Comparison of three spatial differencing schemes in discrete ordinates method using three-dimensional unstructured meshes

A radiative heat transfer code based on the discrete ordinates method applied to unstructured grids has been developed to be coupled with a finite volume CFD code for combustion applications. The constraints are that: (1) Accurate coupling with a finite volume CFD code requires that the output is the integrated radiative source term within each mesh; (2) The resulting computation times must remain acceptable within the combustion requirements (of the order of an hour for realistic industrial geometries); (3) the line spectra of combustion gases must be accurately represented across the whole infrared range. Here, gaseous line spectra properties are represented with the SNB-ck model using narrow bands parallelization. The radiative transfer equation is discretized with a finite volume approach and three schemes are tested (“exponential”, “step” and “diamond mean flux”) in terms of accuracy and computational requirement. They are first tested for academic gray cases, solutions being compared to reference solutions provided by the Ray Tracing Method and the Monte Carlo Method. The behavior of the three schemes is also discussed for a spherical geometry, using an analytical solution in order to perform a parametric study of the absorption optical thickness influence in a wide range typical of spectral line gaseous radiation. Final tests involving a complete water vapor spectrum are performed in order to test the effects of preceding conclusions in terms of expected accuracies for combustion applications.