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

摘要

Purpose - This paper sets out to implement bounded high-order (HO) resolution schemes in a hybridrnfinite volume/finite element method for the solution of the radiative transfer equation.rnDesign/methodology/approach - The hybrid finite volume/finite element method had formerlyrnbeen developed using the step scheme, which is only first-order accurate, for the spatial discretization.rnHere, several bounded HO resolution schemes, namely the MINMOD, CLAM, MUSCL and SMARTrnschemes, lormulated using the normalized variable diagram, were implemented using the deferredrncorrection procedure.rnFindings - The results obtained reveal an interaction between spatial and angular discretizationrnerrors, and show that the HO resolution schemes yield improved accuracy over the step scheme if thernangular discretization error is small.rnResearch limitations/implications - Although the HO resolution schemes reduce the spatialrndiscretization error, they do not influence the angular discretization error. Therefore, the global error isrnonly reduced if the angular discretization error is also small.rnPractical implications - The use of HO resolution schemes is only effective if the angularrnrefinement yields low-angular discretization errors. Moreover, spatial and angular refinement shouldrnbe carried out simultaneously.rnOriginality/value - The paper extends a methodology formerly developed in computational fluidrndynamics, and aimed at the improvement of the solution accuracy, to the hybrid finite volume/finiternelement method for the solution of the radiative transfer equation.