Application of the Transport-Driven Diffusion Approach for Criticality Calculations

The work presents the application of the transport-driven diffusion (TDD) approximation for the determination of the fundamental eigenvalue of multiplying systems. TDD, recently proposed for source-driven problems by Picca and Furfaro (2014), is a solution method which combines multi-collision transport with diffusion to approximate neutral particle transport in scattering and multiplying media. The method is here extended to deal with eigen-problems (i.e., source-free problems), embedding TDD in the power iteration cycle. The solution approach is assessed on a selection of 1D benchmarks from the literature comparing its performances against diffusion and transport reference solutions. A test on a 2D configuration is also provided to demonstrate the feasibility to extend this approach to more realistic problems. Results show the competitive performance of TDD and, once validated in more general problem settings, this method appears to be particularly interesting in applications where fast evaluations of several configurations are required (e.g., core loading problems). On the basis of its convergence property (for T going to infinity, TDD_T tends the transport solution, Picca and Furfaro, 2014), the methodology also offers the opportunity to seek highly accurate solutions by combining a sequence of low-order TDD solutions with powerful non-linear extrapolation techniques, as tested in the paper.