# [P17] On the accuracy of the non-classical transport equation in 1- D random periodic media

### Conference paper

Proceedings of Joint International Conference on Mathematics and Computation, Supercomputing in Nuclear Applications and the Monte Carlo Method, Nashville, TN, 2015 Apr

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### Cite

**APA**

Vasques, R., & Krycki, K. (2015). [P17] On the accuracy of the non-classical transport equation in 1- D random periodic media. In Proceedings of Joint International Conference on Mathematics and Computation, Supercomputing in Nuclear Applications and the Monte Carlo Method. Nashville, TN.

**Chicago/Turabian**

Vasques, Richard, and Kai Krycki. “[P17] On the Accuracy of the Non-Classical Transport Equation in 1- D Random Periodic Media.” In Proceedings of Joint International Conference on Mathematics and Computation, Supercomputing in Nuclear Applications and the Monte Carlo Method. Nashville, TN, 2015.

**MLA**

Vasques, Richard, and Kai Krycki. “[P17] On the Accuracy of the Non-Classical Transport Equation in 1- D Random Periodic Media.” Proceedings of Joint International Conference on Mathematics and Computation, Supercomputing in Nuclear Applications and the Monte Carlo Method, 2015.

**ABSTRACT:**We present a first numerical investigation of the accuracy of the recently proposed non-classical transport equation. This equation contains an extra independent variable (the path-length s), and models particle transport taking place in random media in which a particle’s distance-to-collision is not exponentially distributed. To solve the non-classical equation, one needs to know the s-dependent ensemble-averaged total cross section t(s), or its corresponding path-length distribution function p(s). We consider a 1-D spatially periodic system consisting of alternating solid and void layers, randomly placed in the infinite line. In this preliminary work, we assume transport in rod geometry: particles can move only in the directions = 1. We obtain an analytical expression for p(s), and use this result to compute the corresponding t(s). Then, we proceed to solve the non-classical equation for different test problems. To assess the accuracy of these solutions, we produce “benchmark" results obtained by (i) generating a large number of physical realizations of the system, (ii) numerically solving the transport equation in each realization, and (iii) ensemble-averaging the solutions over all physical realizations. We show that the results obtained with the non-classical equation accurately model the ensemble-averaged scalar flux in this 1-D random system, generally outperforming the widely-used atomic mix model for problems with low scattering. We conclude by discussing plans to extend the present work to slab geometry, as well as to more general random mixtures.