SIMULAÇÕES COMPUTACIONAIS UTILIZANDO SMOOTHED PARTICLE HYDRODYNAMICS PARA A BUSCA DE MÍNIMOS DE FUNÇÕES
DOI:
https://doi.org/10.47820/recima21.v6i12.7119Palavras-chave:
Hidrodinâmica de Partículas Suavizadas. Problemas de otimização. Simulação computacional.Resumo
A Hidrodinâmica de Partículas Suavizadas, ou do inglês Smoothed Particle Hydrodynamics (SPH), é um procedimento computacional usado para simulações em meios contínuos, como processos mecânicos e fluxos de fluidos, ganhando crescente destaque na representação da dinâmica de fluidos. Dado um sistema físico composto por partículas, o SPH calcula a pressão sobre cada partícula considerando as interações com suas partículas vizinhas, simulando a dinâmica do sistema como um fluido. A proposta deste trabalho é utilizar a técnica SPH para a busca por mínimos de funções, simulando a queda, por gravidade, de um conjunto de partículas sob uma superfície. Esta superfície é representada por uma função matemática cujo mínimo global se deseja encontrar. O uso do SPH, tradicionalmente aplicado em simulações físicas e industriais, é aqui explorado como prova de conceito, demonstrando que a técnica também pode ser adaptada para problemas de otimização. Com a dinâmica de escoamento das partículas sob a superfície em análise é possível identificar a partícula que alcança o valor de mínimo, localizando o ponto de mínimo no domínio da função. Foram realizados diversos experimentos com funções que possuem múltiplos mínimos locais e um mínimo global, e os resultados mostraram que o SPH é capaz de identificar esse mínimo com precisão. Para comparação, também foram realizados testes com a técnica PSO (Particle Swarm Optimization). Os resultados demonstram que o desempenho do SPH é comparável ao do PSO.
Downloads
Referências
ADAMI, Stefan; HU, Xiangyu; ADAMS, Nikolaus A. A transport-velocity formulation for smoothed particle hydrodynamics. Journal of Computational Physics, v. 241, p. 292–307, 2013. DOI: https://doi.org/10.1016/j.jcp.2013.01.043
ANTONY, Justin; MANIYERI, Ranjith. Numerical simulation of fluid flow in a channel using smoothed particle hydrodynamics. In: Proceedings of 65th Congress of ISTAM, 2020. Disponível em: https://istam.iitkgp.ac.in/resources/2020/proceedings/Full_paper/FM/90fullpaper.pdf. Acesso em: 9 set. 2025.
ANTUONO, M.; DI MASCIO, A.; ASADI, H. et al. Smoothed particle hydrodynamics method from a large eddy simulation perspective: generalization to a quasi-Lagrangian model. Physics of Fluids, v. 33, n. 1, p. 015102, 2021. DOI: https://doi.org/10.1063/5.0034568
ARORA, Krishan; KUMAR, Ashok; KAMBOJ, Vikram Kumar et al. Optimization methodologies and testing on standard benchmark functions of load frequency control for interconnected multi-area power system in smart grids. Mathematics, v. 8, n. 6, p. 980, 2020. DOI: https://doi.org/10.3390/math8060980
ASADI, Hossein; RIAZI, Masoud; MOHAMMADI, Masoud. Investigation of hydrodynamically dominated membrane rupture using smoothed particle hydrodynamics–finite element method. Fluids, v. 4, n. 3, p. 149, 2019. DOI: https://doi.org/10.3390/fluids4030149
ATLURI, Satya N.; ZHU, Tulong. A new meshless local Petrov–Galerkin (MLPG) approach in computational mechanics. Computational Mechanics, v. 22, n. 2, p. 117–127, 1998. DOI: https://doi.org/10.1007/s004660050346
AZRAG, Mohammed Adam Kunna; KADIR, Tuty Asmawaty Abdul; ALI, Noorlin Mohd. A comparison of particle swarm optimization and global African buffalo optimization. In: IOP Conference Series: Materials Science and Engineering. IOP Publishing, 2020. p. 012034. DOI: https://doi.org/10.1088/1757-899X/769/1/012034
BASHIR, Hassan Abdullahi. Diversity control in evolutionary computation using asynchronous dual-populations with search space partitioning. Nigerian Journal of Technological Development, v. 17, n. 3, p. 175–188, 2020. DOI: https://doi.org/10.4314/njtd.v17i3.4
BELYTSCHKO, Ted; LU, Yun Yun; GU. Lei. Element‐free Galerkin methods. International Journal for Numerical Methods in Engineering, v. 37, n. 2, p. 229–256, 1994. DOI: https://doi.org/10.1002/nme.1620370205
CISTERNAS, Luis A.; LUCAY, Freddy A.; BOTERO, Yesica L. Trends in modeling, design, and optimization of multiphase systems in minerals processing. Minerals, v. 10, n. 1, p. 22, 2019. DOI: https://doi.org/10.3390/min10010022
CLEARY, Paul W. et al. Inclusion of incremental damage breakage of particles and slurry rheology into a particle scale multiphase model of a SAG mill. Minerals Engineering, v. 128, p. 92–105, 2018. DOI: https://doi.org/10.1016/j.mineng.2018.08.026
CLEARY, Paul W.; SINNOTT, Matt; MORRISON, Rob. Prediction of slurry transport in SAG mills using SPH fluid flow in a dynamic DEM based porous media. Minerals Engineering, v. 19, n. 15, p. 1517–1527, 2006. DOI: https://doi.org/10.1016/j.mineng.2006.08.018
CUNDALL, P. A.; STRACK, O. D. L. A discrete numerical model for granular assemblies. Géotechnique, v. 29, n. 1, p. 47–65, 1979. DOI: https://doi.org/10.1680/geot.1979.29.1.47
DE ANDA-SUÁREZ, Juan et al. Evolutionary Gaussian-gradient: a new optimization algorithm for the electromechanical design of gravitational batteries. In: Hybrid Intelligent Systems Based on Extensions of Fuzzy Logic, Neural Networks and Metaheuristics. Cham: Springer Nature Switzerland, 2023. p. 347–364. DOI: https://doi.org/10.1007/978-3-031-28999-6_22
DOMÍNGUEZ, J. M. et al. Neighbour lists in smoothed particle hydrodynamics. International Journal for Numerical Methods in Fluids, v. 67, n. 12, p. 2026–2042, 2011. DOI: https://doi.org/10.1002/fld.2481
DUAN, Shaomi; LUO, Huilong; LIU, Haipeng. A multi-strategy seeker optimization algorithm for optimization constrained engineering problems. IEEE Access, v. 10, p. 7165–7195, 2022. DOI: https://doi.org/10.1109/ACCESS.2022.3141908
FUCHS, Sebastian L. et al. An SPH framework for fluid–solid and contact interaction problems including thermo-mechanical coupling and reversible phase transitions. Advanced Modeling and Simulation in Engineering Sciences, v. 8, n. 1, p. 1–33, 2021. DOI: https://doi.org/10.1186/s40323-021-00200-w
GAO, Hongwei et al. Robust bacterial foraging algorithms based on few-excellent-individuals guidance strategy. Sensors & Materials, v. 32, 2020. DOI: https://doi.org/10.18494/SAM.2020.2571
GINGOLD, Robert A.; MONAGHAN, Joseph J. Smoothed particle hydrodynamics: theory and application to non-spherical stars. Monthly Notices of the Royal Astronomical Society, v. 181, n. 3, p. 375–389, 1977. DOI: https://doi.org/10.1093/mnras/181.3.375
GOMEZ-GESTEIRA, Moncho et al. State-of-the-art of classical SPH for free-surface flows. Journal of Hydraulic Research, v. 48, n. sup1, p. 6–27, 2010. DOI: https://doi.org/10.1080/00221686.2010.9641242
GRANT-PETERS, Jonathan; HAUSER, Raphael. A seven-point algorithm for piecewise smooth univariate minimization. arXiv preprint, arXiv:2012.06553, 2020. Disponível em: https://arxiv.org/abs/2012.06553. Acesso em: 9 set. 2025.
HERNQUIST, Lars; KATZ, Neal. TREESPH-A unification of SPH with the hierarchical tree method. Astrophysical Journal Supplement Series, v. 70, p. 419–446, 1989. DOI: https://doi.org/10.1086/191344
HU, D. A. et al. A meshless local Petrov–Galerkin method for large deformation contact analysis of elastomers. Engineering Analysis with Boundary Elements, v. 31, n. 7, p. 657–666, 2007. DOI: https://doi.org/10.1016/j.enganabound.2006.11.005
INFINITY77. A one-dimensional test functions platform with multiple local and global minima. [S. l.]: INFINITY77, s. d. Disponível em: https://infinity77.net/global_optimization/test_functions_1d.html#d-test-functions. Acesso em: 18 dez. 2023.
KASHYAP, Katyayani; SHARMA, Tarun K.; RAJPUROHIT, Jitendra. Logistic map and wavelet transform based differential evolution. International Journal of System Assurance Engineering and Management, v. 11, p. 506–514, 2020. DOI: https://doi.org/10.1007/s13198-019-00920-8
KENNEDY, James; EBERHART, Russell. Particle swarm optimization. In: Proceedings of ICNN'95-International Conference on Neural Networks - IEEE, 1995. p. 1942–1948. DOI: https://doi.org/10.1109/ICNN.1995.488968
KOSCHIER, Dan et al. Smoothed particle hydrodynamics techniques for the physics-based simulation of fluids and solids. arXiv preprint, arXiv:2009.06944, 2020. Disponível em: https://arxiv.org/abs/2009.06944. Acesso em: 9 set. 2025.
LEVEQUE, Randall J. Finite Volume Methods for Hyperbolic Problems. Cambridge: Cambridge University Press, 2002. Disponível em: https://link.springer.com/book/10.1007/978-0-8176-8394-8. Acesso em: 22 jun. 2025. DOI: https://doi.org/10.1017/CBO9780511791253
LIND, Steven J.; ROGERS, Benedict D.; STANSBY, Peter K. Review of smoothed particle hydrodynamics: towards converged Lagrangian flow modelling. Proceedings of the Royal Society A, v. 476, n. 2241, p. 20190801, 2020. DOI: https://doi.org/10.1098/rspa.2019.0801
LIU, Gui-Rong; LIU, Moubin B. Smoothed particle hydrodynamics: a meshfree particle method. World Scientific, 2003. DOI: https://doi.org/10.1142/9789812564405
LIU, Wing-Kam; LI, Shaofan; BELYTSCHKO, Ted. Moving least-square reproducing kernel methods (I) methodology and convergence. Computer Methods in Applied Mechanics and Engineering, v. 143, n. 1-2, p. 113–154, 1997. DOI: https://doi.org/10.1016/S0045-7825(96)01132-2
LUCY, Leon B. A numerical approach to the testing of the fission hypothesis. Astronomical Journal, v. 82, p. 1013–1024, 1977. DOI: https://doi.org/10.1086/112164
MIRANDA, J. Pyswarm: Particle Swarm Optimization (PSO) for Python. [S. l. s. n.], s. d. Disponível em: https://github.com/tisimst/pyswarm. Acesso em: 27 jun. 2025.
MOHAMMADI, Masoud; RIAZI, Masoud. Applicable investigation of SPH in characterization of fluid flow in uniform and non-uniform periodic porous media. Sustainability, v. 14, n. 21, p. 14320, 2022. DOI: https://doi.org/10.3390/su142114320
MONAGHAN, Joe J. Smoothed particle hydrodynamics. Annual Review of Astronomy and Astrophysics, v. 30, p. 543–574, 1992. DOI: https://doi.org/10.1146/annurev.astro.30.1.543
MONAGHAN, Joe J. Smoothed particle hydrodynamics. Reports on Progress in Physics, v. 68, n. 8, p. 1703–1759, 2005. DOI: https://doi.org/10.1088/0034-4885/68/8/R01
MORTON, Guy M. A computer oriented geodetic data base and a new technique in file sequencing. [S. l. s. n.], 1966. Disponível em: https://apps.dtic.mil/sti/citations/AD0253260. Acesso em: 9 set. 2025.
MOUNTRIS, Konstantinos A. et al. An explicit total Lagrangian fragile points method for finite deformation of hyperelastic materials. Engineering Analysis with Boundary Elements, v. 151, p. 255–264, 2023. DOI: https://doi.org/10.1016/j.enganabound.2023.03.001
MYERS, Conner et al. A hybrid finite volume method and smoothed particle hydrodynamics approach for efficient and accurate blast simulations. Frontiers in Physics, v. 11, p. 1325294, 2024. DOI: https://doi.org/10.3389/fphy.2023.1325294
MYERS, Conner; PALMER, Todd; PALMER, Camille. A hybrid finite volume-smoothed particle hydrodynamics approach for shock capturing applications. Computer Methods in Applied Mechanics and Engineering, v. 417, p. 116412, 2023. DOI: https://doi.org/10.1016/j.cma.2023.116412
PAHLKE, Johannes; SBALZARINI, Ivo F. A unifying mathematical definition of particle methods. IEEE Open Journal of the Computer Society, 2023. DOI: https://doi.org/10.1109/OJCS.2023.3254466
RAJA, Vijayakumar et al. Modeling and simulation of 3D food printing systems: scope, advances, and challenges. Foods, v. 12, n. 18, p. 3412, 2023. DOI: https://doi.org/10.3390/foods12183412
RAMACHANDRAN, Prabhu et al. PySPH: a Python-based framework for smoothed particle hydrodynamics. ACM Transactions on Mathematical Software (TOMS), v. 47, n. 4, p. 1–38, 2021. DOI: https://doi.org/10.1145/3460773
RAMACHANDRAN, Prabhu; PURI, Kunal. Entropically damped artificial compressibility for SPH. Computers & Fluids, v. 179, p. 579–594, 2019. DOI: https://doi.org/10.1016/j.compfluid.2018.11.023
SPRINGEL, Volker. The cosmological simulation code GADGET-2. Monthly Notices of the Royal Astronomical Society, v. 364, n. 4, p. 1105–1134, 2005. DOI: https://doi.org/10.1111/j.1365-2966.2005.09655.x
TSENG, Hsuan-Yu et al. Particle swarm optimization for nonlinear constrained optimization problems. IEEE Access, v. 9, p. 124757–124767, 2021. DOI: https://doi.org/10.1109/ACCESS.2021.3110708
VACONDIO, Renato et al. Grand challenges for smoothed particle hydrodynamics numerical schemes. Computational Particle Mechanics, v. 8, p. 575–588, 2021. DOI: https://doi.org/10.1007/s40571-020-00354-1
VIOLEAU, Damien. Fluid mechanics and the SPH method: theory and applications. Oxford: Oxford University Press, 2012. DOI: https://doi.org/10.1093/acprof:oso/9780199655526.001.0001
WANG, Chau-Shing et al. Process parameter prediction and modeling of laser percussion drilling by artificial neural networks. Micromachines, v. 13, n. 4, p. 529, 2022. DOI: https://doi.org/10.3390/mi13040529
WANG, Mengdi et al. Thin-film smoothed particle hydrodynamics fluid. ACM Transactions on Graphics (TOG), v. 40, n. 4, p. 1–16, 2021. DOI: https://doi.org/10.1145/3450626.3459864
WU, Qiang; PENG, PiaoPiao; CHENG, YuMin. The interpolating element-free Galerkin method for elastic large deformation problems. Science China Technological Sciences, v. 64, n. 2, p. 364–374, 2021. DOI: https://doi.org/10.1007/s11431-019-1583-y
XI, Runping et al. Survey on smoothed particle hydrodynamics and the particle systems. IEEE Access, v. 8, p. 3087–3105, 2019. DOI: https://doi.org/10.1109/ACCESS.2019.2962082
YE, Ting et al. Smoothed particle hydrodynamics (SPH) for complex fluid flows: recent developments in methodology and applications. Physics of Fluids, v. 31, n. 1, p. 017101, 2019. DOI: https://doi.org/10.1063/1.5068697
ZHANG, Tingyu et al. SPH modeling of water-related natural hazards. Scientific Journal of Technology, v. 3, n. 9, p. 1–12, 2021.
Downloads
Publicado
Licença
Copyright (c) 2025 RECIMA21 - Revista Científica Multidisciplinar - ISSN 2675-6218
Este trabalho está licenciado sob uma licença Creative Commons Attribution 4.0 International License.
Os direitos autorais dos artigos/resenhas/TCCs publicados pertecem à revista RECIMA21, e seguem o padrão Creative Commons (CC BY 4.0), permitindo a cópia ou reprodução, desde que cite a fonte e respeite os direitos dos autores e contenham menção aos mesmos nos créditos. Toda e qualquer obra publicada na revista, seu conteúdo é de responsabilidade dos autores, cabendo a RECIMA21 apenas ser o veículo de divulgação, seguindo os padrões nacionais e internacionais de publicação.
