A model-integrated localized collocation meshless method (MIMS)

• Autorzy: Gerace S. , Erhart K. , Kassab A. , Divo E.
• Języki publikacji: EN

Abstrakty

EN

A model integrated meshless solver (MIMS) tailored to solve practical large-scale industrial problems is based on robust meshless methods strategies that integrate a native model-based point generation procedures. The MIMS approach fully exploits strengths of meshless methods to achieve automation, stability, and accuracy by blending meshless solution strategies based on a variety of shape functions to achieve stable and accurate iteration process that is integrated with a newly developed, highly adaptive model generation employing quaternary triangular surface discretization for the boundary, a binary-subdivision discretization for the interior, and a unique shadow layer discretization for near-boundary regions. Together, these discretization techniques provide directionally independent, automatic refinement of the underlying native problem model to generate accurate adaptive solutions without need for intermediate user intervention. By coupling the model generation with the solution process, MIMS addresses issues posed by ill-constructed geometric input and pathologies often generated from solid models in the course of CAD design.

Słowa kluczowe

EN

meshless methods; heat transfer; large-scale problems

PL

metody bezsiatkowe; wymiana ciepła; problemy dużej skali

• Wydawca: Instytut Podstawowych Problemów Techniki PAN
• Czasopismo: Computer Assisted Methods in Engineering and Science
• Rocznik: 2013
• Tom: Vol. 20, no. 3
• Strony: 207--225
• Opis fizyczny: Bibliogr. 47 poz., il., rys., wykr.

Twórcy

autor

Gerace S.

• Mechanical and Aerospace Engineering Department, University of Central Florida, 4000 Central Florida Blvd., Orlando, FL, 32816, USA

autor

Erhart K.

• Mechanical and Aerospace Engineering Department, University of Central Florida, 4000 Central Florida Blvd., Orlando, FL, 32816, USA

autor

Kassab A.

• Mechanical and Aerospace Engineering Department, University of Central Florida, 4000 Central Florida Blvd., Orlando, FL, 32816, USA

autor

Divo E.

• Department of Mechanical Engineering, Embry-Riddle Aeronautical University, Daytona Beach, FL, USA

Bibliografia

• [1] G.R. Liu. Mesh free methods: moving beyond the finite element method. CRC Press, Boca Raton, FL, 2003.
• [2] B. Nayroles, G. Touzot, P. Villon. Generalizing the finite element method: diffuse approximation and diffuse elements. Computational Mechanics, 10(5): 307–318, 1992.
• [3] T. Belytschko, L. Gu, Y.Y. Lu. Fracture and crack growth by element free Galerkin methods. Modeling and Simulation in Materials Science and Engineering, 2(3): 519–534, 1994.
• [4] Y.Y. Lu, T. Belytschko, L. Gu. A new implementation of the element free Galerkin method. Computer methods in applied mechanics and engineering, 113(3): 397–414, 1994.
• [5] J.G. Wang, G.R. Liu. Radial point interpolation method for elastoplastic problems. In Proceedings of the 1st International Conference on Structural Stability and Dynamics, pp. 703–708, Taipei, Taiwan, 2000.
• [6] J.G. Wang, G.R. Liu. Radial point interpolation method for no-yielding surface models. In Proceedings of the First M.I.T. Conference on Computational Fluid and Solid Mechanics, pp. 538–540, Cambridge, MA, 2001.
• [7] G. Fasshauer. RBF collocation methods as pseudo-spectral methods. In Proc. of Boundary Elements XVII, A. Kassab, C.A. Brebbia, E. Divo, eds. WIT Press, pp. 45–57, 2005.
• [8] G. Kosec. Local meshless methods for multiphase fluid problems, Ph.D. Dissertation. University of Nova Gorica, Slovenia, 2010.
• [9] G. Kosec, B. Šarler. H-adaptive local radial basis function collocation meshless method. CMC: Computers, Materials & Continua, 26: 227–54, 2011.
• [10] E. Divo, A. Kassab. An efficient localized RBF meshless method applied to fluid flow and conjugate heat transfer. ASME Paper IMECE – 2005-82150, 2005.
• [11] E. Divo, E.A. Kassab. A meshless method for conjugate heat transfer. Engineering Analysis, 29: 136–149, 2005.
• [12] B. Šarler. Advances in meshfree techniques, vol. 5 of ˇ Computational Methods in Applied Sciences, chap. from Global to local radial basis function collocation method for transport phenomena, Springer-Verlag, pp. 257–282, 2007.
• [13] A. Kassab, E. Divo. An efficient localized radial basis function meshless method for fluid flow and conjugate heat transfer. ASME Journal of Heat Transfer, 129: 179–183, 2007.
• [14] B. Šarler, R. Vertnik. Meshfree explicit local radial basis function collocation method for diffusion problems. Computers and Mathematics with Applications, 51: 1269–1282, 2006.
• [15] R. Vertnik, B. Šarler. Meshless local radial basis function collocation method for convective-diffusive solid-liquid phase change problems. International Journal of Numerical Methods for Heat and Fluid Flow, 16: 617–640, 2006.
• [16] R. Vertnik, B. Šarler. Solution of incompressible turbulent flow by a mesh-free method. ˇ CMES: Computer Modeling in Engineering & Sciences, 44: 65–95, 2009.
• [17] G. Kosec, B. Šarler. Local RBF collocation method for Darcy flow. CMES: Computer Modeling in Engineering & Sciences, 25: 197–208, 2008.
• [18] G. Kosec, B. Šarler. Meshless aproach to solving freezing driven by a natural convection. Materials Science Forum, 649: 205–210, 2008.
• [19] G. Kosec, B. Šarler. Solution of phase change problems by collocation with local pressure correction. CMES: Computer Modeling in Engineering & Sciences, 47: 191–216, 2009.
• [20] S. Gerace. An interactive framework for meshless methods analysis in computational mechanics and thermofluid. Master’s thesis, University of Central Florida, 2007.
• [21] S. Gerace, K. Erhart, E. Divo, A. Kassab. Generalized finite difference meshless method in computational mechanics and thermofluids. In: Proceedings of the Int. Conf. on Comp. Methods for Coupled Problems in Science and Engineering, COUPLED PROBLEMS, 2009.
• [22] R. Vertnik, B. Šarler. Solution of incompressible turbulent flow by a mesh-free method. Computer Modeling in Engineering and Sciences, 44(1): 65–95, 2009.
• [23] Z. El-Zahab, E. Divo, A.J. Kassab. Minimization of the wall shear stress gradients in bypass grafts anastomoses using meshless CFD and genetic algorithms optimization. Computer Methods in Biomechanics and Biomedical Engineering, 13(1): 35–47, 2010.
• [24] Z. El-Zahab, E. Divo, A.J. Kassab. A localized collocation meshless method (LCMM) for incompressible flows CFD modeling with applications to transient hemodynamics. Engineering Analysis, 33: 1045–1061, 2009.
• [25] Z. El Zahab, E. Divo, A.J.Kassab. A meshless CFD approach for evolutionary shape optimization of bypass grafts anastomoses. Journal Inverse Problems in Science and Engineering, 17(3): 411–435, 2009.
• [26] K. Erhart, S. Gerace, E. Divo, A.J. Kassab. An RBF interpolated generalized finite difference meshless method for compressible turbulent flows. AMSE Paper IMECE-2009-11452, 2009.
• [27] S. Gerace, K. Erhart, E. Divo, A.J. Kassab. Adaptively refined hybrid FDM/meshless scheme with applications to laminar and turbulent flows. CMES: Computer Modeling in Engineering and Science, 81(1): 35–68, 2011.
• [28] M.J.D. Powell. The Theory of Radial Basis Function Approximation. In Advances in Numerical Analysis, Vol. II, W. Light, ed., Oxford Science Publications, Oxford, pp. 143–167, 1992.
• [29] M.D. Buhmann. Radial Basis Functions: Theory and Implementation. Cambridge University Press, Cambridge, 2003.
• [30] R.L. Hardy. Multiquadric equations of topography and other irregular surfaces. Journal of Geophysical Research, 176: 1905–1915, 1971.
• [31] E.J. Kansa. Multiquadrics- a scattered data approximation scheme with applications to computational fluid dynamics. I-surface approximations and partial derivative estimates. Comp. Math. Appl., 19: 127–145, 1990.
• [32] E.J. Kansa. Multiquadrics- a scattered data approximation scheme with applications to computational fluid dynamics. II-solutions to parabolic, hyperbolic and elliptic partial differential equations, Comp. Math. Appl., 19: 147–161, 1990.
• [33] E.J. Kansa, E.J.Y.C. Hon. Circumventing the Ill-conditioning problem with multiquadric radial basis functions: applications to elliptic partial differential equations. Comp. Math. Appl., 39: 123–137, 2000.
• [34] M. Bern, D. Eppstein. Computing in Euclidean geometry chap. Mesh Generation and Optimal Triangulation. Lecture Notes Series on Computing, World Scientific, 23(90), 1992.
• [35] L.P. Chew. Guaranteed-quality mesh generation for curved surfaces. In SCG ’93: Proceedings of the ninth annual symposium on Computational geometry, ACM, San Diego, California, USA, 1993.
• [36] J. Ruppert, A. Delaunay. Refinement algorithm for quality 2-dimensional mesh generation. Journal of Algo rithms, 18(3): 548–585, 1995.
• [37] S. Gerace. A model integrated meshless solver (MIMS) for fluid flow and heat transfer. Ph.D. Dissertation, University of Central Florida, 2010.
• [38] L. De Floriani, E. Puppo. Hierarchical triangulation for multiresolution surface description. ACM Trans. Graph., 14(4): 363–411, 1995.
• [39] X. Zhao, J. Chen, Z. Li. A QTM-based algorithm for generation of the Voronoi diagram on a sphere. In Ad vances in Spatial Data Handling: Proceedings from the 10th International Symposium on Spatial Data Handling, D. Richardson and P. van Oosterom, eds., pp. 269–285, Springer Berlin, 2002.
• [40] G. Dutton. Encoding and handling geospatial data with hierarchical triangular meshes. In Advances In GIS Research II: Proceedings of the Sixth International Symposium on Spatial Data Handling, M.J. Kraak and M. Molenaar, eds., pp. 505–518, Taylor & Francis Publishing, 1996.
• [41] G.H. Dutton. A Hierarchical Coordinate System for Geoprocessing and Cartography, vol. 79 of Lecture Notes in Earth Sciences, chap. Computational aspects of a quaternary triangular mesh, Springer Berlin Heidelberg, pp. 41–70, 1999.
• [42] P. Frey, H. Borouchaki. Geometric surface mesh optimization. Computing and Visualization in Science, 1(3): 113–121, 1998.
• [43] D. Wang, O. Hassan, K. Morgan, N. Weatherill. EQSM: an efficient high quality surface grid generation method based on remeshing. Computer Methods in Applied Mechanics and Engineering, 195(41): 5621–5633, 2006.
• [44] J. Tournois, P. Alliez, O. Devillers. Interleaving Delaunay refinement and optimization for 2D triangle mesh generation. In Proceedings of the 16th International Meshing Roundtable, M.L. Brewer and D. Marcum, eds., Springer Berlin Heidelberg, Seattle, Washington, USA, pp. 83–101, 2007.
• [45] H. Luo, J.D. Bauma, R. Lohner. A hybrid Cartesian grid and gridless method for compressible flows. Journal of Computational Physics, 214(2): 618–632, 2006.
• [46] Z.J. Wang, R.F. Chen, N. Hariharan, A.J. Przekwas, D. Grove. A 2n tree based automated viscous Cartesian grid methodology for feature capturing. AIAA, Paper AIAA-99-3300, 1999.
• [47] P. Lancaster, K. Salkauskas. Surfaces generated by moving least squares methods. Mathematics of Computation, 37(155): 141–158, 1981.