New implementation of local RBF meshless scheme for radiative heat transfer in participating media

• A new implementation of local RBF meshless method (nLRBFM) is developed.
• Multiquadric (MQ) RBF is employed to construct the trial functions.
• The outflow-boundary intensity correction interpolation eliminates numerical oscillations.
• The nLRBFM is of high accuracy and excellent stability for solving RTE.

The local radial basis function meshless method (LRBFM) is an effective numerical scheme for solving radiative heat transfer in participating media, in which radial basis functions (RBF) augmented with polynomial basis are employed to construct the trial functions, and radiative transfer equations are discretized directly at nodes by collocation method. The LRBFM belongs to a class of truly meshless methods which do not need any mesh, and can be implemented on a set of uniform or irregular nodes without nodes’ connectivity. The main drawback of this method is that like most of the other numerical methods, the solution to RTE by LRBFM also suffers much from nonphysical oscillations. In the present work a new implementation of local RBF meshless scheme (nLRBFM) is proposed, based on the RBF correction interpolation of outflow-boundary intensity which can easily eliminate numerical oscillations of results without any extra stabilization technique. Classical cases are studied to illustrate the numerical performance of this new implementation. From comparisons it is shown that the new implementation of local RBF meshless scheme (nLRBFM) is of high effectiveness, high accuracy and excellent stability, to solve radiative heat transfer in homogeneous participating media.