The Improved Direct Collocation Meshless Approach for Radiative Heat Transfer in Participating Media

The moving least-squares (MLS) direct collocation meshless method (DCM) is an effective numerical scheme for solving the radiative heat transfer in participating media. In this method the trial function is constructed by a MLS approximation and the radiative transfer equation (RTE) is discretized directly at nodes by collocation. The main drawback of this method is that, like most of the other numerical methods, the solution to the RTE by the DCM also suffers much from nonphysical oscillations in some cases caused by the convection-dominated property of the RTE. To overcome the numerical oscillations, special stabilization techniques are usually adopted, which increases the complexity and computation time of problem. In the present work a new scheme based on the outflow-boundary intensity interpolation correction is proposed that can easily ensure a large reduction in numerical oscillations of results without any complex stabilization technique. Adaptive support domain technique is also adopted, and the size of the support domain of each evaluated point changes with the density of nodes with irregular distribution. Five cases are studied to illustrate the numerical performance of these improvements. The numerical results compare well with the benchmark approximate solutions, and it is shown that the improved moving least-square direct collocation meshless method (iDCM) is easily implemented, efficient, of high accuracy, and excellent stability, to solve radiative heat transfer in homogeneous participating media.