Numerical predictions of short-pulsed laser transport in absorbing and scattering media. I—A time-based approach with flux limiters

Abstract

A one-dimensional transient radiative transfer problem in the Cartesian coordinate system involving an absorbing and scattering medium illuminated by a short laser pulse has computationally been solved by use of a finite volume method (FVM). Previous works have shown that first order spatial interpolation schemes cannot represent the physics of the problem adequately as transmitted fluxes emerge before the minimal physical time required to leave the medium. In this paper, the Van Leer and Superbee flux limiters, combined with the second order Lax–Wendroff scheme, are used in an attempt to prevent this. Results presented in this work show that, despite significant improvement, flux limiters fail to completely eliminate the physically unrealistic behaviour. Therefore, a numerical approach into which temporal variables are transformed into frequency-dependent variables is presented in the companion paper to this work.

Keywords:

• Radiative transfer
• Transient regime
• Short laser pulse
• Flux limiters
• Finite volume method

Acknowledgements

The author acknowledges Mathieu Francoeur (Radiative Transfer Laboratory, University of Kentucky) and Rodolphe Vaillon (CETHIL, INSA de Lyon) for their collaboration during these research works. The author is also grateful to Alan Wright (Invited professor, UQAR-Lévis) and to the Natural Sciences and Engineering Research Council of Canada (NSERC).