BOUNDARY TREATMENT TECHNIQUES IN SMOOTHED PARTICLE HYDRODYNAMICS: IMPLEMENTATIONS IN FLUID AND THERMAL SCIENCES AND RESULTS ANALYSIS
DOI:
https://doi.org/10.26512/ripe.v2i11.21270Palavras-chave:
Boundary conditions. SPH. Heat transfer. Thermal sciences. Fluid mechanics.Resumo
Appropriate boundary treatment technique is one of the greatest challenges found in the Smoothed Particle Hydrodynamics (SPH) Lagrangian method. This paper focuses on the treatment of different boundary condition techniques and their implementation in the SPH code developed by the authors. The boundary conditions implemented and tested in this work involve the use of virtual particles, repulsive force, geometric reflection, and dynamic particle treatments. A code was written in Fortran language in order to solve the system of algebraic equations that result from the application of the SPH method in the discretization of the conservation equations. The implemented boundary conditions are tested and the numerical results are compared with results from non-commercial codes and analytical ones. In general, the numerical results obtained in the present work are in agreement with those reported in the literature.
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Referências
Batchelor, G.K., 2000. An Introduction to Fluid Dynamics. Cambridge University Press, 3rd edition, Cambridge, UK.
Chen, J.K., Beraun, J. E., & Carney, T.C., 1999. A Corrective Smoothed Patricle Method for Boundary Value Problems in Heat Conduction. International Journal for Numerical Methods in Engineering, 46: 231-252.
Courant R., Friedrichs K., & Lewy H., 1967. On the partial difference equations of mathematical physics. IBM Journal, 11:215-234.
Crespo A.J.C., Dominguez J.M., Barreiro A., Gomez-Gesteira M., & Rogers B.D., 2011. GPUs, a new tool of acceleration in CFD: efficiency and reliability on Smoothed Particle Hydrodynamics methods. PLoS ONE 6 (6). Available at:
http://journals.plos.org/plosone/article?id=10.1371/journal.pone.0020685 [Acessed: 25 June 2016].
Cruchaga M.A., Celentano D.J., & Tezduyar T.E., 2007. Collapse of a liquid column: numerical simulation and experimental validation. Comput. Mech., 39: 453-476.
Ferrand M., Laurence D. R., Rogers B. D., Violeau D., & Kassiotis C., 2013. Unified semi-analytical wall boundary conditions for inviscid, laminar or turbulent flows in the meshless SPH method. International Journal for Numerical Methods in Fluids, 71(4): 446-472.
Fourtakas, G., Vacondio, R., & Rogers, B.D., 2015. On the approximate zeroth and first-order consistency in the presence of 2-D irregular boundaries in SPH obtained by the virtual boundary particle methods. International Journal Numerical Methods in Fluids, published online in Wiley Online Library (wileyonlinelibrary.com).
Fraga Filho, C.A.D., & Chacaltana, J.T.A., 2014. Numerical Study of Heat Diffusion Employing the Lagrangian Smoothed Particle Hydrodynamics Method: an Analysis of the Applicability of the Laplacian Operator and the Influence of the Boundaries on the Solution. International Review on Modelling and Simulations (I.RE.MO.S.), 2014, vol. 7, N. 6, pp. 994-1002.
Fraga Filho, C.A.D., 2014. Estudo da Fase Gravitacional-inercial do Espalhamento de Óleo em Mar Calmo empregando o Método Lagrangiano de Partículas Smoothed Particle Hydrodynamics. PhD Thesis, Federal University of Espírito Santo, Brazil. Available at:
http://cfd.mace.manchester.ac.uk/sph/SPH_PhDs/2014/Carlos_Alberto_DUTRA_FRAGA_FILHO_PhD_Thesis_2014.pdf [Accessed: 20 March 2016].
Fraga Filho, C.A.D, Piccoli, F. P., Barbosa, D.A. & Chacaltana, J.T.A., 2015. Estudo numérico da propagação de ondas em praias planas utilizando os modelos Lagrangiano sem malhas e Euleriano. Revista Brasileira de Recursos Hídricos, vol. 20, nº 1, pp. 91-105.
Gingold, R. A., & Monaghan, J. J., 1977. Smoothed Particle Hydrodynamics: Theory and Application to Non-spherical stars. Monthly Notices of the Royal Astronomical Society, vol. 181, pp. 375-338.
Gomez-Gesteira, M., Rogers, B.D., Crespo, A.J.C., Dalrymple, R.A., & Narayanaswamy, M., 2010. User Guide for SPHysics Code. Available at:
https://wiki.manchester.ac.uk/sphysics/images/SPHysics v2.2.000 GUIDE.pdf [Acessed: 25 June 2016]
Gomez-Gesteira M., Crespo A.J.C., Rogers B.D., Dalrymple R.A., Dominguez J.M., & Barreiro A., 2012. SPHysics development of a free-surface fluid solver Part 2: Efficiency and test cases. Computers & Geosciences, 48:300-307.
Kleefsman K.M.T., Fekken G., Veldman A.E.P., Iwanowski B. & Buchner B.A., 2008. Volume-of-Fluid based simulation method for wave impact problems. J. Comput. Phys. 206: 363-393.
Kulasegaram S., Bonet J., Lewis R., & Profit M., 2006. A variational formulation based contact algorithm for rigid boundaries in two-dimensional SPH applications. Computational Mechanics, 33(4): 316-325.
Leroy, A., Violeau D., Ferrand M., & Kassiotis C., 2014. Unified semi-analytical wall boundary conditions applied to 2-D incompressible SPH. Journal of Computational Physics, 261:106-129.
Liu G.R., & Liu M.B., 2003. Smoothed particle hydrodynamics: a meshfree particle method. World Scientific, Singapore.
Liu, M.B., & Liu, G.R, 2010. Smoothed Particle Hydrodynamics (SPH): an Overview and Recent Developments. Archives of Computational Methods in Engineering, 17: 25-76.
Lucy, L.B., 1977. Numerical approach to testing the fission hypothesis. Astronomical Journal, 82: 1013-1024. Marques, A.C.H., & Doricio, J. L., 2006. Numerical investigation of the flow in a two-dimensional cavity: Meshless, Finite Volumes and Finite Difference Methods. Latin American Journal of Solids and Structures, vol.3, pp. 301-324.
Monaghan, J.J., 1992. Smoothed Particle Hydrodynamics. Annual Review of Astronomy and Astrophysics, vol. 30, pp. 543-574.
Nwogu, O. G., 1996. Numerical Prediction of Breaking Waves and Currents with a Boussinesq Model. Proceedings of the 25th International Conference on Coastal Engineering, ICCE '96, Orlando, Vol. 4, 4807-4820.
Pinto, W.J.N., Fraga Filho, C.A.D., & Chacaltana, J.T.A., 2011. Aplicação do Método Lagrangiano SPH (Smoothed Particle Hydrodynamics) para a Solução do Problema das Cavidades. Anais do XIV Encontro de Modelagem Computacional (XIV EMC) e do II Encontro de Ciência e Tecnologia de Materiais (II ECTM). Nova Friburgo: Editora: Rede SIRIUS, Universidade do Estado do Rio de Janeiro, vol. 01, pp. 500-508. Pinto, W.J.N. Aplicação do Método Lagrangiano SPH (Smoothed Particle Hydrodynamics) para a Solução do Problema das Cavidades, 2013. Masters Dissertation, Federal University of Espírito Santo (UFES), Brazil. Pletcher, R.H., Tanehill, J.C., & Anderson D.A. 1997. Computational Fluid Mechanics and Heat Transfer, Taylor and Francis, 2nd edition, London, UK.
Rapaport D.C., 2004. The art of molecular dynamics simulation. Cambridge University Press, 2nd edition, Cambridge, UK.
Vaughan G.L., Healy, T.R., Bryan, K.R., Sneyd A.D., & Gorman, R. M., 2008. Completeness, conservation and error in SPH for fluids. International Journal for Numerical Methods in Fluids, vol. 56, pp. 37”“62.
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