Abstract
The meccano method was recently introduced to construct simultaneously tetrahedral meshes and volumetric parameterizations of solids. The method requires the information of the solid geometry that is defined by its surface, a meccano, i.e., an outline of the solid defined by connected polyhedral pieces, and a tolerance that fixes the desired approximation of the solid surface. The method builds an adaptive tetrahedral mesh of the solid (physical domain) as a deformation of an appropriate tetrahedral mesh of the meccano (parametric domain). The main stages of the procedure involve an admissible mapping between the meccano and the solid boundaries, the nested Kossaczký’s refinement, and our simultaneous untangling and smoothing algorithm. In this chapter, we focus on the application of the method to build tetrahedral meshes over complex terrain, that is interesting for simulation of environmental processes. A digital elevation map of the terrain, the height of the domain, and the required orography approximation are given as input data. In addition, the geometry of buildings or stacks can be considered. In these applications, we have considered a simple cuboid as meccano.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
References
Bazaraa MS, Sherali HD, Shetty CM (1993) Nonlinear programing: theory and algorithms. Wiley, New York
Benítez D, Rodríguez E, Escobar JM, Montenegro R (2014) Performance evaluation of a parallel algorithm for simultaneous untangling and smoothing of tetrahedral meshes. In: Proceedings of the 22nd international meshing roundtable. Springer Science Business Media, pp 579–598. https://doi.org/10.1007/978-3-319-02335-9_32
Carey GF (1997) Computational grids: generation adaptation and solution strategies. Taylor, Washington
Carey GF (2006) A perspective on adaptive modeling and meshing (AM&M). Comput Methods Appl Mech Eng 195(4–6):214–235. https://doi.org/10.1016/j.cma.2004.11.027. 1st ADMOS Conference 2003, Goteborg, SWEDEN, Sep, 2003
Cascón JM, Montenegro R, Escobar JM, Rodríguez E, Montero G (2007) A new meccano technique for adaptive 3-d triangulations. In: Proceedings of the 16th international meshing roundtable. Springer, Berlin, Germany, pp 103–120. https://doi.org/10.1007/978-3-540-75103-8_6
Cascón JM, Rodríguez E, Escobar JM, Montenegro R (2015) Comparison of the meccano method with standard mesh generation techniques. Eng Comput 31(1):161–174. https://doi.org/10.1007/s00366-013-0338-6
Escobar JM, Montero G, Montenegro R, Rodríguez E (2006) An algebraic method for smoothing surface triangulations on a local parametric space. Int J Numer Meth Eng 66(4):740–760. https://doi.org/10.1002/nme.1584
Escobar JM, Rodríguez E, Montenegro R, Montero G, González-Yuste JM (2003) Simultaneous untangling and smoothing of tetrahedral meshes. Comput Methods Appl Mech Eng 192(25):2775–2787. https://doi.org/10.1016/S0045-7825(03)00299-8
Escobar JM, Rodríguez E, Montenegro R, Montero G, González-Yuste JM (2010) SUS code: simultaneous mesh untangling and smoothing code. http://www.dca.iusiani.ulpgc.es/SUScode
Floater MS (1997) Parametrization and smooth approximation of surface triangulations. Comput Aided Geom Des 14(3):231–250. https://doi.org/10.1016/S0167-8396(96)00031-3
Floater MS (2003) Mean value coordinates. Comput Aided Geom Des 20(1):19–27. https://doi.org/10.1016/S0167-8396(03)00002-5
Frey PJ, George PL (2000) Mesh generation. Hermes Science Publishing, Oxford
George PL, Borouchaki H (1998) Delaunay triangulation and meshing: application to finite elements. Editions Hermes, Paris
González-Yuste JM, Montenegro R, Escobar JM, Montero G, Rodríguez E (2004) Local refinement of 3-d triangulations using object-oriented methods. Adv Eng Softw 35(10):693–702. https://doi.org/10.1016/j.advengsoft.2003.07.003. Engineering Computational Technology
Knupp PM (2001) Algebraic mesh quality metrics. SIAM J Sci Comput 23(1):193–218. https://doi.org/10.1137/s1064827500371499
Kossaczký I (1994) A recursive approach to local mesh refinement in two and three dimensions. J Comput Appl Math 55(3):275–288. https://doi.org/10.1016/0377-0427(94)90034-5
Löhner R, Baum JD (1992) Adaptive h-refinement on 3-D unstructured grids for transient problems. Int J Numer Meth Fluids 14:1407–1419. https://doi.org/10.1002/fld.1650141204
Montenegro R, Cascón JM, Escobar JM, Rodríguez E, Montero G (2009) An automatic strategy for adaptive tetrahedral mesh generation. Appl Numer Math 59(9):2203–2217. https://doi.org/10.1016/j.apnum.2008.12.010
Montenegro R, Cascón JM, Escobar JM, Rodríguez E, Montero G (2010) The meccano method for simultaneous volume parametrization and mesh generation of complex solids. IOP Conf Ser Mater Sci Eng 10(1):012–018. https://doi.org/10.1088/1757-899X/10/1/012018
Montenegro R, Cascón JM, Rodríguez E, Escobar JM, Montero G (2010) The meccano method for automatic three-dimensional triangulation and volume parametrization of complex solids. In: Topping B, Adam J, Pallarés F, Bru R, Romero M (eds) Developments and applications in engineering computational technology, seventh edn., Chap. 2. Saxe-Coburg Publications, Stirlingshire, pp 19–48. https://doi.org/10.4203/csets.26.2
Oliver A, Montero G, Montenegro R, Rodríguez E, Escobar JM, Pérez-Foguet A (2013) Adaptive finite element simulation of stack pollutant emissions over complex terrains. Energy 49:47–60. https://doi.org/10.1016/j.energy.2012.10.051
Prieto D, Asensio MI, Ferragut L, Cascón JM, Morillo A (2017) A gis-based fire spread simulator integrating a simplified physical wildland fire model and a wind field model. Int J Geogr Inf Sci 31(11):2142–2163. https://doi.org/10.1080/13658816.2017.1334889
Rivara M (1987) A grid generator bases on 4-triangles conforming mesh-refinement algorithms. Int J Numer Meth Eng 24(7):1343–1354. https://doi.org/10.1002/nme.1620240710
Thompson JF, Soni B, Weatherill N (1999) Handbook of grid generation. CRC Press, London
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2018 Springer International Publishing AG, part of Springer Nature
About this chapter
Cite this chapter
Cascón , J.M., Escobar, J.M., Montenegro, R. (2018). Discretization of the Region of Interest. In: Perez, R. (eds) Wind Field and Solar Radiation Characterization and Forecasting. Green Energy and Technology. Springer, Cham. https://doi.org/10.1007/978-3-319-76876-2_3
Download citation
DOI: https://doi.org/10.1007/978-3-319-76876-2_3
Published:
Publisher Name: Springer, Cham
Print ISBN: 978-3-319-76875-5
Online ISBN: 978-3-319-76876-2
eBook Packages: EnergyEnergy (R0)