eu-repo/grantAgreement/AEI//PLEC2023-010251 The data presented in this study are openly available in FigShare at https://doi.org/10.6084/m9.figshare.25625478. http://creativecommons.org/licenses/by/4.0/ Open Access Attribution 4.0 International application/pdf MDPI