МЕТОДИ ПОБУДОВИ ДИСКРЕТНИХ МОДЕЛЕЙ: СТРУКТУРОВАНІ ТА БЛОЧНО-СТРУКТУРОВАНІ СІТКИ
Ключові слова:
дискретна модель, сітка, скінченний елемент, структурована сітка, блочно-структурована сітка
Анотація
У статті проведено огляд актуальних підходів і методів побудови структурованих і блочно-структурованих дискретних моделей. Зокрема, виконано аналіз методів на основі алгебраїчних перетворень і методів на основі диференційних рівнянь. Також розглянуто методи побудови блочно-структурованих дискретних моделей.
Посилання
1. Thompson J. F. Handbook of grid generation / J. F. Thompson, B. Sony, N. Weatherill. – New York : CRC Press, 1999. – 1136 p.
2. Gordon W. N. Construction of curvilinear coordinate systems and application to mesh generation / W. N. Gordon, C. A. Hall // International Journal for Numerical Methods in Engineering. – 1973. – Vol. 7. – P. 461-477.
3. Cook W. A. Body oriented (natural) co-ordinates for generating three dimensional meshes / W. A. Cook // International Journal for Numerical Methods in Engineering. – 1974. – Vol. 8. – P. 27-43.
4. Haber R. A general two-dimensional, graphical finite element preprocessor utilizing discrete transfinite mapping / R. Haber, M. S. Shephard, J. F. Abel, R. H. Gallagher, D. P. Greenberg // International Journal for Numerical Methods in Engineering. – 1982. – Vol. 17. – P. 1015-1044.
5. Haber R. Discrete transfinite mappings for description and meshing of three-dimensional surfaces using interactive computer graphics / R. Haber, J. F. Abel // International Journal for Numerical Methods in Engineering. – 1982. – Vol. 18. – P. 41-66.
6. Eiseman P. R. A multi-surface method of coordinate generation / P. R. Eiseman // Journal of Computational Physics. – 1979. – Vol. 33, iss. 1. – P. 118-150.
7. Флетчер К. Вычислительные методы в динамике жидкостей / К. Флетчер. – М. : Мир, 1991. – Т. 2 : Методы расчета различных течений. – 552 с.
8. Floater M. S. Parametrization and smooth approximation of surface triangulations / M. S. Floater // Computer Aided Geometric Design. – 1997. – Vol. 14, iss. 3. – P. 231-250.
9. Floater M. S. A general construction of barycentric coordinates over convex polygons / M. S. Floater, K. Hormann, G. Kós // Advances in Computational Mathematics. – 2006. – Vol. 24, iss. 1. – P. 311-331.
10. Meyer M. Generalized barycentric coordinates on irregular polygons / M. Meyer, A. Barr, H. Lee, M. Desbrun // Journal of Graphics Tools. – 2002. – Vol. 7, iss. 1. – P. 13-22.
11. Warren J. Barycentric coordinates for convex polytopes / J. Warren // Advances in Computational Mathematics. – 1996. – Vol. 6, iss. 1. – P. 97-108.
12. Akinlar M. A. A Method for Orthogonal Grid Generation / M. A. Akinlar, S. Salako, G. Liao // General Mathematics Notes. – 2011. – Vol. 3. – No 1. – P. 55-72.
13. Мартюшов С. Н. Расчет пространственных задач обтекания на основе TVD схемы Хартена / С. Н. Мартюшов // Вычислительные технологии. – 1995. – Т. 14. – № 12. – С. 219-228.
14. Мартюшов С. Н. Построение дву- и трехмерных сеток для задач газодинамики на основе уравнения Пуассона / С. Н. Мартюшов // Известия высших учебных заведений. Математика. – 1997. – № 4. – С. 108-110.
15. Мартюшов С. Н. Численное моделирование струйных течений методом конечного объема на основе TVD-схемы 2-го порядка точности / С. Н. Мартюшов, Я. Г. Мартюшова // Вычислительные технологии. – 2004. – Т. 9. – № 4. – С. 57-65.
16. Мартюшов С. Н. Численное моделирование течений детонации газовых смесей методом конечного объема / С. Н. Мартюшов, Я. Г. Мартюшова // Вычислительные технологии. – 2008. – Т. 13. – № 1. – С. 88-98.
17. Ashrafizadeh A. Direct Design Solution of the Elliptic Grid Generation Equations / A. Ashrafizadeh, G. D. Raithby // Numerical Heat Transfer. – 2006. – Vol. 50. – P. 217-230.
18. Ashrafizadeh A. Structured Grid Generation Via Constraint on Displacement of Internal Nodes / A. Ashrafizadeh, R. Jalalabadi // International Journal of Basic & Applied Science. – 2011. – Vol. 11, No 4. – P. 79-87.
19. Zhang Y. 2D Nearly Orthogonal Mesh Generation / Y. Zhang, Y. Jia, S. S. Y. Wang // International Journal for Numerical Methods in Fluids. – 2004. – Vol. 46, iss. 7. – P. 685-707.
20. Zhang Y. 2D Nearly Orthogonal Mesh Generation with Controls of Distortion Function / Y. Zhang, Y. Jia, S. S. Y. Wang // Journal of Computational Physics. – 2006. – Vol. 218, iss. 2. – P. 549-571.
21. Zhang Y. Structured Mesh Generation with Smoothness Controls / Y. Zhang, Y. Jia, S. S. Y. Wang // International Journal for Numerical Methods in Fluids. – 2006. – Vol. 51, iss. 11. – P. 1255-1276.
22. Lehtimaki R. An Algebraic Boundary Orthogonalization Procedure for Structured Grids / R. Lehtimaki // International Journal for Numerical Methods in Fluids. – 2000. – Vol. 32, iss. 5. – P. 605-618.
23. Zhou Q. A Simple Grid Generation Method / Q. Zhou // International Journal for Numerical Methods in Fluids. – 1998. – Vol. 26, iss. 6. – P. 713-724.
24. Yerry M. A. A modified quadtree approach to finite element mesh generation / M. A. Yerry, M. S. Shephard // IEEE Computer Graphics and Applications. – 1983. – Vol. 3, iss. 1. – P. 39-46.
25. Baehmann P. L. Robust, geometrically based, automatic two-dimensional mesh generation / P. L. Baehmann, S. L. Wittchen, M. S. Shephard, K. R. Grice, M. A. Yerry // International Journal for Numerical Methods in Engineering. – 1987. – Vol. 24, iss. 6. – P. 1043-1078.
26. Liang X. Guaranteed-quality all-quadrilateral mesh generation with feature preservation / X. Liang, M. S. Ebeida, Y. Zhang // Computer Methods in Applied Mechanics and Engineering. – 2010. – Vol. 199. – P. 2072-2083.
27. Yiu K. F. C. Quadtree grid generation: information handling, boundary fitting and CFD applications / K. F. C. Yiu, D. M. Greaves, S. Cruz, A. Saalehi, A. G. L. Borthwick // Computers & Fluids. – 1996. – Vol. 25, iss. 8. – P. 759-769.
28. Ito Y. Octree-based reasonable-quality hexahedral mesh generation using a new set of refinement templates / Y. Ito, A. M. Shih, B. K. Soni // International Journal for Numerical Methods in Engineering. – 2009. – Vol. 77. – P. 1809-1833.
29. Kolšek T. Generation of block-structured grids in complex computational domains using templates / T. Kolšek, M. Šubelj, J. Duhovnik // Finite Elements in Analysis and Design. – 2003. – Vol. 39. – P. 1139-1154.
30. Miranda A. C. O. Hierarchical template‐based quadrilateral mesh generation / A. C. O. Miranda, L. F. Martha // Engineering with Computers. – 2015. – Vol. 31. – P. 1-15.
31. Yerry M. A. Automatic three-dimensional mesh generation by the modified-octree technique / M. A. Yerry, M. S. Shephard // International Journal for Numerical Methods in Engineering. – 1984. – Vol. 20, iss. 11. – P. 1965-1990.
32. Zhang H. Adaptive hexahedral mesh generation based on local domain curvature and thickness using a modified grid-based method / H. Zhang, G. Zhao // Finite Elements in Analysis and Design. – 2007. – Vol. 43, iss. 9. – P. 691-704.
33. Quadros W. R. LayTracks: a new approach to automated geometry adaptive quadrilateral mesh generation using medial axis transform / W. R. Quadros, K. Ramaswami, F. B. Prinz, B. Gurumoorthy // International Journal for Numerical Methods in Engineering. – 2004. – Vol. 61, iss. 2. – P. 209-237.
34. Tam T. K. H. 2D finite element mesh generation by medial axis subdivision / T. K. H. Tam, C. G. Armstrong // Advances in Engineering Software and Workstations. – 1991. – Vol. 13. – No 5-6. – P. 313-324.
35. Guoy D. Automatic Blocking Scheme for Structured Meshing in 2D Multiphase Flow Simulation / D. Guoy, J. Erickson // The 13th International Meshing Roundtable : International Conference, Willimasburg, Virginia, USA, September 19-22, 2004 : proceedings. – Sandia : Sandia National Laboratories, 2004. – P. 121-132.
36. Taghavi R. Automatic block decomposition using fuzzy logic analysis / R. Taghavi // The 9th International meshing roundtable : International Conference, New Orleans, Louisiana, USA, 2-5 October 2000 : proceedings. – Sandia : Sandia National Laboratories, 2000. – P. 187-192.
37. Takahashi H. A general purpose automatic mesh generation using shape recognition technique / H. Takahashi, H. Shimizu // ASME Computers in Engineering. – 1991. – Vol. 1. – P. 519-526.
38. Takahashi H. A Three-Dimensional Automatic Mesh Generation System Using Shape Recognition Technique / H. Takahashi, H. Shimizu, H. Moriyama, Y. Yamashita, N. Chiba // Transactions of the Japan Society of Mechanical Engineers. – 1993. – Vol. 59. – No 560. – Series A. – P. 1161-1167.
39. Müller-Hannemann M. High quality quadrilateral surface meshing without template restrictions: a new approach based on network flow techniques / M. Müller-Hannemann // The International Journal of Computational Geometry and Applications. – 1999. – Vol. 10, iss. 3. – P. 285-307.
40. Jablonowski C. Block-structured adaptive meshes and reduced grids for atmospheric general circulation models / C. Jablonowski, R. C. Oehmke, Q. F. Stout // Philosophical Transactions of the Royal Society A. – 2009. – Vol. 367. – P. 4497-4522.
41. Zheng J. Z. X. Block-Based Adaptive Mesh Refinement Finite-vol. Scheme for Hybrid Multi-Block Meshes / J. Z. X. Zheng, C. P. T. Groth // Seventh International Conference on Computational Fluid Dynamics (ICCFD7) : International Conference, Big Island, Hawaii, July 9-13, 2012 : proceedings. – Hawaii : 2012. – P. 1-19.
42. Ahusborde E. A 2D Block-structured Mesh Partitioner for Accurate Flow Simulations on Non-rectangular Geometries / E. Ahusborde, S. Glockner // Computers & Fluids. – 2011. – Vol. 43. – P. 2-13.
43. Steensland J. A partitioner-centric model for structured adaptive mesh refinement partitioning trade-off optimization: Part I / J. Steensland, J. Ray // The International Journal of High Performance Computing Applications. – 2005. – Vol. 19. – No 4. – P. 409-422.
44. Steensland J. A partitioner-centric model for structured adaptive mesh refinement partitioning trade-off optimization: Part II / J. Steensland, J. Ray // Parallel Processing Workshops : International Conference, Montreal, QC, Canada, 15-18 Aug 2004 : proceedings. – 2004. – P. 231-238.
2. Gordon W. N. Construction of curvilinear coordinate systems and application to mesh generation / W. N. Gordon, C. A. Hall // International Journal for Numerical Methods in Engineering. – 1973. – Vol. 7. – P. 461-477.
3. Cook W. A. Body oriented (natural) co-ordinates for generating three dimensional meshes / W. A. Cook // International Journal for Numerical Methods in Engineering. – 1974. – Vol. 8. – P. 27-43.
4. Haber R. A general two-dimensional, graphical finite element preprocessor utilizing discrete transfinite mapping / R. Haber, M. S. Shephard, J. F. Abel, R. H. Gallagher, D. P. Greenberg // International Journal for Numerical Methods in Engineering. – 1982. – Vol. 17. – P. 1015-1044.
5. Haber R. Discrete transfinite mappings for description and meshing of three-dimensional surfaces using interactive computer graphics / R. Haber, J. F. Abel // International Journal for Numerical Methods in Engineering. – 1982. – Vol. 18. – P. 41-66.
6. Eiseman P. R. A multi-surface method of coordinate generation / P. R. Eiseman // Journal of Computational Physics. – 1979. – Vol. 33, iss. 1. – P. 118-150.
7. Флетчер К. Вычислительные методы в динамике жидкостей / К. Флетчер. – М. : Мир, 1991. – Т. 2 : Методы расчета различных течений. – 552 с.
8. Floater M. S. Parametrization and smooth approximation of surface triangulations / M. S. Floater // Computer Aided Geometric Design. – 1997. – Vol. 14, iss. 3. – P. 231-250.
9. Floater M. S. A general construction of barycentric coordinates over convex polygons / M. S. Floater, K. Hormann, G. Kós // Advances in Computational Mathematics. – 2006. – Vol. 24, iss. 1. – P. 311-331.
10. Meyer M. Generalized barycentric coordinates on irregular polygons / M. Meyer, A. Barr, H. Lee, M. Desbrun // Journal of Graphics Tools. – 2002. – Vol. 7, iss. 1. – P. 13-22.
11. Warren J. Barycentric coordinates for convex polytopes / J. Warren // Advances in Computational Mathematics. – 1996. – Vol. 6, iss. 1. – P. 97-108.
12. Akinlar M. A. A Method for Orthogonal Grid Generation / M. A. Akinlar, S. Salako, G. Liao // General Mathematics Notes. – 2011. – Vol. 3. – No 1. – P. 55-72.
13. Мартюшов С. Н. Расчет пространственных задач обтекания на основе TVD схемы Хартена / С. Н. Мартюшов // Вычислительные технологии. – 1995. – Т. 14. – № 12. – С. 219-228.
14. Мартюшов С. Н. Построение дву- и трехмерных сеток для задач газодинамики на основе уравнения Пуассона / С. Н. Мартюшов // Известия высших учебных заведений. Математика. – 1997. – № 4. – С. 108-110.
15. Мартюшов С. Н. Численное моделирование струйных течений методом конечного объема на основе TVD-схемы 2-го порядка точности / С. Н. Мартюшов, Я. Г. Мартюшова // Вычислительные технологии. – 2004. – Т. 9. – № 4. – С. 57-65.
16. Мартюшов С. Н. Численное моделирование течений детонации газовых смесей методом конечного объема / С. Н. Мартюшов, Я. Г. Мартюшова // Вычислительные технологии. – 2008. – Т. 13. – № 1. – С. 88-98.
17. Ashrafizadeh A. Direct Design Solution of the Elliptic Grid Generation Equations / A. Ashrafizadeh, G. D. Raithby // Numerical Heat Transfer. – 2006. – Vol. 50. – P. 217-230.
18. Ashrafizadeh A. Structured Grid Generation Via Constraint on Displacement of Internal Nodes / A. Ashrafizadeh, R. Jalalabadi // International Journal of Basic & Applied Science. – 2011. – Vol. 11, No 4. – P. 79-87.
19. Zhang Y. 2D Nearly Orthogonal Mesh Generation / Y. Zhang, Y. Jia, S. S. Y. Wang // International Journal for Numerical Methods in Fluids. – 2004. – Vol. 46, iss. 7. – P. 685-707.
20. Zhang Y. 2D Nearly Orthogonal Mesh Generation with Controls of Distortion Function / Y. Zhang, Y. Jia, S. S. Y. Wang // Journal of Computational Physics. – 2006. – Vol. 218, iss. 2. – P. 549-571.
21. Zhang Y. Structured Mesh Generation with Smoothness Controls / Y. Zhang, Y. Jia, S. S. Y. Wang // International Journal for Numerical Methods in Fluids. – 2006. – Vol. 51, iss. 11. – P. 1255-1276.
22. Lehtimaki R. An Algebraic Boundary Orthogonalization Procedure for Structured Grids / R. Lehtimaki // International Journal for Numerical Methods in Fluids. – 2000. – Vol. 32, iss. 5. – P. 605-618.
23. Zhou Q. A Simple Grid Generation Method / Q. Zhou // International Journal for Numerical Methods in Fluids. – 1998. – Vol. 26, iss. 6. – P. 713-724.
24. Yerry M. A. A modified quadtree approach to finite element mesh generation / M. A. Yerry, M. S. Shephard // IEEE Computer Graphics and Applications. – 1983. – Vol. 3, iss. 1. – P. 39-46.
25. Baehmann P. L. Robust, geometrically based, automatic two-dimensional mesh generation / P. L. Baehmann, S. L. Wittchen, M. S. Shephard, K. R. Grice, M. A. Yerry // International Journal for Numerical Methods in Engineering. – 1987. – Vol. 24, iss. 6. – P. 1043-1078.
26. Liang X. Guaranteed-quality all-quadrilateral mesh generation with feature preservation / X. Liang, M. S. Ebeida, Y. Zhang // Computer Methods in Applied Mechanics and Engineering. – 2010. – Vol. 199. – P. 2072-2083.
27. Yiu K. F. C. Quadtree grid generation: information handling, boundary fitting and CFD applications / K. F. C. Yiu, D. M. Greaves, S. Cruz, A. Saalehi, A. G. L. Borthwick // Computers & Fluids. – 1996. – Vol. 25, iss. 8. – P. 759-769.
28. Ito Y. Octree-based reasonable-quality hexahedral mesh generation using a new set of refinement templates / Y. Ito, A. M. Shih, B. K. Soni // International Journal for Numerical Methods in Engineering. – 2009. – Vol. 77. – P. 1809-1833.
29. Kolšek T. Generation of block-structured grids in complex computational domains using templates / T. Kolšek, M. Šubelj, J. Duhovnik // Finite Elements in Analysis and Design. – 2003. – Vol. 39. – P. 1139-1154.
30. Miranda A. C. O. Hierarchical template‐based quadrilateral mesh generation / A. C. O. Miranda, L. F. Martha // Engineering with Computers. – 2015. – Vol. 31. – P. 1-15.
31. Yerry M. A. Automatic three-dimensional mesh generation by the modified-octree technique / M. A. Yerry, M. S. Shephard // International Journal for Numerical Methods in Engineering. – 1984. – Vol. 20, iss. 11. – P. 1965-1990.
32. Zhang H. Adaptive hexahedral mesh generation based on local domain curvature and thickness using a modified grid-based method / H. Zhang, G. Zhao // Finite Elements in Analysis and Design. – 2007. – Vol. 43, iss. 9. – P. 691-704.
33. Quadros W. R. LayTracks: a new approach to automated geometry adaptive quadrilateral mesh generation using medial axis transform / W. R. Quadros, K. Ramaswami, F. B. Prinz, B. Gurumoorthy // International Journal for Numerical Methods in Engineering. – 2004. – Vol. 61, iss. 2. – P. 209-237.
34. Tam T. K. H. 2D finite element mesh generation by medial axis subdivision / T. K. H. Tam, C. G. Armstrong // Advances in Engineering Software and Workstations. – 1991. – Vol. 13. – No 5-6. – P. 313-324.
35. Guoy D. Automatic Blocking Scheme for Structured Meshing in 2D Multiphase Flow Simulation / D. Guoy, J. Erickson // The 13th International Meshing Roundtable : International Conference, Willimasburg, Virginia, USA, September 19-22, 2004 : proceedings. – Sandia : Sandia National Laboratories, 2004. – P. 121-132.
36. Taghavi R. Automatic block decomposition using fuzzy logic analysis / R. Taghavi // The 9th International meshing roundtable : International Conference, New Orleans, Louisiana, USA, 2-5 October 2000 : proceedings. – Sandia : Sandia National Laboratories, 2000. – P. 187-192.
37. Takahashi H. A general purpose automatic mesh generation using shape recognition technique / H. Takahashi, H. Shimizu // ASME Computers in Engineering. – 1991. – Vol. 1. – P. 519-526.
38. Takahashi H. A Three-Dimensional Automatic Mesh Generation System Using Shape Recognition Technique / H. Takahashi, H. Shimizu, H. Moriyama, Y. Yamashita, N. Chiba // Transactions of the Japan Society of Mechanical Engineers. – 1993. – Vol. 59. – No 560. – Series A. – P. 1161-1167.
39. Müller-Hannemann M. High quality quadrilateral surface meshing without template restrictions: a new approach based on network flow techniques / M. Müller-Hannemann // The International Journal of Computational Geometry and Applications. – 1999. – Vol. 10, iss. 3. – P. 285-307.
40. Jablonowski C. Block-structured adaptive meshes and reduced grids for atmospheric general circulation models / C. Jablonowski, R. C. Oehmke, Q. F. Stout // Philosophical Transactions of the Royal Society A. – 2009. – Vol. 367. – P. 4497-4522.
41. Zheng J. Z. X. Block-Based Adaptive Mesh Refinement Finite-vol. Scheme for Hybrid Multi-Block Meshes / J. Z. X. Zheng, C. P. T. Groth // Seventh International Conference on Computational Fluid Dynamics (ICCFD7) : International Conference, Big Island, Hawaii, July 9-13, 2012 : proceedings. – Hawaii : 2012. – P. 1-19.
42. Ahusborde E. A 2D Block-structured Mesh Partitioner for Accurate Flow Simulations on Non-rectangular Geometries / E. Ahusborde, S. Glockner // Computers & Fluids. – 2011. – Vol. 43. – P. 2-13.
43. Steensland J. A partitioner-centric model for structured adaptive mesh refinement partitioning trade-off optimization: Part I / J. Steensland, J. Ray // The International Journal of High Performance Computing Applications. – 2005. – Vol. 19. – No 4. – P. 409-422.
44. Steensland J. A partitioner-centric model for structured adaptive mesh refinement partitioning trade-off optimization: Part II / J. Steensland, J. Ray // Parallel Processing Workshops : International Conference, Montreal, QC, Canada, 15-18 Aug 2004 : proceedings. – 2004. – P. 231-238.
Опубліковано
2016-10-13
Як цитувати
Чопоров, С. В., Гоменюк, С. І., & Алатамнех, Х. Х. (2016). МЕТОДИ ПОБУДОВИ ДИСКРЕТНИХ МОДЕЛЕЙ: СТРУКТУРОВАНІ ТА БЛОЧНО-СТРУКТУРОВАНІ СІТКИ. Computer Science and Applied Mathematics, (1), 272-284. вилучено із http://journalsofznu.zp.ua/index.php/comp-science/article/view/1366
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