Particle Transport in a 3D duct by adding and doubling

TL;DR

This paper demonstrates that the method of doubling effectively computes particle reflectance and transmittance in a 3D duct with Lambertian walls, matching or surpassing traditional numerical methods in accuracy with less effort.

Contribution

It shows that the method of doubling is a highly accurate and efficient alternative for particle transport problems in ducts, filling a gap in existing numerical approaches.

Findings

Method of doubling achieves comparable or better accuracy than NDO and ADO methods.

Doubling method requires less mathematical and numerical effort.

Validated for particle transport in a 3D duct with Lambertian reflection.

Abstract

Particle transport through a duct by Lambertian reflection from duct walls is again considered. This popular transport example has been solved by most numerical transport methods except notably one- the method of doubling. We shall show that the method of doubling provides every bit as, or more, accurate reflectances and transmittances as the numerical discrete ordinates (NDO) and analytical discrete ordinates (ADO) methods with less mathematical and numerical effort.