Characteristics and Improvements of the discrete ordinates interpolation method applied to irregular two- and three-dimensional geometries

Abstract

The discrete ordinates interpolation method (DOIM) developed for the numerical solution of the radiative transfer equation is applied to unstructured grid systems in arbitrary two- and three-dimensional geometries. Basic solution method is explained and the interpolation method applicable to an unstructured grid system is discussed. Several geometries with absorbing-emitting and nonscattering media with given temperature or in radiative equilibrium are considered to demonstrate the applicability and accuracy. The typical optical depths in the problem are changed from highly transparent (κL = 0.1) to highly opaque cases (κL = 10.0). The wall heat flux is calculated and compared with the exact solution or a reference. In two-dimensional cases, the computations are performed for seven shapes such as a triangle, a quadrilateral enclosure, a hexagonal geometry, and a j-shaped enclosure, etc. In addition, the wall heat fluxes are calculated in unstructured grids as well as in structured grids. Especially in a square enclosure, the results of two different grid systems are compared with each other. In all of the tested cases, the solutions of the DOIM agree fairly well with the exact ones or the references. The results successfully reveal the applicability of the DOIM for any geometry and optical depth. Any grid system employed in FDM, FEM or FVM may be thus adopted and any desired level of numerical accuracy can be obtained with finer or imbedded grids. Another series of sample computations for concentric circular and elliptical cylinders containing absorbing/emitting and nonscattering medium with no heat source is performed. The nondimensional emissive power and heat flux by the DOIM are calculated, and are compared with the reference Monte Carlo solutions. In case of concentric circular cylinder, the results of the DOIM generally agree well with those of Monte Carlo simulation. In the elliptical problem, when the wall is not black, the heat fluxes obtained using st...