Meshless method for radiation heat transfer in graded index medium

Because ray goes along a curved path determined by the Fermat principle, curved ray tracing is very difficult and complex in graded index media. To avoid the difficult and complex computation of curved ray trajectories, a meshless local Petrov–Galerkin approach based on discrete-ordinate equations is developed to solve the radiative transfer problem in multi-dimensional absorbing–emitting–scattering semitransparent graded index media. A moving least square approximation is used to construct the shape function. Two particular test problems in radiative transfer are taken as examples to verify this meshless approach. The predicted temperature distributions and the dimensionless radiative heat fluxes are determined by the proposed method and compared with the other benchmark approximate solutions. The results show that the meshless local Petrov–Galerkin approach based on discrete-ordinate equations has a good accuracy in solving the radiative transfer problems in absorbing–emitting–scattering semitransparent graded index media.