Least-squares collocation meshless approach for coupled radiative and conductive heat transfer

A least-squares collocation meshless method is employed for solving the coupled radiative and conductive heat transfer in absorbing, emitting, and scattering media. The least-squares collocation meshless method for radiative transfer is based on the discrete ordinates equation. A moving least-squares approximation is applied to construct the trial functions. In addition to the collocation points which are used to construct the trial functions, a number of auxiliary points are also adopted to form the total residuals of the problem. The least-squares technique is used to obtain the solution of the problem by minimizing the summation of residuals of all collocation and auxiliary points. Three numerical examples are studied to illustrate the performance of this new solution method. The numerical results are compared with other benchmark approximate solutions. By comparison, the results show that the least-squares collocation meshless method is efficient, accurate, and stable, and can be used for solving coupled radiative and conductive heat transfer in absorbing, emitting, and scattering media.