Application of high-order spatial resolution schemes to the hybrid finite volume/finite element method for radiative transfer in participating media

Purpose - This paper sets out to implement bounded high-order (HO) resolution schemes in a hybrid finite volume/finite element method for the solution of the radiative transfer equation. Design/methodology/approach - The hybrid finite volume/finite element method had formerly been developed using the step scheme, which is only first-order accurate, for the spatial discretization. Here, several bounded HO resolution schemes, namely the MINMOD, CLAM, MUSCL and SMART schemes, formulated using the normalized variable diagram, were implemented using the deferred correction procedure. Findings - The results obtained reveal an interaction between spatial and angular discretization errors, and show that the HO resolution schemes yield improved accuracy, over the step scheme if the angular discretization error is small. Research limitations/implications - Although the HO resolution schemes reduce the spatial discretization error, they do not influence the angular discretization error. Therefore, the global error is only reduced if the angular discretization error is also small. Practical implications - The use of HO resolution schemes is only effective if the angular refinement yields low-angular discretization errors. Moreover, spatial and angular refinement should be carried out simultaneously. Originality/value - The paper extends a methodology formerly developed in computational fluid dynamics, and aimed at the improvement of the solution accuracy, to the hybrid finite volume/finite element method for the solution of the radiative transfer equation.