Implementation of the Rosseland and the P1 radiation models in the system of Navier-Stokes equations with the boundary element method

Abstract

The objective of this article is to develop a boundary element numerical model to solve coupled problems involving heat energy diffusion, convection and radiation in a participating medium. In this study, the contributions from radiant energy transfer are presented using two approaches for optical thick fluids: the Rosseland diffusion approximation and the P1 approximation. The governing Navier–Stokes equations are written in the velocity–vorticity formulation for the kinematics and kinetics of the fluid motion. The approximate numerical solution algorithm is based on a boundary element numerical model in its macro-element formulation. Validity of the proposed implementation is tested on a one-dimensional test case using a grey participating medium at radiative equilibrium between two isothermal black surfaces.