Estimation of Ray Effect and False Scattering in Approximate Solution Method for Thermal Radiative Transfer Equation

A Concept of Discretization Error Indicator for Simulating Thermal Radiation by Finite Volume Method Based on an Entropy Generation Approach

“…Its premise is that: intensity at certain grids is related to other grids by space deferential schemes, and these grids are not in the transfer direction. In a multi-dimensional problem, if a derivative is substituted by first-order difference, if the profile of radiative intensity is assumed by spatial differencing schemes and if the direction of transfer is intersected with grid and non-negative intensity gratitude exists in the direction perpendicular with transportation direction, numerical scattering is still generated (Tan et al, 2004).…”

“…For brevity, the detailed explanation of the reason towards its generation can be referred in the previous works (Zhang & Tan, 2009;Tan et al, 2004;Zhang et al 2011). …”

“…Only the error caused by spatial discretization is discussed in this paper, and it is also referred to as numerical scattering or numerical smearing (Zhang & Tan, 2009), which is analogous to false diffusion in the context of computational fluid dynamics caused by discretization of spatial coordinates (Patankar, 1980). It has been shown that many factors can cause false scattering (Tan et al, 2004) influencing solution accuracy, including grid quality (Kallinderis & Kontzialis, 2009), spatial discretization schemes (Coelho, 2008), radiative properties and volumetric heat sources (Kamel et al, 2006). However, there are few effective routines for evaluating the spatial discretization error, and it is necessary to formulate an innovative framework to explore parameters or define indicator to analyze its uncertainty and accuracy.…”

“…In this chapter, an artificial benchmark model of central laser incidence on a twodimensional (2D) rectangle containing a semi-transparent medium is used as a framework to investigate the numerical scattering, using reference data from the Monte Carlo method (MCM), which has been proven to generate no false scattering (Tan et al, 2004). Based on the local entropy generation approach (Herwig & Kock, 2004) derived from the second law of thermodynamics, which is considered a very effective method to analyze the process of energy transfer, a discretization error indicator is defined.…”

Radiative heat transfer in a participating medium with specular–diffuse surfaces

“…Ref. [16] pointed out that the false scattering was generated by the discretization of the derivative term of radiative intensity along the space coordinate, and the ray effect was produced by the discretization of the solid angle. So the false scattering exists in the FVM, FEM and DOM, and the ray effect exists in the FVM, FEM, DOM, and DTM [16].…”