Two-dimensional mesh generator and quality analysis of elements on the curvilinear coordinates system
DOI:
https://doi.org/10.5433/1679-0375.2021v42n1p29Keywords:
Automated two-dimensional mesh generator, Parametric linear spline, Generalized coordinates, Python languageAbstract
Through mathematical models, it is possible to turn a problem of the physical domain to the computational domain. In this context, the paper presents a two-dimensional mesh generator in generalized coordinates, which uses the parametric linear spline method and partial differential equations. The generator is automated and able to treat real complex domains and, consequently, more realistic problems. However, there is a possibility that lower quality elements may be introduced into the computational mesh. Thus, metrics are investigated that identify elements considered to be of lower quality. Experiments are carried out to verify the efficiency of the adopted metrics, considering meshes with single block, and multi-blocks. According to the experiments, the work allowed the detection of elements of lower quality, contributing to the realization of an adequate modeling of geometriesDownloads
Download data is not yet available.
References
ALMEIDA, J; LOBAO, D.; STAMPA, C; ALVAREZ, G. Multi-block technique applied to Navier-Stokes equations in two dimensions, Semina: Ciências Exatas e Tecnológicas, 39(2), 2018, 115-124. DOI: http://dx.doi.org/10.5433/1679- 0375.2018v39n2p115
BELINELLI, E. O.; NATTI, P. L.; ROMEIRO, N. M. L.; CIRILO, E. R.; FANTIN, L. H.; OLIVEIRA, K. B.; CANTERI, M. G.; NATTI, E. R. T. Geração de malha para descrever a dispersão da ferrugem da soja no Paraná. In: Júlio Cesar Ribeiro. (Org.). Ciências Exatas e da Terra: Conhecimentos Estratégicos para o Desenvolvimento do País. Ponta Grossa: Atena Editora, 2020. p. 225-239.
BOROUCHAKI, H; FREY, P. J. Adaptive triangular–quadrilateral mesh generation, International Journal for Numerical Methods in Engineering, Chichester, v. 45, n. 5, p. 915-934, 1998. Available from: https://hal.inria.fr/inria-00073738. Acess in: 20 oct. 2020
BORTOLI, A. L. Introdução à dinâmica de fluidos computacional. Porto Alegre: Editora da UFRG, 2000.
BURDEN, R. L.; FAIRES, J. D.; BURDEN, A.M. Numerical Analysis. Boston: Cengage Learning, 2015.
CAI, X.; LANGTANGEN, H. P.; MOE, H. On the performance of the Python programming language for serial and parallel scientific computations. Scientific Programming, New York, v. 13, n. 1, pp. 31-56, 2005.
CIRILO, E. R.; BORTOLI, A. L. Cubic splines for trachea and bronchial tubes grid generation. Semina: Ciências Exatas e Tecnológicas, Londrina, v. 27(2), p. 147-155, 2006. DOI: http://dx.doi.org/10.5433/1679- 0375.2006v27n2p147
CIRILO, E. R.; BARBA, A. N. D.; NATTI, P. L.; ROMEIRO, N. M. L. A numerical model based on the curvilinear coordinate system for the MAC method simplified. Semina: Ciências Exatas e Tecnológicas, Londrina, v. 39, p. 87, 2018.
COELHO, F. U.; LOURENCO, M. L. Curso de álgebra linear, Editora da Universidade de São Paulo, Ed. 1, v. 34, 2001.
FORTUNA, A. O. Técnicas computacionais para dinâmica de fluidos: Conceitos básicos e aplicações. São Paulo: EDUSP, 2012.
GONZALEZ, R. C.; WOODS, R. E. Processamento digital de imagens, Addison Wesley Pearson Brasil, 2011.
GOOGLE. Google Earth. Available from: https://www.google.com/earth/. Access in: oct. 2020.
GOSE, E.; JOHNSONBAUGH, R.; JOST, S. Pattern recognition and image analysis, Prentice-Hall, Inc., 1996.
HSU, J.; JAMESON, A. An implicit-explicit hybrid scheme for calculating complex unsteady flows (2002), American Institute of Aeronautics and Astronautics 40th AIAA Aerospace Sciences Meeting & Exhibit - Reno, 2002. DOI: https://doi.org/10.2514/6.2002-714.
KOOMULLIL, R.; SONI B.; SINGH R. A comprehensive generalized mesh system for CFD applications. Mathematics and Computers in Simulation, vol. 78, pp. 605-617, 2008.
JOHNEN, A.; ERNST, D.; GEUZAINE, C. Sequential decision-making approach for quadrangular mesh generation, Engineering with Computers, v. 31, n. 4, pp. 729-735, 2015. DOI: http://dx.doi.org/10.1007/s00366-014-0383-9
LAIPING, Z.; ZHONG, Z.; XINGHUA, C., XITHAMES, H. A 3D hybrid grid generation technique and a multigrid/parallel algorithm based on anisotropic agglomeration approach. Chinese Journal of Aeronautics, vol. 26, n.1, pp. 47-62, 2013.
MAGANIN, J.; ROMEIRO, N. M. L.; CIRILO, E. R.; NATTI, P. L. Simulation of a mathematical model of tumoral growth using finite differences. Brazilian Journal of Development, v. 6, pp. 87696-87709, 2020. DOI: https://doi.org/10.34117/bjdv6n11-261
MALISKA, C. R. Transferência de calor e mecânica dos fluidos computacional. São Paulo: LTC, 2004. NAOZUKA, G. T. Geração e análise de qualidade de malhas computacionais em coordenadas curvelíneas, Master’s Dissertation, Postgraduate Program in Computer Science - Computer Science Department, Londrina State University, 2018.
PARDO, S. R.; NATTI, P. L.; ROMEIRO, N. M. L.; CIRILO, E. R. A transport modeling of the carbonnitrogen cycle at Igapó I Lake-Londrina, Paraná State, Brazil. Acta Scientiarum. Technology, v. 34, p. 217-226, 2012. DOI: https://doi.org/10.4025/actascitechnol.v34i2.11792
PARK, J.; SHONTZ, J. M. Two derivative-free optimization algorithms for mesh quality improvement. Procedia Computer Science, v. 1, n.1, p. 387-396, 2010. DOI: https://doi.org/10.1016/j.procs.2010.04.042.
R CORE TEAM A language and environment for statistical computing. R Foundation for Statistical Computing, Vienna: R Core Team, 2020. Available from: https://www.R-project.org/. Acess in: 20 aug. 2020.
ROMEIRO, N. L. M.; CIRILO, E. R.; NATTI, P. L.; DOY OKAMOTO, L. M.; JULIANOTTI, T. Chimney height, a determining factor in the dispersion of pollutants and their concentration. World Journal of Engineering and Technology, v. 9, p. 173-193, 2021. DOI: https://doi.org/10.4236/wjet.2021.91013
ROMEIRO, N. L. M.; CASTRO, R. G. S.; CIRILO, E. R.; NATTI, P. L. Local calibration of coliforms parameters of water quality problem at Igapó I Lake - Londrina, Paraná, Brazil. Ecological Modelling, v. 222, p. 1888-1896, 2011. DOI: https://doi.org/10.1016/j.ecolmodel.2011.03.018
ROMEIRO, N. L. M.; MANGILI, F. B.; COSTANZI, R. N.; CIRILO, E. R.; NATTI, P. L. Numerical simulation of BOD5 dynamics in Igapó I lake, Londrina, Paraná, Brazil: Experimental measurement and mathematical modeling. Semina: Ciências Exatas e Tecnológicas, Londrina, v. 38, p. 50-58, 2017. DOI: http://dx.doi.org/10.5433/1679- 0375.2017v38n2p50
ALMEIDA, J; LOBAO, D.; STAMPA, C; ALVAREZ, G. Multi-block technique applied to Navier-Stokes equations in two dimensions, Semina: Ciências Exatas e Tecnológicas, Londrina, v. 39, n. 2, p. 115-124, 2018. DOI: http://dx.doi.org/10.5433/1679- 0375.2018v39n2p115
BELINELLI, E. O.; NATTI, P. L.; ROMEIRO, N. M. L.; CIRILO, E. R.; FANTIN, L. H.; OLIVEIRA, K. B.; CANTERI, M. G.; NATTI, E. R. T. Geração de malha para descrever a dispersão da ferrugem da soja no Paraná. In: RIBEIRO, J. C. (Org.). Ciências Exatas e da Terra: Conhecimentos Estratégicos para o Desenvolvimento do País. Ponta Grossa: Atena Editora, 2020. p. 225-239.
BOROUCHAKI, H; FREY, P. J. Adaptive triangular–quadrilateral mesh generation, International Journal for Numerical Methods in Engineering, Chichester, v. 45, n. 5, p. 915-934, 1998. Available from: https://hal.inria.fr/inria-00073738. Acess in: 20 oct. 2020
BORTOLI, A. L. Introdução à dinâmica de fluidos computacional. Porto Alegre: Editora da UFRG, 2000.
BURDEN, R. L.; FAIRES, J. D.; BURDEN, A.M. Numerical Analysis. Boston: Cengage Learning, 2015.
CAI, X.; LANGTANGEN, H. P.; MOE, H. On the performance of the Python programming language for serial and parallel scientific computations. Scientific Programming, New York, v. 13, n. 1, pp. 31-56, 2005.
CIRILO, E. R.; BORTOLI, A. L. Cubic splines for trachea and bronchial tubes grid generation. Semina: Ciências Exatas e Tecnológicas, Londrina, v. 27, n.2, p. 147-155, 2006. DOI: http://dx.doi.org/10.5433/1679- 0375.2006v27n2p147
CIRILO, E. R.; BARBA, A. N. D.; NATTI, P. L.; ROMEIRO, N. M. L. A numerical model based on the curvilinear coordinate system for the MAC method simplified. Semina: Ciências Exatas e Tecnológicas, Londrina, v. 39, p. 87, 2018.
COELHO, F. U.; LOURENCO, M. L. Curso de álgebra linear, Editora da Universidade de São Paulo, Ed. 1, v. 34, 2001.
FORTUNA, A. O. Técnicas computacionais para dinâmica de fluidos: Conceitos básicos e aplicações. São Paulo: EDUSP, 2012.
GONZALEZ, R. C.; WOODS, R. E. Processamento digital de imagens, Addison Wesley Pearson Brasil, 2011.
GOOGLE. Google Earth. Available from: https://www.google.com/earth/. Access in: oct. 2020.
GOSE, E.; JOHNSONBAUGH, R.; JOST, S. Pattern recognition and image analysis, Prentice-Hall, Inc., 1996.
HSU, J.; JAMESON, A. An implicit-explicit hybrid scheme for calculating complex unsteady flows (2002), American Institute of Aeronautics and Astronautics 40th AIAA Aerospace Sciences Meeting & Exhibit - Reno, 2002. DOI: https://doi.org/10.2514/6.2002-714.
KOOMULLIL, R.; SONI B.; SINGH R. A comprehensive generalized mesh system for CFD applications. Mathematics and Computers in Simulation, v. 78, pp. 605-617, 2008.
JOHNEN, A.; ERNST, D.; GEUZAINE, C. Sequential decision-making approach for quadrangular mesh generation, Engineering with Computers, v. 31, n. 4, pp. 729-735, 2015. DOI: http://dx.doi.org/10.1007/s00366-014-0383-9
LAIPING, Z.; ZHONG, Z.; XINGHUA, C., XITHAMES, H. A 3D hybrid grid generation technique and a multigrid/parallel algorithm based on anisotropic agglomeration approach. Chinese Journal of Aeronautics, v. 26, n.1, p. 47-62, 2013.
MAGANIN, J.; ROMEIRO, N. M. L.; CIRILO, E. R.; NATTI, P. L. Simulation of a mathematical model of tumoral growth using finite differences. Brazilian Journal of Development, v. 6, pp. 87696-87709, 2020. DOI: https://doi.org/10.34117/bjdv6n11-261
MALISKA, C. R. Transferência de calor e mecânica dos fluidos computacional. São Paulo: LTC, 2004.
NAOZUKA, G. T. Geração e análise de qualidade de malhas computacionais em coordenadas curvelíneas, Master’s Dissertation, Postgraduate Program in Computer Science - Computer Science Department, Londrina State University, 2018.
PARDO, S. R.; NATTI, P. L.; ROMEIRO, N. M. L.; CIRILO, E. R. A transport modeling of the carbonnitrogen cycle at Igapó I Lake-Londrina, Paraná State, Brazil. Acta Scientiarum. Technology, v. 34, p. 217-226, 2012. DOI: 10.4025/actascitechnol.v34i2.11792
PARK, J.; SHONTZ, J. M. Two derivative-free optimization algorithms for mesh quality improvement. Procedia Computer Science, v. 1, n.1, p. 387-396, 2010. DOI: https://doi.org/10.1016/j.procs.2010.04.042.
R CORE TEAM A language and environment for statistical computing. R Foundation for Statistical Computing, Vienna: R Core Team, 2020. Available from: https://www.r-project.org/. Acess in: 20 aug. 2020.
ROMEIRO, N. L. M.; CIRILO, E. R.; NATTI, P. L.; DOY OKAMOTO, L. M.; JULIANOTTI, T. Chimney height, a determining factor in the dispersion of pollutants and their concentration. World Journal of Engineering and Technology, v. 9, p. 173-193, 2021. DOI: 10.4236/wjet.2021.91013
ROMEIRO, N. L. M.; CASTRO, R. G. S.; CIRILO, E. R.; NATTI, P. L. Local calibration of coliforms parameters of water quality problem at Igapó I Lake - Londrina, Paraná, Brazil. Ecological Modelling, v. 222, p. 1888-1896, 2011. DOI: https://doi.org/10.1016/j.ecolmodel.2011.03.018
ROMEIRO, N. L. M.; MANGILI, F. B.; COSTANZI, R. N.; CIRILO, E. R.; NATTI, P. L. Numerical simulation of BOD5 dynamics in Igapó I lake, Londrina, Paraná, Brazil: Experimental measurement and mathematical modeling. Semina: Ciências Exatas e Tecnológicas, Londrina, v. 38, p. 50-58, 2017. DOI: http://dx.doi.org/10.5433/1679- 0375.2017v38n2p50
RUSSUM, G. Python reference manual, Centre for Mathematics and Computer Science, Amsterdam, The Netherlands, 1995. Available from: http://www.ncstrl.org:8900/ncstrl/servlet/search?formname=detail&id=oai%3Ancstrlh%3Aercim_cwi%3Aercim.cwi%2F%2FCS-R9525. Access in: oct. 2018.
SAITA, T. M.; NATTI, P. L.; CIRILO, E. R.; ROMEIRO, N. L. M.; CANDEZANO, M. A. C.; ACUNA, R. A. B.; MORENO, L. C. G. Simulação numérica da dinâmica de coliformes fecais no lago Luruaco, Colômbia. Trends in Applied and Computational Mathematics, v. 18, p. 435-447, 2017. DOI: https://doi.org/10.5540/tema.2017.018.03.0435
SCIPY-NUMPY. In http://www.numpy.org/. Access in: oct. 2020.
SCIPY-MATPLOTLIB. In http://matplotlib.org/. Access in: oct. 2020.
THOMPSON, J. F.; THAMES, F. C.; MASTIN, C. W. TOMCAT - A Code for Numerical Generation of Boundary Fitted Curvilinear Coordinate Systems on Fields Containing Any Number of Arbitrary Two-Dimensional Bodies. Journal of Computational Physics, v. 24, p. 274-302, 1977. DOI: https://doi.org/10.1016/0021-9991(77)90038-9
THOMPSON, J. F.; WARSI, Z. U. A.; MASTIN, C. W. Numerical grid generation: foundations and applications. New York: Elsevier Science Publishing, 1985.
THOMPSON, J. F.; SONI, B. K.; WEATHERILL, N. P. Handbook of Grid Generation. Florida: CRC Press, 1998.
BELINELLI, E. O.; NATTI, P. L.; ROMEIRO, N. M. L.; CIRILO, E. R.; FANTIN, L. H.; OLIVEIRA, K. B.; CANTERI, M. G.; NATTI, E. R. T. Geração de malha para descrever a dispersão da ferrugem da soja no Paraná. In: Júlio Cesar Ribeiro. (Org.). Ciências Exatas e da Terra: Conhecimentos Estratégicos para o Desenvolvimento do País. Ponta Grossa: Atena Editora, 2020. p. 225-239.
BOROUCHAKI, H; FREY, P. J. Adaptive triangular–quadrilateral mesh generation, International Journal for Numerical Methods in Engineering, Chichester, v. 45, n. 5, p. 915-934, 1998. Available from: https://hal.inria.fr/inria-00073738. Acess in: 20 oct. 2020
BORTOLI, A. L. Introdução à dinâmica de fluidos computacional. Porto Alegre: Editora da UFRG, 2000.
BURDEN, R. L.; FAIRES, J. D.; BURDEN, A.M. Numerical Analysis. Boston: Cengage Learning, 2015.
CAI, X.; LANGTANGEN, H. P.; MOE, H. On the performance of the Python programming language for serial and parallel scientific computations. Scientific Programming, New York, v. 13, n. 1, pp. 31-56, 2005.
CIRILO, E. R.; BORTOLI, A. L. Cubic splines for trachea and bronchial tubes grid generation. Semina: Ciências Exatas e Tecnológicas, Londrina, v. 27(2), p. 147-155, 2006. DOI: http://dx.doi.org/10.5433/1679- 0375.2006v27n2p147
CIRILO, E. R.; BARBA, A. N. D.; NATTI, P. L.; ROMEIRO, N. M. L. A numerical model based on the curvilinear coordinate system for the MAC method simplified. Semina: Ciências Exatas e Tecnológicas, Londrina, v. 39, p. 87, 2018.
COELHO, F. U.; LOURENCO, M. L. Curso de álgebra linear, Editora da Universidade de São Paulo, Ed. 1, v. 34, 2001.
FORTUNA, A. O. Técnicas computacionais para dinâmica de fluidos: Conceitos básicos e aplicações. São Paulo: EDUSP, 2012.
GONZALEZ, R. C.; WOODS, R. E. Processamento digital de imagens, Addison Wesley Pearson Brasil, 2011.
GOOGLE. Google Earth. Available from: https://www.google.com/earth/. Access in: oct. 2020.
GOSE, E.; JOHNSONBAUGH, R.; JOST, S. Pattern recognition and image analysis, Prentice-Hall, Inc., 1996.
HSU, J.; JAMESON, A. An implicit-explicit hybrid scheme for calculating complex unsteady flows (2002), American Institute of Aeronautics and Astronautics 40th AIAA Aerospace Sciences Meeting & Exhibit - Reno, 2002. DOI: https://doi.org/10.2514/6.2002-714.
KOOMULLIL, R.; SONI B.; SINGH R. A comprehensive generalized mesh system for CFD applications. Mathematics and Computers in Simulation, vol. 78, pp. 605-617, 2008.
JOHNEN, A.; ERNST, D.; GEUZAINE, C. Sequential decision-making approach for quadrangular mesh generation, Engineering with Computers, v. 31, n. 4, pp. 729-735, 2015. DOI: http://dx.doi.org/10.1007/s00366-014-0383-9
LAIPING, Z.; ZHONG, Z.; XINGHUA, C., XITHAMES, H. A 3D hybrid grid generation technique and a multigrid/parallel algorithm based on anisotropic agglomeration approach. Chinese Journal of Aeronautics, vol. 26, n.1, pp. 47-62, 2013.
MAGANIN, J.; ROMEIRO, N. M. L.; CIRILO, E. R.; NATTI, P. L. Simulation of a mathematical model of tumoral growth using finite differences. Brazilian Journal of Development, v. 6, pp. 87696-87709, 2020. DOI: https://doi.org/10.34117/bjdv6n11-261
MALISKA, C. R. Transferência de calor e mecânica dos fluidos computacional. São Paulo: LTC, 2004. NAOZUKA, G. T. Geração e análise de qualidade de malhas computacionais em coordenadas curvelíneas, Master’s Dissertation, Postgraduate Program in Computer Science - Computer Science Department, Londrina State University, 2018.
PARDO, S. R.; NATTI, P. L.; ROMEIRO, N. M. L.; CIRILO, E. R. A transport modeling of the carbonnitrogen cycle at Igapó I Lake-Londrina, Paraná State, Brazil. Acta Scientiarum. Technology, v. 34, p. 217-226, 2012. DOI: https://doi.org/10.4025/actascitechnol.v34i2.11792
PARK, J.; SHONTZ, J. M. Two derivative-free optimization algorithms for mesh quality improvement. Procedia Computer Science, v. 1, n.1, p. 387-396, 2010. DOI: https://doi.org/10.1016/j.procs.2010.04.042.
R CORE TEAM A language and environment for statistical computing. R Foundation for Statistical Computing, Vienna: R Core Team, 2020. Available from: https://www.R-project.org/. Acess in: 20 aug. 2020.
ROMEIRO, N. L. M.; CIRILO, E. R.; NATTI, P. L.; DOY OKAMOTO, L. M.; JULIANOTTI, T. Chimney height, a determining factor in the dispersion of pollutants and their concentration. World Journal of Engineering and Technology, v. 9, p. 173-193, 2021. DOI: https://doi.org/10.4236/wjet.2021.91013
ROMEIRO, N. L. M.; CASTRO, R. G. S.; CIRILO, E. R.; NATTI, P. L. Local calibration of coliforms parameters of water quality problem at Igapó I Lake - Londrina, Paraná, Brazil. Ecological Modelling, v. 222, p. 1888-1896, 2011. DOI: https://doi.org/10.1016/j.ecolmodel.2011.03.018
ROMEIRO, N. L. M.; MANGILI, F. B.; COSTANZI, R. N.; CIRILO, E. R.; NATTI, P. L. Numerical simulation of BOD5 dynamics in Igapó I lake, Londrina, Paraná, Brazil: Experimental measurement and mathematical modeling. Semina: Ciências Exatas e Tecnológicas, Londrina, v. 38, p. 50-58, 2017. DOI: http://dx.doi.org/10.5433/1679- 0375.2017v38n2p50
ALMEIDA, J; LOBAO, D.; STAMPA, C; ALVAREZ, G. Multi-block technique applied to Navier-Stokes equations in two dimensions, Semina: Ciências Exatas e Tecnológicas, Londrina, v. 39, n. 2, p. 115-124, 2018. DOI: http://dx.doi.org/10.5433/1679- 0375.2018v39n2p115
BELINELLI, E. O.; NATTI, P. L.; ROMEIRO, N. M. L.; CIRILO, E. R.; FANTIN, L. H.; OLIVEIRA, K. B.; CANTERI, M. G.; NATTI, E. R. T. Geração de malha para descrever a dispersão da ferrugem da soja no Paraná. In: RIBEIRO, J. C. (Org.). Ciências Exatas e da Terra: Conhecimentos Estratégicos para o Desenvolvimento do País. Ponta Grossa: Atena Editora, 2020. p. 225-239.
BOROUCHAKI, H; FREY, P. J. Adaptive triangular–quadrilateral mesh generation, International Journal for Numerical Methods in Engineering, Chichester, v. 45, n. 5, p. 915-934, 1998. Available from: https://hal.inria.fr/inria-00073738. Acess in: 20 oct. 2020
BORTOLI, A. L. Introdução à dinâmica de fluidos computacional. Porto Alegre: Editora da UFRG, 2000.
BURDEN, R. L.; FAIRES, J. D.; BURDEN, A.M. Numerical Analysis. Boston: Cengage Learning, 2015.
CAI, X.; LANGTANGEN, H. P.; MOE, H. On the performance of the Python programming language for serial and parallel scientific computations. Scientific Programming, New York, v. 13, n. 1, pp. 31-56, 2005.
CIRILO, E. R.; BORTOLI, A. L. Cubic splines for trachea and bronchial tubes grid generation. Semina: Ciências Exatas e Tecnológicas, Londrina, v. 27, n.2, p. 147-155, 2006. DOI: http://dx.doi.org/10.5433/1679- 0375.2006v27n2p147
CIRILO, E. R.; BARBA, A. N. D.; NATTI, P. L.; ROMEIRO, N. M. L. A numerical model based on the curvilinear coordinate system for the MAC method simplified. Semina: Ciências Exatas e Tecnológicas, Londrina, v. 39, p. 87, 2018.
COELHO, F. U.; LOURENCO, M. L. Curso de álgebra linear, Editora da Universidade de São Paulo, Ed. 1, v. 34, 2001.
FORTUNA, A. O. Técnicas computacionais para dinâmica de fluidos: Conceitos básicos e aplicações. São Paulo: EDUSP, 2012.
GONZALEZ, R. C.; WOODS, R. E. Processamento digital de imagens, Addison Wesley Pearson Brasil, 2011.
GOOGLE. Google Earth. Available from: https://www.google.com/earth/. Access in: oct. 2020.
GOSE, E.; JOHNSONBAUGH, R.; JOST, S. Pattern recognition and image analysis, Prentice-Hall, Inc., 1996.
HSU, J.; JAMESON, A. An implicit-explicit hybrid scheme for calculating complex unsteady flows (2002), American Institute of Aeronautics and Astronautics 40th AIAA Aerospace Sciences Meeting & Exhibit - Reno, 2002. DOI: https://doi.org/10.2514/6.2002-714.
KOOMULLIL, R.; SONI B.; SINGH R. A comprehensive generalized mesh system for CFD applications. Mathematics and Computers in Simulation, v. 78, pp. 605-617, 2008.
JOHNEN, A.; ERNST, D.; GEUZAINE, C. Sequential decision-making approach for quadrangular mesh generation, Engineering with Computers, v. 31, n. 4, pp. 729-735, 2015. DOI: http://dx.doi.org/10.1007/s00366-014-0383-9
LAIPING, Z.; ZHONG, Z.; XINGHUA, C., XITHAMES, H. A 3D hybrid grid generation technique and a multigrid/parallel algorithm based on anisotropic agglomeration approach. Chinese Journal of Aeronautics, v. 26, n.1, p. 47-62, 2013.
MAGANIN, J.; ROMEIRO, N. M. L.; CIRILO, E. R.; NATTI, P. L. Simulation of a mathematical model of tumoral growth using finite differences. Brazilian Journal of Development, v. 6, pp. 87696-87709, 2020. DOI: https://doi.org/10.34117/bjdv6n11-261
MALISKA, C. R. Transferência de calor e mecânica dos fluidos computacional. São Paulo: LTC, 2004.
NAOZUKA, G. T. Geração e análise de qualidade de malhas computacionais em coordenadas curvelíneas, Master’s Dissertation, Postgraduate Program in Computer Science - Computer Science Department, Londrina State University, 2018.
PARDO, S. R.; NATTI, P. L.; ROMEIRO, N. M. L.; CIRILO, E. R. A transport modeling of the carbonnitrogen cycle at Igapó I Lake-Londrina, Paraná State, Brazil. Acta Scientiarum. Technology, v. 34, p. 217-226, 2012. DOI: 10.4025/actascitechnol.v34i2.11792
PARK, J.; SHONTZ, J. M. Two derivative-free optimization algorithms for mesh quality improvement. Procedia Computer Science, v. 1, n.1, p. 387-396, 2010. DOI: https://doi.org/10.1016/j.procs.2010.04.042.
R CORE TEAM A language and environment for statistical computing. R Foundation for Statistical Computing, Vienna: R Core Team, 2020. Available from: https://www.r-project.org/. Acess in: 20 aug. 2020.
ROMEIRO, N. L. M.; CIRILO, E. R.; NATTI, P. L.; DOY OKAMOTO, L. M.; JULIANOTTI, T. Chimney height, a determining factor in the dispersion of pollutants and their concentration. World Journal of Engineering and Technology, v. 9, p. 173-193, 2021. DOI: 10.4236/wjet.2021.91013
ROMEIRO, N. L. M.; CASTRO, R. G. S.; CIRILO, E. R.; NATTI, P. L. Local calibration of coliforms parameters of water quality problem at Igapó I Lake - Londrina, Paraná, Brazil. Ecological Modelling, v. 222, p. 1888-1896, 2011. DOI: https://doi.org/10.1016/j.ecolmodel.2011.03.018
ROMEIRO, N. L. M.; MANGILI, F. B.; COSTANZI, R. N.; CIRILO, E. R.; NATTI, P. L. Numerical simulation of BOD5 dynamics in Igapó I lake, Londrina, Paraná, Brazil: Experimental measurement and mathematical modeling. Semina: Ciências Exatas e Tecnológicas, Londrina, v. 38, p. 50-58, 2017. DOI: http://dx.doi.org/10.5433/1679- 0375.2017v38n2p50
RUSSUM, G. Python reference manual, Centre for Mathematics and Computer Science, Amsterdam, The Netherlands, 1995. Available from: http://www.ncstrl.org:8900/ncstrl/servlet/search?formname=detail&id=oai%3Ancstrlh%3Aercim_cwi%3Aercim.cwi%2F%2FCS-R9525. Access in: oct. 2018.
SAITA, T. M.; NATTI, P. L.; CIRILO, E. R.; ROMEIRO, N. L. M.; CANDEZANO, M. A. C.; ACUNA, R. A. B.; MORENO, L. C. G. Simulação numérica da dinâmica de coliformes fecais no lago Luruaco, Colômbia. Trends in Applied and Computational Mathematics, v. 18, p. 435-447, 2017. DOI: https://doi.org/10.5540/tema.2017.018.03.0435
SCIPY-NUMPY. In http://www.numpy.org/. Access in: oct. 2020.
SCIPY-MATPLOTLIB. In http://matplotlib.org/. Access in: oct. 2020.
THOMPSON, J. F.; THAMES, F. C.; MASTIN, C. W. TOMCAT - A Code for Numerical Generation of Boundary Fitted Curvilinear Coordinate Systems on Fields Containing Any Number of Arbitrary Two-Dimensional Bodies. Journal of Computational Physics, v. 24, p. 274-302, 1977. DOI: https://doi.org/10.1016/0021-9991(77)90038-9
THOMPSON, J. F.; WARSI, Z. U. A.; MASTIN, C. W. Numerical grid generation: foundations and applications. New York: Elsevier Science Publishing, 1985.
THOMPSON, J. F.; SONI, B. K.; WEATHERILL, N. P. Handbook of Grid Generation. Florida: CRC Press, 1998.
Downloads
Published
2021-05-07
How to Cite
Naozuka, G. T., Romeiro, N. M. L., Felinto, A. S., Natti, P. L., & Cirilo, E. R. (2021). Two-dimensional mesh generator and quality analysis of elements on the curvilinear coordinates system. Semina: Ciências Exatas E Tecnológicas, 42(1), 29–44. https://doi.org/10.5433/1679-0375.2021v42n1p29
Issue
Section
Original Article
License
The Copyright Declaration for articles published in this journal is the author’s right. Since manuscripts are published in an open access Journal, they are free to use, with their own attributions, in educational and non-commercial applications. The Journal has the right to make, in the original document, changes regarding linguistic norms, orthography, and grammar, with the purpose of ensuring the standard norms of the language and the credibility of the Journal. It will, however, respect the writing style of the authors. When necessary, conceptual changes, corrections, or suggestions will be forwarded to the authors. In such cases, the manuscript shall be subjected to a new evaluation after revision. Responsibility for the opinions expressed in the manuscripts lies entirely with the authors.
This journal is licensed with a license Creative Commons Attribution-NonCommercial 4.0 International.
