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<p>This study proposes an efficient two-dimensional numerical approach for solving the monochromatic radiative transfer equation (RTE) governing thermal radiation propagation through a water curtain (WC) with arbitrary optical properties. The developed SH Spatial Grid (SHSG) model couples a spherical harmonic (SH) expansion of the angular radiance field with a discrete spatial grid formulation, and the resulting system is solved iteratively using a conjugate gradient (CG) algorithm. The proposed approach substantially reduces computational cost while preserving high accuracy, with simulations involving tens of thousands of grid points completed within minutes. The numerical results demonstrate the capability of the model to accurately capture the combined effects of absorption, scattering, and reflection in homogeneous WCs. Predicted hemispherical reflectance and transmittance distributions confirm the robustness of the method for the analysis of radiative shielding performance in fire-protection applications.</p>

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2D radiative transfer through water curtain using SH and CG methods

  • 期刊论文

  • 发表日期：

    2026年3月16日

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  • Robertine Kang,
  • Arantes Fokou,
  • Pierre Marie Wakeu Pola,
  • Fabien Kenmogne,
  • Gerard Nfor Junior Bawe,
  • Réné Tchinda

摘要

This study proposes an efficient two-dimensional numerical approach for solving the monochromatic radiative transfer equation (RTE) governing thermal radiation propagation through a water curtain (WC) with arbitrary optical properties. The developed SH Spatial Grid (SHSG) model couples a spherical harmonic (SH) expansion of the angular radiance field with a discrete spatial grid formulation, and the resulting system is solved iteratively using a conjugate gradient (CG) algorithm. The proposed approach substantially reduces computational cost while preserving high accuracy, with simulations involving tens of thousands of grid points completed within minutes. The numerical results demonstrate the capability of the model to accurately capture the combined effects of absorption, scattering, and reflection in homogeneous WCs. Predicted hemispherical reflectance and transmittance distributions confirm the robustness of the method for the analysis of radiative shielding performance in fire-protection applications.