Least-squares radial point interpolation collocation meshless method for radiative heat transfer

A least-squares radial point interpolation collocation meshless method based on the discrete ordinates equation is developed for solving the radiative transfer in absorbing, emitting, and scattering media, in which compact support radial basis functions augmented with polynomial basis are employed to construct the trial functions. In addition to the collocation nodes, 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 typical examples of radiative transfer in semitransparent media are examined to verify this new solution method. The numerical results are compared with other benchmark approximate solutions in references. By comparison, the results show that the least-squares radial point interpolation collocation meshless method has good accuracy in solving radiative transfer problems within absorbing, emitting, and scattering media.