QUANTUM COMPUTING APPLICATIONS IN SOLVING COMPLEX NONLINEAR EQUATIONS FOR ADVANCING COMPUTATIONAL FLUID DYNAMICS IN AEROSPACE ENGINEERING
Indonesia Indonesia 
China 
Abstract
Increasing complexity in computational fluid dynamics (CFD) simulations demands faster, more accurate, and scalable approaches for solving highly nonlinear equations. Conventional high-performance computing remains effective in aerospace engineering but faces limitations in large-scale turbulence modeling, compressible flows, multiphysics interactions, and optimization requiring intensive iterations. This study evaluated the effectiveness of hybrid quantum-classical computing for solving complex nonlinear CFD equations and improving aerospace simulation performance. A mixed-methods sequential explanatory design involved 540 computational benchmark simulations and 240 experimental scenarios covering conventional solvers, hybrid quantum-classical optimization, and quantum-enhanced nonlinear solvers. Quantitative analyses used descriptive statistics, structural equation modeling, hierarchical regression, mediation, and moderation analysis, while qualitative evidence from expert interviews, computational observations, software evaluations, and document reviews underwent thematic analysis. Results showed that hybrid quantum-classical computing significantly improved convergence efficiency, numerical accuracy, turbulence prediction, scalability, residual error reduction, and simulation reliability. Hybrid optimization partially mediated the effect of quantum algorithms on computational efficiency, while mesh optimization strengthened convergence and engineering accuracy. These findings support integrating quantum computing with established CFD methods to enable faster optimization, stronger prediction, and scalable next-generation aerospace simulations.
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References
Ahmad, S., & Alsalmah, H. A. (2025). Exploring the thermal attributes of nano-composition (GQDs+Bi2Se3+Ag) suspended in therminol VP-1: An artificial intelligence based approach. Case Studies in Thermal Engineering, 72, 106231. https://doi.org/https://doi.org/10.1016/j.csite.2025.106231
Ahmadi Azar, A. (2025). Python implementation of the hybrid analytical and numerical method for analytical conversion of numerical thermofluidic boundary layer solutions. International Journal of Thermofluids, 30, 101419. https://doi.org/https://doi.org/10.1016/j.ijft.2025.101419
Ahmed, S., Jahan, S., Ansari, K. J., Shah, K., & Abdeljawad, T. (2024). Wavelets collocation method for singularly perturbed differential–difference equations arising in control system. Results in Applied Mathematics, 21, 100415. https://doi.org/https://doi.org/10.1016/j.rinam.2023.100415
Ai, J., Huang, W., Zhang, J., & Liu, C. (2024). Study on the flow characteristics of double-cone in hypersonic flows. Aerospace Science and Technology, 155, 109645. https://doi.org/https://doi.org/10.1016/j.ast.2024.109645
Akhare, D., Du, P., Luo, T., & Wang, J.-X. (2025). Implicit neural differentiable model for spatiotemporal dynamics. Computer Methods in Applied Mechanics and Engineering, 446, 118280. https://doi.org/https://doi.org/10.1016/j.cma.2025.118280
Akhter, R., & Maktedar, S. S. (2023). MXenes: A comprehensive review of synthesis, properties, and progress in supercapacitor applications. Journal of Materiomics, 9(6), 1196–1241. https://doi.org/https://doi.org/10.1016/j.jmat.2023.08.011
Al Kez, D., Foley, A. M., Hasan Wong, F. W. B. M., Dolfi, A., & Srinivasan, G. (2025). AI-driven cooling technologies for high-performance data centres: state-of-the-art review and future directions. Sustainable Energy Technologies and Assessments, 82, 104511. https://doi.org/https://doi.org/10.1016/j.seta.2025.104511
Alaofi, Z. M., & Abdel Wahid, T. Z. (2025). Analytical solution of Boltzmann-Maxwell PDE for plasma Couette flow among two coaxial rotating cylinders: Novel velocity dependent enhanced collision frequency. Ain Shams Engineering Journal, 16(7), 103392. https://doi.org/https://doi.org/10.1016/j.asej.2025.103392
Alves Ribeiro, J., Alves Ribeiro, B., Pimenta, F., M.O. Tavares, S., Zhang, J., & Ahmed, F. (2025). Offshore wind turbine tower design and optimization: A review and AI-driven future directions. Applied Energy, 397, 126294. https://doi.org/https://doi.org/10.1016/j.apenergy.2025.126294
Arif, M. S., Abodayeah, K., & Abbas, I. (2025). A machine learning-assisted computational study of heat transfer in magnetized non-Newtonian nanofluids through porous media. International Journal of Thermofluids, 29, 101358. https://doi.org/https://doi.org/10.1016/j.ijft.2025.101358
Bailly, C., Durox, D., Juniper, M., Noiray, N., Poinsot, T., Schuller, T., & Veynante, D. (2025). A dedicated paper for Pr Sébastien Candel EM2C laboratory, CentraleSupélec. Combustion and Flame, 279, 114301. https://doi.org/https://doi.org/10.1016/j.combustflame.2025.114301
Bhowmick, S., Nagarajaiah, S., & Kyrillidis, A. (2023). Data- and theory-guided learning of partial differential equations using SimultaNeous basis function Approximation and Parameter Estimation (SNAPE). Mechanical Systems and Signal Processing, 189, 110059. https://doi.org/https://doi.org/10.1016/j.ymssp.2022.110059
Chen, Z.-Y., Ma, T.-Y., Ye, C.-C., Xu, L., Bai, W., Zhou, L., Tan, M.-Y., Zhuang, X.-N., Xu, X.-F., Wang, Y.-J., Sun, T.-P., Chen, Y., Du, L., Guo, L.-L., Zhang, H.-F., Tao, H.-R., Wang, T.-L., Yang, X.-Y., Zhao, Z.-A., … Guo, G.-P. (2024). Enabling large-scale and high-precision fluid simulations on near-term quantum computers. Computer Methods in Applied Mechanics and Engineering, 432, 117428. https://doi.org/https://doi.org/10.1016/j.cma.2024.117428
Das Goswami, B. R., Mastrogiorgio, M., Ragone, M., Jabbari, V., Shahbazian-Yassar, R., Mashayek, F., & Yurkiv, V. (2024). A combined multiphysics modeling and deep learning framework to predict thermal runaway in cylindrical Li-ion batteries. Journal of Power Sources, 595, 234065. https://doi.org/https://doi.org/10.1016/j.jpowsour.2024.234065
Du, Z., & Bao, G. (2025). Metal-organic framework membranes for lithium extraction from Mg/Li brines: Advances in design, machine learning-driven optimization, and scalability challenges. Separation and Purification Technology, 369, 133044. https://doi.org/https://doi.org/10.1016/j.seppur.2025.133044
Guo, Z., Fu, X., & Rossi, R. (2024). Study on rheological properties of composite propellant slurry in the mixing process by using experimental and numerical simulation Electronic supplementary information (ESI) available. See DOI: https://doi.org/10.1039/d4ra05964f. RSC Advances, 14(51), 38162–38170. https://doi.org/https://doi.org/10.1039/d4ra05964f
Huang, Q., Zeng, W., Liu, J., Zhang, Z., Deng, J., Qiu, Z., Xu, L., Wei, Z., Lu, Q., Gong, L., Shi, C., & Zhong, X. (2025). Shaping the future of nuclear reactors with digital twins: Current developments and perspectives. Applied Energy, 402, 126922. https://doi.org/https://doi.org/10.1016/j.apenergy.2025.126922
Jacobsen, C., Zanardi, I., Bhola, S., Duraisamy, K., & Panesi, M. (2024). Information theoretic clustering for coarse-grained modeling of non-equilibrium gas dynamics. Journal of Computational Physics, 507, 112977. https://doi.org/https://doi.org/10.1016/j.jcp.2024.112977
Jhangeer, A., Munawar, M., Imran, M., & Abdelkader, A. (2025). Chaotic demonstration of the twin-core couplers with Kerr law non-linearity employing beta derivative. Partial Differential Equations in Applied Mathematics, 14, 101197. https://doi.org/https://doi.org/10.1016/j.padiff.2025.101197
Khalid, M., Ahmed, I., AlMuhaini, M., & Savkin, A. V. (2024). A novel computational paradigm for scheduling of hybrid energy networks considering renewable uncertainty limitations. Energy Reports, 11, 1959–1978. https://doi.org/https://doi.org/10.1016/j.egyr.2024.01.047
Khan, Z. H., Makinde, O. D., Usman, M., Ahmad, R., & Khan, W. A. (2025). Fractional order unsteady mixed convection in porous-filled concentric pipes: Entropy analysis. Alexandria Engineering Journal, 129, 483–503. https://doi.org/https://doi.org/10.1016/j.aej.2025.06.047
Liu, S., Sun, T., Li, P., & Zhao, X. (2025). Degradation-resilient transient control of aero-engines via neural dynamic programming: A model-free framework for rate-constrained safety. Neurocomputing, 653, 131079. https://doi.org/https://doi.org/10.1016/j.neucom.2025.131079
Mankodi, T. K., Ejtehadi, O., Chourushi, T., Rahimi, A., & Myong, R. S. (2024). nccrFOAM suite: Nonlinear coupled constitutive relation solver in the OpenFOAM framework for rarefied and microscale gas flows with vibrational non-equilibrium. Computer Physics Communications, 296, 109024. https://doi.org/https://doi.org/10.1016/j.cpc.2023.109024
Maraghi, Z. K., Mirhaj, S. A., & Civalek, Ö. (2025). Instability and vibration behaviour of sandwich plate on Kerr foundation. Engineering Structures, 341, 120876. https://doi.org/https://doi.org/10.1016/j.engstruct.2025.120876
Mesgarpour, M., Mahian, O., Zhang, P., Wongwises, S., Wang, L.-P., Ahmadi, G., Nižeti?, S., Sheremet, M., & Shadloo, M. S. (2023). A hybrid deep learning - CFD approach for modeling nanoparticles’ sedimentation processes for possible application in clean energy systems. Journal of Cleaner Production, 399, 136532. https://doi.org/https://doi.org/10.1016/j.jclepro.2023.136532
Mohammed, H. I., Rashid, F. L., Togun, H., Agyekum, E. B., Ameen, A., Hammoodi, K. A., Parveen, R., Kadhim, S. A., & Abbas, W. N. (2025). The role of nanotechnology and artificial intelligence in optimizing thermal energy systems. Applied Energy, 400, 126576. https://doi.org/https://doi.org/10.1016/j.apenergy.2025.126576
Munir, T., Farid, M. U., Zeb, H., Elkotb, M. A., & Ghodhbani, R. (2025). Computational investigation of air and water flow past laminar wake characteristics behind a circular cylinder. Chinese Journal of Physics, 98, 578–590. https://doi.org/https://doi.org/10.1016/j.cjph.2025.10.011
Nabavi, S. F., Garmestani, H., & Fekri, F. (2025). AI-powered language models for alloy design and laser-based manufacturing: A review of NLP applications in materials science. Journal of Manufacturing Processes, 156, 86–120. https://doi.org/https://doi.org/10.1016/j.jmapro.2025.11.035
Obalalu, A. M., Isarinade, A. F., Khan, U., Zaib, A., Khashi’ie, N. S., & Elkamchouchi, D. H. (2025). Significance of thermal radiation in a non-Newtonian (Reiner-Rivlin) model past a cylindrical surface with application in a thermal management system. Journal of Radiation Research and Applied Sciences, 18(4), 101879. https://doi.org/https://doi.org/10.1016/j.jrras.2025.101879
R., R., E., K., S.B.M., P., & S., N. P. (2024). Dynamic mode decomposition analysis and aerodynamic characteristics prediction of circular cylinder with variously modified ridges. International Journal of Numerical Methods for Heat & Fluid Flow, 35(10), 3715–3748. https://doi.org/https://doi.org/10.1108/HFF-09-2024-0656
Shams, M., Kausar, N., Akgül, A., & Ça??n, T. (2025). Converging efficiency: Computational and fractal insights into parallel non-linear schemes. Ain Shams Engineering Journal, 16(11), 103670. https://doi.org/https://doi.org/10.1016/j.asej.2025.103670
Shao, Y., Pasha, A. A., Raja, M. A. Z., Arshad, Z., Shah, Z., Abbasi, I., Khan, W. A., Alam, M. M., & Ansari, M. I. H. (2025). Optimizing the thermo-fluidic properties of ternary hybrid nanofluid for appliance of solar energy through an artificial intelligence integrated numerical solver technique. Chaos, Solitons & Fractals, 192, 115961. https://doi.org/https://doi.org/10.1016/j.chaos.2024.115961
Sharma, H., & Kramer, B. (2024). Preserving Lagrangian structure in data-driven reduced-order modeling of large-scale dynamical systems. Physica D: Nonlinear Phenomena, 462, 134128. https://doi.org/https://doi.org/10.1016/j.physd.2024.134128
Shen, J.-W., Luo, X.-P., Xu, J.-Y., Guo, Y., & Yi, H.-L. (2025). Phonon hydrodynamic transport in bilayer graphene. International Journal of Heat and Mass Transfer, 247, 127086. https://doi.org/https://doi.org/10.1016/j.ijheatmasstransfer.2025.127086
Suma, U. K., Masum Billah, M., & Khan, A. R. (2025). Optimization and sensitivity analysis of unsteady MHD mixed convective heat transfer in a lid-driven cavity containing a double-pipe circular cylinder using nanofluids. International Journal of Thermofluids, 27, 101197. https://doi.org/https://doi.org/10.1016/j.ijft.2025.101197
Tawalbeh, M., Farooq, A., Martis, R., & Al-Othman, A. (2024). Optimization techniques for electrochemical devices for hydrogen production and energy storage applications. International Journal of Hydrogen Energy, 52, 1058–1092. https://doi.org/https://doi.org/10.1016/j.ijhydene.2023.06.264
Wu, Q., Dong, K., Qin, X., Hu, Z., & Xiong, X. (2024). Magnetic particle inspection: Status, advances, and challenges Demands for automatic non-destructive testing. NDT & E International, 143, 103030. https://doi.org/https://doi.org/10.1016/j.ndteint.2023.103030
Zadeh, C., Stepanova, T., Zarei, A., Huang, Y., Smith, P. M., Li, G., & Pilla, S. (2025). Establishing a process-structure-property-performance framework for SLS additive manufacturing through integrated multiscale modeling. Materials & Design, 257, 114431. https://doi.org/https://doi.org/10.1016/j.matdes.2025.114431
Zainali, S., Lu, S. M., Fernández-Solas, Á., Cruz-Escabias, A., Fernández, E. F., Zidane, T. E. K., Honningdalsnes, E. H., Nygård, M. M., Leloux, J., Berwind, M., Trommsdorff, M., Amaducci, S., Gorjian, S., & Campana, P. E. (2025). Modelling, simulation, and optimisation of agrivoltaic systems: a comprehensive review. Applied Energy, 386, 125558. https://doi.org/https://doi.org/10.1016/j.apenergy.2025.125558
Zanardi, I., Padovan, A., Bodony, D. J., & Panesi, M. (2025). Petrov-Galerkin model reduction for thermochemical nonequilibrium gas mixtures. Journal of Computational Physics, 533, 113999. https://doi.org/https://doi.org/10.1016/j.jcp.2025.113999
Zhang, H., Xu, Y., Liu, Q., & Li, Y. (2023). Deep learning framework for solving Fokker–Planck equations with low-rank separation representation. Engineering Applications of Artificial Intelligence, 121, 106036. https://doi.org/https://doi.org/10.1016/j.engappai.2023.106036
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Copyright (c) 2026 Joni Wilson Sitopu, Darwan Edyanto Saragih, Li Wei
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