Abstract
The reproducing kernel particle method (RKPM), which is a Lagrangian meshless method, is employed for the calculation of radiative heat transfer in participating media. In the present method, for each discrete particle (i.e., spatial node) within a local support domain, the approximate formulas of the radiative intensity and its derivatives are constructed by the reproducing kernel interpolation function, and the residual function is obtained when these parameters are substituted into the radiative transfer equation. Then the least-squares point collocation technique (LSPCT) is introduced by minimizing the summation of residual function. Five test cases are considered and quantified to verify the meshless method, including isotropic scattering medium, first-order forward scattering medium, pure absorbing medium, absorbing scattering medium, and absorbing, scattering emitting medium. The results are in good agreement with the benchmark methods, showing the reproducing kernel particle method is an efficient, accurate, and stable method for the calculation of radiative transfer in participating media.
Highlights
Radiative heat transfer among absorbing, scattering, and emitting medium plays an important role in many engineering application, that is, glass fabrication, laser pulse heating, and diesel fuel droplets burners
Sadat [1] presented a moving least-squares collocation method to solve the radiative transfer equation, and the results showed that, for small absorption coefficient, the primitive variables formulation is unstable while the even parity formulation is always stable and accurate
A reproducing kernel particle method based on the discreteordinate equation is extended to solve the radiative transfer problem in participating medium
Summary
Radiative heat transfer among absorbing, scattering, and emitting medium plays an important role in many engineering application, that is, glass fabrication, laser pulse heating, and diesel fuel droplets burners. Numerical simulation is adopted widely in the study of radiative heat transfer, in which some methods have been developed to solve the radiative heat transfer in participating medium, such as the Monte Carlo method, the zonal method, the discrete-ordinates method (DOM), the finite volume method (FVM), and the finite element method (FEM). Some meshless methods are proposed to avoid the drawback. Sadat [1] presented a moving least-squares collocation method to solve the radiative transfer equation, and the results showed that, for small absorption coefficient, the primitive variables formulation is unstable while the even parity formulation is always stable and accurate.
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