Assessment of different spatial/angular agglomeration multigrid schemes for the acceleration of FVM radiative heat transfer computations

References

• G. N. Lygidakis and I. K. Nikolos, A Parallel Agglomeration Multigrid Method for the Acceleration of Compressible Flow Computations on 3D Hybrid Unstructured Grids, Proceedings of 11th World Congress on Computational Mechanics, WCCM 2014, ECCM 2014, ECFD 2014, Barcelona, Spain, 20–25 July, 2014.
   Google Scholar
• A. Brandt, Multigrid Techniques with Applications to Fluid Dynamics: 1984 Guide, VKI Lecture Series, pp. 1–176, 1984.
   Google Scholar
• J. Blazek, Computational Fluid Dynamics: Principles and Applications, Elsevier Science, Kidlington, 2001.
   Google Scholar
• J. H. Ferziger and M. Peric, Computational Methods for Fluid Dynamics, 3rd ed., Springer-Verlag, New York, 2002.
   Google Scholar
• G. N. Lygidakis, and I. K. Nikolos, Numerical Analysis of Flow over the NASA Common Research Model Using the Academic CFD Code Galatea, ASME J. Fluids Eng, vol. 137, 071103, 2015.
   Google Scholar
• H. Nishikawa and B. Diskin, Development and Application of Parallel Agglomerated Multigrid Methods for Complex Geometries, AIAA 2011–3232, Proceedings of 20th AIAA Computational Fluid Dynamics Conference, Honolulu, Hawaii, USA, 27–30 June, 2011.
   Google Scholar
• G. N. Lygidakis and I. K. Nikolos, Using a Parallel Spatial/Angular Agglomeration Multigrid Scheme to Accelerate the FVM Radiative Heat Transfer Computation – Part I: Methodology, Numer. Heat Transfer, Part B, vol. 66, pp. 471–497, 2014.
   Web of Science ®Google Scholar
• G. N. Lygidakis and I. K. Nikolos, Using a Parallel Spatial/Angular Agglomeration Multigrid Scheme to Accelerate the FVM Radiative Heat Transfer Computation – Part II: Numerical Results, Numer. Heat Transfer, Part B, vol. 66, pp. 498–525, 2014.
   Web of Science ®Google Scholar
• G. Kim, S. Kim, and Y. Kim, Parallelized Unstructured-Grid Finite Volume Method for Modeling Radiative Heat Transfer, J. Mech. Sci. Tech., vol. 19, pp. 1006–1017, 2005.
   Web of Science ®Google Scholar
• P. J. Coelho, Bounded Skew High-Order Resolution Schemes for the Discrete Ordinates Method, J. Comput. Phy., vol. 175, pp. 412–437, 2002.
   Web of Science ®Google Scholar
• R. Capdevila, C. D. Perez-Segarra, and A. Oliva, Development and Comparison of Different Spatial Numerical Schemes for the Radiative Transfer Equation Resolution Using Three-Dimensional Unstructured Meshes, J. Quant. Spectrosc. Radiat. Transfer, vol. 111, pp. 264–273, 2010.
   Web of Science ®Google Scholar
• G. N. Lygidakis and I. K. Nikolos, Using a High-Order Spatial/Temporal Scheme and Grid Adaptation with a Finite-Volume Method for Radiative Heat Transfer, Numer. Heat Transfer, Part B, vol. 64:2, pp. 89–117, 2013.
   Web of Science ®Google Scholar
• P. Hassanzadeh and G. D. Raithby, Finite-Volume Solution of the Second Order Radiative Transfer Equation: Accuracy and Solution Cost, Numer. Heat Transfer, Part B, vol. 53, pp. 374–382, 2008.
   Web of Science ®Google Scholar
• M. H. Lallemand, Schemas decentres multigrilles pour la resolution des equations d’ Euler en elements finis, PhD thesis, Universite de Provence, France, 1988.
   Google Scholar
• D. J. Mavriplis, Directional Coarsening and Smoothing for Anisotropic Navier-Stokes Problems, Electron. Trans. Numer. Anal., vol. 6, pp. 182–197, 1997.
   Google Scholar
• N. K. Lambropoulos, D. G. Koubogiannis, and K. C. Giannakoglou, Acceleration of a Navier-Stokes Equation Solver for Unstructured Grids Using Agglomeration Multigrid and Parallel Processing, Comput. Methods Appl. Mech. Eng., vol. 193, pp. 781–803, 2004.
   Web of Science ®Google Scholar
• H. Nishikawa, B. Diskin, and J. L. Thomas, Critical Study of Agglomerated Multigrid Methods for Diffusion, AIAA J., vol. 48, pp. 839–847, 2010.
   Google Scholar
• H. Nishikawa, B. Diskin, and J. L. Thomas, Recent Advances in Agglomerated Multigrid, AIAA 2013–0863, Proceedings of 51st AIAA Aerospace Sciences Meeting, Grapevine, Texas, USA, 7–10 January, 2013.
   Google Scholar
• V. Hannemann, Structured Multigrid Agglomeration on a Data Structure for Unstructured Meshes, Int. J. Numer. Methods Fluids, vol. 40, pp. 361–368, 2002.
   Web of Science ®Google Scholar
• G. N. Lygidakis and I. K. Nikolos, Using the Finite-Volume Method and Hybrid Unstructured Meshes to Compute Radiative Heat Transfer in 3-D Geometries, Numer. Heat Transfer, Part B, vol. 62, pp. 289–314, 2012.
   Web of Science ®Google Scholar
• T. K. Kim and H. Lee, Effect of Anisotropic Scattering on Radiative Heat Transfer in Two-Dimensional Rectangular Enclosures, Int. J. Heat Mass Transfer, vol. 31, pp. 1711–1721, 1988.
   Web of Science ®Google Scholar
• M. Y. Kim, S. W. Baek, and J. H. Park, Unstructured Finite-Volume Method for Radiative Heat Transfer in a Complex Two-Dimensional Geometry with Obstacles, Numer. Heat Transfer, Part B, vol. 39, pp. 617–635, 2001.
   Web of Science ®Google Scholar
• J. C. Chai, One-Dimensional Transient Radiation Heat Transfer Modeling Using a Finite-Volume Method, Num. Heat Transfer B, vol. 44, pp. 187–208, 2003.
   Web of Science ®Google Scholar
• R. Das, S. C. Mishra, and R. Uppaluri, Multiparameter Estimation in a Transient Conduction-Radiation Problem Using the Lattice Boltzmann Method and the Finite-Volume Method Coupled with the Genetic Algorithms, Numer. Heat Transfer, Part A, vol. 53, pp. 1321–1338, 2008.
   Web of Science ®Google Scholar
• B. Hunter and Z. Guo, Comparison of the Discrete-Ordinates Method and the Finite-Volume Method for Steady-State and Ultrafast Radiative Transfer Analysis in Cylindrical Coordinates, Numer. Heat Transfer, Part B, vol. 59, pp. 339–359, 2011.
   Web of Science ®Google Scholar
• G. D. Raithby, Discussion of the Finite Volume-Method for Radiation, and its Application Using 3D Unstructured Meshes, Numer. Heat Transfer, Part B, vol. 35, pp. 389–405, 1999.
   Web of Science ®Google Scholar
• H. Jimbo, R. Liming, and T. Heping, Effect of Anisotropic Scattering on Radiative Heat Transfer in Two-Dimensional Rectangular Media, J. Quant. Spectrosc. Radiat. Transfer, vol. 78, pp. 151–161, 2003.
   Web of Science ®Google Scholar
• D. N. Trivic, T. J. O’Brien, and C. H. Amon, Modeling the Radiation of Anisotropically Scattering Media by Coupling Mie Theory with Finite Volume Method, Int. J. Heat Mass Transfer, vol. 47, pp. 5675–5780, 2004.
   Web of Science ®Google Scholar
• G. D. van Albada, B. van Leer, and W. W. Roberts, Jr., A Comparative Study of Computational Methods in Cosmic Gas Dynamics, Astron. Astrophys., vol. 108, pp. 76–84, 1982.
   Web of Science ®Google Scholar
• P. K. Sweby, High Resolution Schemes Using Flux Limiters for Hyperbolic Conservation Laws, SIAM J. Numer. Anal., vol. 21, pp. 995–1011, 1984.
   Web of Science ®Google Scholar
• J. H. Lienhard IV and J. H. Lienhard V, A Heat Transfer Textbook, 3rd ed., Phlogiston Press, chap. 10, Cambridge, Massachusetts, 2002.
   Google Scholar
• M. H. Lallemand, Etude de Schemas Runge-Kutta a 4 pas pour la Resolution Multigrille des Equations d’ Euler 2D, Raport de Recherche, INRIA, 1988.
   Google Scholar
• V. Venkatakrishnan, Implicit Schemes and Parallel Computing in Unstructured Grid CFD, Proceedings of 26th Computational Fluid Dynamics Lecture Series Program, VKI, Rhode Saint-Genese, Belgium,13–17 March, 1995.
   Google Scholar
• B. Smith, P. Bjorstad, and W. Gropp, Domain Decomposition. Parallel Multilevel Methods for Elliptic Partial Differential Equations, Cambridge University Press, Cambridge, 1996.
   Google Scholar
• S. Lanteri, Parallel Solutions of Compressible Flows Using Overlapping and Non-Overlapping Mesh Partitioning Strategies, Parallel Comput., vol. 22, pp. 943–968, 1996.
   Web of Science ®Google Scholar
• K. A. Sorensen, O. Hassan, K. Morgan, and N. P. Weatherill, A Multigrid Accelerated Hybrid Unstructured Mesh Method for 3D Compressible Turbulent Flows, Comput. Mech., vol. 31, pp. 101–114, 2003.
   Web of Science ®Google Scholar
• G. Carre and S. Lanteri, Parallel Linear Multigrid by Agglomeration for the Acceleration of 3D Compressible Flow Calculations on Unstructured Meshes, Numer. Algorithms, vol. 24, pp. 309–332, 2000.
   Web of Science ®Google Scholar
• J. Liu, H. M. Shang, and Y. S. Chen, Development of an Unstructured Radiation Model Applicable for Two-Dimensional Planar, Axisymmetric, and Three-Dimensional Geometries, J. Quant. Spectrosc. Radiat. Transfer, vol. 66, pp. 17–33, 2000.
   Web of Science ®Google Scholar
• K. Guedri, M. A. Abbassi, M. N. Borjini, K. Halouani, and R. Said, Application of the Finite-Volume Method to Study the Effects of Baffles on Radiative Heat Transfer in Complex Enclosures, Numer. Heat Transfer, Part A, vol. 55, pp. 780–806, 2009.
   Web of Science ®Google Scholar
• F. Asllanaj, V. Feldheim, and P. Lybaert, Solution of Radiative Heat Transfer in 2-D Geometries by a Modified Finite-Volume Method Based on a Cell Vertex Scheme Using Unstructured Triangular Meshes, Numer. Heat Transfer, Part B, vol. 51, pp. 97–119, 2007.
   Web of Science ®Google Scholar