Bruno Turcksin, Jean C. Ragusa, Wolfgang Bangerth
Goal-oriented h-adaptivity for the multigroup SPN equations
Nuclear Science and Engineering, vol. 165 (2010), pp. 305-319.
This article is also available as IAMCS preprint 2009-068.

We investigate application of goal-oriented mesh adaptivity to the SPN multigroup equations. This technique utilizes knowledge of the computational goal and combines it with mesh adaptivity to accurately and rapidly compute quantities of interest. Specifically, the local error is weighted by the importance of a given cell towards the computational goal, resulting in appropriate goal-oriented error estimates. Even though this approach requires the solution of an adjoint (dual) problem, driven by a specific source term for a given quantity of interest, the work reported here clearly shows the benefits of such a method.
We demonstrate the level of accuracy this method can achieve using 2D and 3D numerical testcases for one-group and two-group models, and compare results with more traditional mesh refinement and uniformly refined meshes. The testcases consider situations in which the radiative flux of a source is shielded and are designed to prototypically explore the range of conditions under which our methods improve on other refinement algorithms. In particular, they model strong contrasts in material properties, a situation ubiquitous in nuclear engineering.

Wolfgang Bangerth
Wed Apr 19 13:44:46 MDT 2017