A high order approximation, the SKN method—a mnemonic for synthetic kernel—is proposed for solving radiative transfer problems in participating medium. The method relies on approximating the integral transfer kernel by a sum of exponential kernels. The radiative integral equation is then reducible to a set of coupled second-order differential equations. The method is tested for one-dimensional plane-parallel participating medium. Three quadrature sets are proposed for the method, and the convergence of the method with the proposed sets is explored. The SKN solutions are compared with the exact, PN, and SN solutions. The SK1 and SK2 approximations using quadrature Set-2 possess the capability of solving radiative transfer problems in optically thin systems.

Issue Section:
Radiative Heat Transfer
Keywords:
radiative transfer, absorbing media, integral equations, Emitting, Numerical Methods, Participating Media, Radiation, Scattering
Topics:
Approximation, Errors, Radiation scattering, Radiative heat transfer, Electromagnetic scattering, Scattering (Physics), Albedo
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