2009 journal article

Spatial Convergence Study of Discrete Ordinates Methods Via the Singular Characteristic Tracking Algorithm

NUCLEAR SCIENCE AND ENGINEERING, 162(1), 41–55.

By: J. Duo* & Y. Azmy n

co-author countries: United States of America πŸ‡ΊπŸ‡Έ
Source: Web Of Science
Added: August 6, 2018

This paper analyzes the spatial discretization of the discrete ordinates (DO) approximation of the transport equation. A new method, the singular characteristics tracking algorithm, is developed to account for potential nonsmoothness across the singular characteristics in the exact solution of the DO approximation to the transport equation. Numerical results in two-dimensional problems show improved rate of convergence of the exact solution of the DO equations in nonscattering and isotropic scattering media. Unlike the standard weighted diamond difference scheme, the new algorithm achieves local convergence in the case of discontinuous angular flux across the singular characteristics. The method also significantly reduces the error for problems where the angular flux presents discontinuous spatial derivatives across these lines. For purposes of testing the performance of the new method, the method of manufactured solutions is used to generate analytical reference solutions that permit accurate estimation of the local error in case of discontinuous flux.