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Numerical Heat Transfer, Part B: Fundamentals
An International Journal of Computation and Methodology
Volume 84, 2023 - Issue 2
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Research Articles

Verification of numerical solutions of thermal radiation problems in participating and nonparticipating media

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Pages 143-165 | Received 22 Aug 2022, Accepted 09 Mar 2023, Published online: 03 Apr 2023

References

  • P. Knupp and K. Salari, Verification of Computer Codes in Computational Science and Engineering. Boca Raton, FL: Chapman & Hall, 2003.
  • W. L. Oberkampf and C. J. Roy, Verification and Validation in Scientific Computing. Cambridge, UK: Cambridge Univ. Press, 2010,
  • P. J. Roache, Fundamentals of Verification and Validation, 2nd ed. Socorro, NM: Hermosa, 2009.
  • American Society of Mechanical Engineers. Standard for Verification and Validation in Computational Fluid Dynamics and Heat Transfer – ASME V&V 20-2009. New York, NY: American Society of Mechanical Engineers, 2009.
  • P. J. Coelho, “Advances in the discrete ordinates and finite volume methods for the solution of radiative heat transfer problems in participating media,” J. Quant. Spectrosc. Radiat. Transf., vol. 145, pp. 121–146, 2014. DOI: 10.1016/j.jqsrt.2014.04.021.
  • S. N. Dhurandhar, A. Bansal, S. P. Boppudi, and M. D. M. Kadiyala, “Application and comparative analysis of radiative heat transfer models for coal-fired furnace,” Numer. Heat Tr. A-Appl., vol. 82, no. 4, pp. 137–168, 2022. DOI: 10.1080/10407782.2022.2067400.
  • E. M. Sparrow and R. D. Cess, Radiation Heat Transfer, Augmented ed. Washington, DC: Hemisphere, 1978.
  • P. J. Roache and P. M. Knupp, “Complete Richardson Extrapolation,” Commun. Numer. Meth. Eng., vol. 9, no. 5, pp. 365–374, 1993. DOI: 10.1002/cnm.1640090502.
  • A. Sidi, Practical Extrapolation Methods – Theory and Applications. Cambridge, UK: Cambridge University Press, 2003.
  • C. H. Marchi, R. Suero, and L. K. Araki, “The lid-driven square cavity flow: Numerical solution with a 1024 × 1024 grid,” J. Braz. Soc. Mech. Sci., vol. 31, no. 3, pp. 186–198, 2009. DOI: 10.1590/S1678-58782009000300004.
  • J. H. Ferziger and M. Perić, Computational Methods for Fluid Dynamics, 3rd ed. Berlin, DE: Springer, 2002, p. 58.
  • C. H. Marchi, L. A. Novak, C. D. Santiago, and A. P. S. Vargas, “Highly accurate numerical solutions with repeated Richardson extrapolation for 2d Laplace equation,” Appl. Math. Model., vol. 37, no. 12–13, pp. 7386–7397, 2013. DOI: 10.1016/j.apm.2013.02.043.
  • B. P. Leonard, “Comparison of truncation error of finite-difference and finite-volume formulations of convection terms,” Appl. Math. Model., vol. 18, no. 1, pp. 46–50, 1994. DOI: 10.1016/0307-904X(94)90182-1.
  • B. P. Leonard, “Order of accuracy of QUICK and related convection-diffusion schemes,” Appl. Math. Model., vol. 19, no. 11, pp. 640–653, 1995. DOI: 10.1016/0307-904X(94)90182-1.
  • C. H. Marchi, 2001. “Verification of unidimensional numerical solutions in computational fluid dynamics,” PhD thesis, Graduate Program in Mechanical Engineering, POSMEC, Santa Catarina Federal Univ. Florianópolis, SC, BR (in portuguese).
  • L. P. da Silva, C. H. Marchi, M. Meneguette, and A. C. Foltran, “Robust RRE technique for increasing the order of accuracy of SPH numerical solutions,” Math. Comput. Simul., vol. 199, pp. 231–252, 2022. DOI: 10.1016/j.matcom.2022.03.016.
  • A. C. Foltran, C. H. Marchi, and L. M. Moura, “Truncation error for the Simpson’s 1/3 rule based on Taylor series expansion,” 18th Brazilian Congress of Thermal Sciences and Engineering, Nov. 2020, pp. 1–10. DOI: 10.26678/ABCM.ENCIT2020.CIT20-0167.
  • J. C. Chai, H. S. Lee, and S. V. Patankar, “Ray effect and false scattering in the discrete ordinates method,” Numer. Heat Tr., B-Fund., vol. 24, no. 4, pp. 373–389, 1993. DOI: 10.1080/10407799308955899.
  • J. P. Jessee and W. A. Fiveland, “Bounded, high resolution differencing schemes applied to the discrete ordinates method,” J. Thermophys. Heat Trans., vol. 11, no. 4, pp. 540–548, 1997. DOI: 10.2514/2.6296.
  • G. D. Raithby, “Evaluation of discretization errors in finite-volume radiant heat transfer predictions,” Numer. Heat Tr., B-Fund., vol. 36, no. 3, pp. 241–264, 1999. DOI: 10.1080/104077999275631.
  • E. D. Larsen and A. B. Wollaber, “A quantitative theory of angular truncation errors in 3-D discrete ordinates calculations,” M&C + SNA Topical Meeting, Joint Int. Topical Meeting Mathematics & Computation Supercomputing Nucl. Applications, vol. 1, pp. 287–304, Apr. 2007.
  • C. H. Marchi and A. F. C. Silva, “Multi-dimensional discretization error estimation for convergent apparent order,” J. Braz. Soc. Mech. Sci. Eng., vol. 27, no. 4, pp. 432–439, 2005. DOI: 10.1590/S1678-58782005000400012.
  • C. M. Usiskin and R. Siegel, “Thermal radiation from a cylindrical enclosure with specified wall heat flux,” J. Heat Transf., vol. 82, no. 4, pp. 369–374, 1960. DOI: 10.1115/1.3679956.
  • C. H. Marchi and A. C. Alves, “Verification of numerical solutions of the advection-diffusion and Burgers equations,” Appl. Comput. Math., vol. 3, no. 2, pp. 1–7, 2014. DOI: 10.4172/2168-9679.1000154.
  • M. A. Heaslet and R. F. Warming, “Radiative transport and wall temperature slip in an absorbing planar medium,” Int. J. Heat Mass Transf., vol. 8, no. 7, pp. 979–994, 1965. DOI: 10.1016/0017-9310(65)90083-9.
  • J. R. Howell, “A catalog of radiation configuration factors,” Department of Mechanical Engineering, Univ. of Texas, Austin, TX. [Online]. Available: http://www.thermalradiation.net/indexCat.html. Accessed: Oct. 24, 2021.

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