Verification of numerical solutions of thermal radiation problems in participating and nonparticipating media

Abstract

This article presents an application of the post-processing technique called Repeated Richardson Extrapolation in participating and nonparticipating media problems of radiative heat transfer. It allows us to achieve very accurate results, reducing the estimates of the discretization error of global variables with negligible additional computational time. The error estimates show to be accurate and reliable for code and solution verification. This work also presents equations that quantify the spatial discretization error inside the domain when the Discrete Ordinates Method is used to simulate participating media problems and when basic numerical integration rules are used to solve nonparticipating media problems.

Keywords:

• Code verification
• discrete ordinates method
• discretization error equation
• Fredholm integral equation
• radiative transfer equation
• Repeated Richardson Extrapolation
• Simpson’s 1/3 rule
• solution verification
• trapezoidal rule
• truncation error

Acknowledgments

The authors would like to thank the reviewers for their observations and contributions to this article. The first author was supported by a CAPES scholarship under the Finance Code 001.

Additional information

Funding

C. H. Marchi was supported by a CNPq scholarship. L. M. Moura was supported by the CNPq scholarship under Grant number 313994/2021-8.