A Corrected HNT-UGKS for Boundary Layer Problems of the Gray Radiative Transfer Equations

doi:10.1007/s42967-024-00376-z

Communications on Applied Mathematics and Computation ›› 2025, Vol. 7 ›› Issue (2): 689-717.doi: 10.1007/s42967-024-00376-z

Previous Articles Next Articles

A Corrected H_N^T-UGKS for Boundary Layer Problems of the Gray Radiative Transfer Equations

Song Jiang¹, Qi Li¹, Wenjun Sun^1,2

1 National Key Laboratory of Computational Physics, Institute of Applied Physics and Computational Mathematics, Beijing 100094, China;
2 Center for Applied Physics and Technology, College of Engineering, Peking University, Beijing 100871, China

Received:2023-07-27 Revised:2024-01-13 Accepted:2024-01-20 Online:2025-06-20 Published:2025-04-21
Supported by:
The current research is supported by the National Key R & D Program (Grant no. 2020YFA0712200) and the Sino-German Science Center (Grant no. GZ 1465) for Jiang, and by the Beijing Natural Science Foundation of China (Grant no. Z230003) and the NSFC (Grant nos. 12292981, 12292982) for Sun.

Abstract

Abstract: In this paper, the corrected method to the original H_N^T-unified gas kinetic scheme (H_N^T-UGKS) is developed in order to solve the nonlinear radiative transfer equations with boundary layers. The H_N^T-UGKS is an asymptotic preserving (AP) scheme that uses UGKS for spatial discretization and the hybrid H_N^T method for angular discretization which is constructed in the paper (Li et al. in Nucl. Sci. Eng. 198(5): 993–1020, 2024). First, the correction idea in Mieussens (J. Comput. Phys. 253: 138–156, 2013) is adopted, such that H_N^T-UGKS can correctly simulate the linear radiative transfer equation with boundary layers. Then, for the nonlinear radiative transfer equations with boundary layers, the transformation from the implicit Monte Carlo (IMC) method is introduced to rewrite the nonlinear transfer equations into a linearized system. It is the key point in the construction of the current scheme to use this linearized system to construct the numerical boundary fluxes. In this way, the boundary density is included in the numerical fluxes, and consequently, the modification method for the linear radiative transfer equation can be used to deal with the nonlinear problem studied in this paper. A number of numerical examples are presented to demonstrate the accuracy and effectiveness of the current scheme for resolving boundary layers in both linear and nonlinear radiative transfer problems.

Key words: Nonlinear radiative transfer, Boundary layer, H_N^T-UGKS, Implicit Monte Carlo (IMC) method

CLC Number:

Song Jiang, Qi Li, Wenjun Sun. A Corrected H_N^T-UGKS for Boundary Layer Problems of the Gray Radiative Transfer Equations[J]. Communications on Applied Mathematics and Computation, 2025, 7(2): 689-717.

TrendMD

References

1. Adams, M.L., Larsen, E.W.: Fast iterative methods for discrete-ordinates particle transport calculations. Prog. Nucl. Energy 40, 3–159 (2002)
2. Azmy, Y., Sartori, E.: Nuclear Computational Science: a Century in Review. Springer, Berlin (2010)
3. Coelho, P.J.: 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. 145, 121–146 (2014)
4. Fleck, J.A., Jr., Cummings, J., Jr.: An implicit Monte Carlo scheme for calculating time and frequency dependent nonlinear radiation transport. J. Comput. Phys. 8(3), 313–342 (1971)
5. Jin, S.: Efficient asymptotic-preserving (AP) schemes for some multiscale kinetic equations. SIAM J. Sci. Comput. 21(2), 441–454 (1999)
6. Jin, S., Ma, Z., Wu, K.: Asymptotic-preserving neural networks for multiscale time-dependent linear transport equations. J. Sci. Comput. 94(3), 57 (2023)
7. Jin, S., Pareschi, L., Toscani, G.: Uniformly accurate diffusive relaxation schemes for multiscale transport equations. SIAM J. Numer. Anal. 38(3), 913–936 (2000)
8. Klar, A.: An asymptotic-induced scheme for nonstationary transport equations in the diffusive limit. SIAM J. Numer. Anal. 35(3), 1073–1094 (1998)
9. Klar, A., Schmeiser, C.: Numerical passage from radiative heat transfer to nonlinear diffusion models. Math. Models Methods Appl. Sci. 11(05), 749–767 (2001)
10. Larsen, E.W., Morel, J.E., Miller, W.F.: Asymptotic solutions of numerical transport problems in optically thick, diffusive regimes II. J. Comput. Phys. 69(2), 283–324 (1989)
11. Larsen, E.W., Pomraning, G.C., Badham, V.C.: Asymptotic analysis of radiative transfer problems. J. Quant. Spectrosc. Radiat. Transf. 29(4), 285–310 (1983)
12. Li, Q., Jiang, S., Sun, W., Xu, X.: An asymptotic-preserving hybrid angular discretization for the gray radiative transfer equations. Nucl. Sci. Eng. 198(5), 993–1020 (2024)
13. Li, Q., Lu, J., Sun, W.: Diffusion approximations and domain decomposition method of linear transport equations: asymptotics and numerics. J. Comput. Phys. 292, 141–167 (2015)
14. McClarren, R.G., Rossmanith, J.A., Shin, M.: Semi-implicit hybrid discrete (hn t ) approximation of thermal radiative transfer. J. Sci. Comput. 90(1), 1–29 (2022)
15. Mieussens, L.: On the asymptotic preserving property of the unified gas kinetic scheme for the diffusion limit of linear kinetic models. J. Comput. Phys. 253, 138–156 (2013)
16. Shin, M.: Hybrid discrete (hn t ) approximations to the equation of radiative transfer. Ph.D. thesis, Iowa State University, Ames, USA (2019)
17. Steinberg, E., Heizler, S.I.: Multi-frequency implicit semi-analog Monte-Carlo (ISMC) radiative transfer solver in two-dimensions (without teleportation). J. Comput. Phys. 450, 110806 (2022)
18. Steinberg, E., Heizler, S.I.: A new discrete implicit Monte Carlo scheme for simulating radiative transfer problems. Astrophys. J. Suppl. Ser. 258(1), 14 (2022)
19. Sun, W., Jiang, S., Xu, K.: An asymptotic preserving unified gas kinetic scheme for gray radiative transfer equations. J. Comput. Phys. 285, 265–279 (2015)
20. Sun, W., Jiang, S., Xu, K.: An implicit unified gas kinetic scheme for radiative transfer with equilibrium and non-equilibrium diffusive limits. Commun. Comput. Phys. 22(4), 889–912 (2017)
21. Sun, W., Jiang, S., Xu, K.: A multidimensional unified gas-kinetic scheme for radiative transfer equations on unstructured mesh. J. Comput. Phys. 351, 455–472 (2017)
22. Sun, W., Jiang, S., Xu, K., Li, S.: An asymptotic preserving unified gas kinetic scheme for frequencydependent radiative transfer equations. J. Comput. Phys. 302, 222–238 (2015)
23. Xu, K.: Direct modeling for computational fluid dynamics. Acta. Mech. Sin. 31(3), 303–318 (2015)
24. Xu, K., Huang, J.-C.: A unified gas-kinetic scheme for continuum and rarefied flows. J. Comput. Phys. 229(20), 7747–7764 (2010)
25. Xu, X., Jiang, S., Sun, W.: A positive and asymptotic preserving filtered PN method for the gray radiative transfer equations. J. Comput. Phys. 444, 110546 (2021)
26. Xu, X., Sun, W., Jiang, S.: An asymptotic preserving angular finite element based unified gas kinetic scheme for gray radiative transfer equations. J. Quant. Spectrosc. Radiat. Transf. 243, 106808 (2020)

A Corrected H_N^T-UGKS for Boundary Layer Problems of the Gray Radiative Transfer Equations

PDF

Knowledge

Abstract

Cite this article

share this article

References

Related Articles 0

Recommended Articles

Metrics

Comments