A parallel solution adaptive method for radiative heat transfer using a Newton-Krylov approach

The discrete ordinates method (DOM) and finitevolume method (FVM) are used extensively to solve the radiative transfer equation (RTE) in furnaces and combusting mixtures due to their balance between numerical efficiency and accuracy. These methods are typically solved using space-marching techniques since they converge rapidly for constant coefficient spatial discretization schemes and non-scattering media. However, space-marching methods lose their effectiveness when applied to scattering media or are used in combination with high-resolution limited totalvariation-diminishing (TVD) schemes. They are also not well-suited to complex geometries and are not readily implemented within parallel CFD algorithms. A pseudo-time marching algorithm is therefore proposed herein to solve the DOM or FVM equations on multi-block body-fitted meshes using a highly scalable parallel-implicit solution approach in conjunction with high-resolution TVD spatial discretization. Adaptive mesh refinement (AMR) is also employed to properly capture disparate solution scales with a reduced number of grid points. The scheme is assessed in terms of discontinuity-capturing capabilities, spatial and angular solution accuracy, scalability, and serial performance through comparisons to other commonly employed solution techniques. The proposed algorithm is shown to possess excellent parallel scaling characteristics and can be readily applied to problems involving complex geometries.