Closed-form solution of the first-order Transport-Driven Diffusion approximation

• A closed-form solution for a hybrid approximation of linear transport is presented.
• The solution explicitly accounts for the uncollided and collided contributions.
• A comparison between TDD1 and analytical diffusion approximation is shown.
• Higher order TDD solutions are presented and model accuracy discussed.

The paper presents a closed-form solution of the first-order Transport-Driven Diffusion (TDD) proposed by Picca and Furfaro (2014). The solution is rigorously derived for two source configurations (i.e. Dirac’s delta and rectangular source) to explicitly describe the contribution of the uncollided component and the collided diffuse term. The results are employed to compare the solution of first-order Transport-Driven Diffusion (TDDT with T = 1) with the analytical diffusion approximation as well as to validate numerical solution of the TDD1. The comparison with higher-order TDD (i.e., (TDDT with T > 1) is also reported.