Avaliação de métodos iterativos aplicados à equação não-linear de Richards

Moura, Mario Jorge dos Reis

Please use this identifier to cite or link to this item: https://rima.ufrrj.br/jspui/handle/20.500.14407/14343

Full metadata record

DC Field	Value	Language
dc.contributor.author	Moura, Mario Jorge dos Reis
dc.date.accessioned	2023-12-22T03:00:03Z	-
dc.date.available	2023-12-22T03:00:03Z	-
dc.date.issued	2022-03-31
dc.identifier.citation	MOURA, Mario Jorge dos Reis. Avaliação de métodos iterativos aplicados à equação não-linear de Richards. 2022. Dissertação (Mestrado em Modelagem Matemática e Computacional) - Instituto de Ciências Exatas, Universidade Federal Rural do Rio de Janeiro, Seropédica, RJ, 2022.	por
dc.identifier.uri	https://rima.ufrrj.br/jspui/handle/20.500.14407/14343	-
dc.description.abstract	O presente trabalho tem como objetivo realizar uma simulação numérica para descrever o escoamento transiente unidimensional de água em solo não-saturado. O movimento da água no solo é descrito pela equação de Richards, obtida das equações de Darcy-Buckingham e da continuidade. Tal equação é não-linear, necessitando de tratamento computacional para obtenção de uma solução aproximada. Existem diversas técnicas para abordar o problema, como o método dos elementos finitos (MEF) e das diferenças finitas (MDF). Neste trabalho foi utilizado o método das diferenças finitas (MDF) para encontrar uma solução para a equação de Richards nas formas h e mista, usando dados de [1], com condições iniciais e de contorno previamente definidas, para diferentes passos de tempo e espaçamentos de malha. Foram comparados diferentes esquemas iterativos no processo de solução da equação de Richards. Além disso, um esquema de marcha dupla no tempo (DTS) foi empregado como uma alternativa aos esquemas tradicionais. Os resultados encontrados sugerem que o esquema DTS é um método capaz de resolver o problema com um aumento razoável no número de iterações. No entanto, para elevados níveis de saturação de solo o esquema DTS demonstrou a possibilidade de maior eficiência computacional.	por
dc.description.sponsorship	CAPES - Coordenação de Aperfeiçoamento de Pessoal de Nível Superior	por
dc.format	application/pdf	*
dc.language	por	por
dc.publisher	Universidade Federal Rural do Rio de Janeiro	por
dc.rights	Acesso Aberto	por
dc.subject	Equação de Richards	por
dc.subject	Ciência do Solo	por
dc.subject	Modelagem Matemática	por
dc.subject	Dual- Time Stepping Method	eng
dc.subject	Diferenças Finitas	por
dc.subject	Richards’ Equation	eng
dc.subject	Soil Science	eng
dc.subject	Mathematical Modeling	eng
dc.subject	Finite Differences	eng
dc.title	Avaliação de métodos iterativos aplicados à equação não-linear de Richards	por
dc.title.alternative	Evaluation of iterative methods applied to the nonlinear Richards’ equation	eng
dc.type	Dissertação	por
dc.description.abstractOther	The present work aims to perform a numerical simulation to describe the one-dimensional transient water flow in unsaturated soil. The movement of water into soil is described by Richards equation, obtained from both Darcy-Buckingham and continuity equations. Such equation is non-linear, requiring computational treatment to obtain an approximate solution. There are several techniques to approach the problem, such as finite element (FEM) and finite difference (FDM) methods. In order to find a solution in both h and mixed forms of Richards equation, finite difference method (FDM) was adopted, using data from [1], with previously defined initial and boundary conditions, for different time steps and mesh spacings. Different iterative schemes were compared in the process of solving Richards equation. In addition, a dual time stepping (DTS) scheme was employed as an alternative to traditional schemes. The obtained results suggest that DTS scheme is a capable method to solve the problem with a reasonable increase in the number of iterations. However, for high levels of soil saturation the DTS scheme demonstrated the possibility of greater computational efficiency.	eng
dc.contributor.advisor1	Teixeira, Renan de Souza
dc.contributor.advisor1ID	057.077.297-47	por
dc.contributor.advisor-co1	Santos, Wilian Jeronimo dos
dc.contributor.advisor-co1ID	103.175.157-21	por
dc.contributor.referee1	Teixeira, Renan de Souza
dc.contributor.referee2	Vera-Tudela, Carlos Andres Reyna
dc.contributor.referee3	Fontes Junior, Edivaldo Figueiredo
dc.contributor.referee4	Chalhub, Daniel José Nahid Mansur
dc.creator.ID	140.020.647-27	por
dc.creator.Lattes	http://lattes.cnpq.br/6228466095164878	por
dc.publisher.country	Brasil	por
dc.publisher.department	Instituto de Ciências Exatas	por
dc.publisher.initials	UFRRJ	por
dc.publisher.program	Programa de Pós-Graduação em Modelagem Matemática e Computacional	por
dc.relation.references	[1] R. HAVERKAMP, M. VAUCLIN, J. TOUMA, P. WIERENGA, and G. VACHAUD, “A comparison of numerical simulation models for one-dimensional infiltration,” Soil Sic. Soc. Am. J., vol. 41, 1977. [2] F. LIST and F. RADU, “A study on iterative methods for solving richards’ equation,” Computational Geosciences, vol. 20, no. 2, pp. 341–353, 2016. [3] J. LIMA, R. FERREIRA, and D. CHRISTOFIDIS, “O uso da irriga¸c˜ao no brasil,” 1999. [4] L. BRITO, A. SILVA, and E. PORTO, “Disponibilidade de ´agua e a ges˜ao dos recursos h´ıdricos.,” Embrapa Sem´arido-Cap´ıtulo em livro cient´ıfico (ALICE), 2007. [5] W. SILVA, M. SILVA, and T. PIRES, “O uso sustent´avel ea qualidade da ´agua na produ¸c˜ao animal,” Nutritime Revista Eletrˆonica, vol. 11, pp. 3617–3636, 2014. [6] F. PIZARRO, “Riegos localizados de alta frecuencia-goteo-microaspersion– exudacion,” Madrid. Mundi-Prensa, 1996. [7] J. F. R. Bezerra, A. J. T. Guerra, and S. C. Rodrigues, “Rela¸c˜oes entre potencial matricial no solo e cobertura vegetal em uma esta¸c˜ao experimental, uberlˆandia-mg,” Sociedade & Natureza, vol. 24, pp. 103–113, 2012. [8] J. FERZIGER, M. PERIC, and R. L. STREET, Computational methods for fluid dynamics, vol. 3. Springer, 2002. [9] H. VEREECKEN, A. SCHNEPF, J. HOPMANS, M. JAVAUX, D. OR, T. ROOSE, J. VANDERBORGHT, M. YOUNG, W. AMELUNG, M. AITKENHEAD, S. ALLISON, S. ASSOULINE, P. BAVEYE, M. BERLI, N. BR¨UGGEMANN, P. FINKE, M. FLURY, T. GAISER, G. GOVERS, T. GHEZZEHE, P. HALLETT, H. H. FRANSSEN, J. HEPPELL, R. HORN, J. HUISMAN, D. JACQUES, F. JONARD, S. KOLLET, F. LAFOLIE, K. LAMORSKI, D. LEITNER, A. MCBRATNEY, B. MINASNY, C. MONTZKA, W. NOWAK, Y. PACHEPSKY, J. PADARIAN, N. ROMANO, K. ROTH, Y. ROTHFUSS, E. ROWE, A. SCHWEN, J. ˇSIM˚UNEK, A. TIKTAK, J. V. DAM, S. V. D. ZEE, H. VOGEL, J. VRUGT, T. W¨OHLING, and I. YOUNG., “Modeling soil processes: Review, key challenges, and new perspectives,” Vadose zone journal, vol. 15, no. 5, 2016. [10] P. L. LIBARDI, Dinˆamica da ´ Agua no Solo. Edusp, 1 ed., 2005. [11] M. FARTHING and F. OGDEN, “Numerical solution of richards’ equation: a review of advances and challenges,” Soil Science Society of America Journal, vol. 81, no. 6, pp. 1257–1269, 2017. [12] M. A. CELIA, E. T. BOULOUTAS, and R. L. ZARBA, “A general mass-conservative numerical solution for the unsaturated flow equation,” Water resources research, vol. 26, no. 7, pp. 1483–1496, 1990. [13] S. PANDYA, S. VENKATESWARAN, and T. PULLIAN, “Implementation of preconditioned dual-time procedures in overflow,” in 41st Aerospace Sciences Meeting and Exhibit, p. 72, 2003. [14] J. NORDSTR¨OM and A. RUGGIU, “Dual time-stepping using second derivatives,” Journal of Scientific Computing, vol. 81, no. 2, pp. 1050–1071, 2019. [15] L. RICHARDS, “Capillary conduction of liquids through porous mediums,” Physics, vol. 1, no. 5, pp. 318–333, 1931. [16] Y. MUALEM, “A new model for predicting the hydraulic conductivity of unsaturated porous media,” Water resources research, vol. 12, no. 3, pp. 513–522, 1976. [17] M. VAN GENUCHTEN, “A closed-form equation for predicting the hydraulic conductivity of unsaturated soils,” Soil science society of America journal, vol. 44, no. 5, pp. 892–898, 1980. [18] P. MILLY, “Advances in modeling of water in the unsaturated zone,” Transport in porous media, vol. 3, no. 5, pp. 491–514, 1988. [19] D. CAVIEDES-VOULLI`EME, P. GARCI, and J. MURILLO, “Verification, conservation, stability and efficiency of a finite volume method for the 1d richards equation,” Journal of hydrology, vol. 480, pp. 69–84, 2013. [20] F. OGDEN and W. LAI, “A mass-conservative finite volume predictor–corrector solution of the 1d richards’ equation,” Journal of Hydrology, vol. 523, pp. 119–127, 2015. [21] C. ZAMBRA, M. DUMBSER, E. TORO, and N. MORAGA, “A novel numerical method of high-order accuracy for flow in unsaturated porous media,” International journal for numerical methods in engineering, vol. 89, no. 2, pp. 227–240, 2012. [22] S. BOUCHEMELLA, A. SERIDI, and I. ALIMI-ICHOLA, “Numerical simulation of water flow in unsaturated soils: comparative study of different forms of richards’s equation,” European Journal of Environmental and Civil Engineering, vol. 19, no. 1, pp. 1–26, 2015. [23] M. SHANMUGAM, G. KUMAR, B. NARASIMHAN, and S. SHRESTHA, “Effective saturation-based weighting for interblock hydraulic conductivity in unsaturated zone soil water flow modelling using one-dimensional vertical finite-difference model,” Journal of Hydroinformatics, pp. 1–19, 2019. [24] C. VASCONCELLOS and J. AMORIM, “Effective saturation-based weighting for interblock hydraulic conductivity in unsaturated zone soil water flow modelling using one-dimensional vertical finite-difference model,” Proceedings of COBEM, Fluid Mechanics, vol. 8, no. 140, 2001. [25] M. ALLEN and C. MURPHY, “A finite element collocation method for variably saturated flows in porous media,” Numerical Methods for Partial Differential Equations, vol. 1, no. 3, pp. 229–239, 1985. [26] M. ALLEN and C. MURPHY, “A finite-element collocation method for variably saturated flow in two space dimensions,” Water Resources Research, vol. 22, no. 11, pp. 1537–1542, 1986. [27] C. MERKLE and Y. CHOI, “Computation of low-speed compressible flows with timemarching procedures,” International Journal for Numerical Methods in Engineering, vol. 25, no. 2, pp. 293–311, 1988. [28] R. TEIXEIRA, L. ALVES, A. KARAGOZIAN, and R. KELLY, “On the solution of the compressible flow equations at small mach numbers,” in Proc. 12th Brazilian Congress of Thermal Engineering and Sciences, Belo Horizonte, MG, pp. 101–110, Citeseer, 2008. [29] R. TEIXEIRA, “Esquemas de marcha com ganho m´ınimo para o desenvolvimento de solu¸c˜oes em regime permanente para problemas inst´aveis,” 2014. [30] R. TEIXEIRA and L. ALVES, “Modelling far-field entrainment in compressible flows,” International Journal of Computational Fluid Dynamics, vol. 26, no. 1, pp. 67–78, 2012. [31] R. TEIXEIRA and L. ALVES, “Minimal gain marching schemes for steady-state solution generation,” In 14th Brazilian Congress of Thermal Engineering and Sciences, 2012. [32] R. TEIXEIRA and L. ALVES, “Minimal gain time marching schemes for the construction of accurate steady-states,” in Instability and Control of Massively Separated Flows, pp. 217–222, Springer, 2015. [33] R. TEIXEIRA and L. ALVES, “Minimal gain marching schemes: searching for unstable steady-states with unsteady solvers,” Theoretical and Computational Fluid Dynamics, vol. 31, no. 5, pp. 607–621, 2017. [34] A. JAMESON, “Application of dual time stepping to fully implicit runge kutta schemes for unsteady flow calculations,” in 22nd AIAA Computational Fluid Dynamics Conference, p. 2753, 2015. [35] J. CARVALHO, G. JUNIOR, and E. CARVALHO, “T´opicos sobre infiltra¸c˜ao: teoria e pr´atica aplicadas a solos tropicais,” Faculdade de Tecnologia, Bras´ılia, 2012. [36] F. M. S. MOREIRA, J. E. CARES, R. ZANETTI, and S. L. ST¨UMER, “O ecossistema solo: componentes, relac˜oes eco´ogicas e efeitos na produ¸c˜ao vegetal,” UFLA, Lavras, 2013. [37] B. QUEIR´ OZ, “Estudo de solu¸c˜oes num´ericas da equa¸c˜ao de richards atrav´es do m´etodo de elementos finitos e diferen¸cas finitas para simula¸c˜ao de fluxo unidimensional em solo n˜ao-saturado,” 2017. [38] C. ANDRADE, D. DOSSA, and F. DUR˜AES, Uso e Manejo de Irriga¸c˜ao. Embrapa, 1 ed., 2008. [39] S. CHAPRA and R. CANALE, M´etodos Num´ericos para Engenharia. McGraw Hill Brasil, 7 ed., 2016. [40] M. MANNICH and A. K. GUETTER, “Erros num´ericos da equa¸c˜ao de richards utilizando o m´etodo dos volumes finitos,” Universidade Federal do Paran´a, 2011. [41] B. GILDING, “Qualitative mathematical analysis of the richards equation,” Transport in Porous Media, vol. 6, no. 5, pp. 651–666, 1991. [42] U. NOWAK and L. WEIMANN, “A family of newton codes for systems of highly nonlinear equations.,” 1992. [43] C. MARONGIU, P. VITAGLIANO, P. CATAIANO, V. TARANTINO, and D. DI SERAFINO, “An improvement of the dual time stepping technique for unsteady rans computations,” in Proceedings of European Conference for Aerospace Sciences (EUCASS), Moscow, 2005.	por
dc.subject.cnpq	Matemática	por
dc.thumbnail.url	https://tede.ufrrj.br/retrieve/69418/2022%20-%20Mario%20Jorge%20dos%20Reis%20Moura.pdf.jpg	*
dc.originais.uri	https://tede.ufrrj.br/jspui/handle/jspui/5688
dc.originais.provenance	Submitted by Jorge Silva (jorgelmsilva@ufrrj.br) on 2022-05-24T18:16:13Z No. of bitstreams: 1 2022 - Mario Jorge dos Reis Moura.pdf: 2465697 bytes, checksum: cd1bf0276a5ee606f75ff06108d37109 (MD5)	eng
dc.originais.provenance	Made available in DSpace on 2022-05-24T18:16:13Z (GMT). No. of bitstreams: 1 2022 - Mario Jorge dos Reis Moura.pdf: 2465697 bytes, checksum: cd1bf0276a5ee606f75ff06108d37109 (MD5) Previous issue date: 2022-03-31	eng
Appears in Collections:	Mestrado em Modelagem Matemática e Computacional

Se for cadastrado no RIMA, poderá receber informações por email.
Se ainda não tem uma conta, cadastre-se aqui!

Files in This Item:

File	Description	Size	Format
2022 - Mario Jorge dos Reis Moura.pdf		2.41 MB	Adobe PDF	View/Open

Show simple item record