@article{schunert_azmy_2015, title={Comparison of spatial discretization methods for solving the S-N equations using a three-dimensional method of manufactured solutions benchmark suite with escalating order of nonsmoothness}, volume={180}, DOI={10.13182/nse14-77}, abstractNote={Abstract A comparison of the accuracy and computational efficiency of spatial discretization methods of the three-dimensional SN equations is conducted, including discontinuous Galerkin finite element methods, the arbitrarily high-order transport method of nodal type (AHOTN), the linear-linear method, the linear-nodal (LN) method, and the higher-order diamond difference method. For this purpose, we have developed a suite of method of manufactured solutions benchmarks that provides an exact solution of the SN equations even in the presence of scattering. Most importantly, our benchmark suite permits the user to set an arbitrary level of smoothness of the exact solution across the singular characteristics. Our study focuses on the computational efficiency of the considered spatial discretization methods. Numerical results indicate that the best-performing method depends on the norm used to measure the discretization error. We employ discrete Lp norms and integral error norms in this work. For configurations with continuous exact angular flux, high-order AHOTNs perform best under Lp error norms, while the LN method performs best when measured by integral error norms. When the angular flux is discontinuous, a new singular-characteristic tracking method for three-dimensional geometries performs best among the considered methods.}, number={1}, journal={Nuclear Science and Engineering}, author={Schunert, S. and Azmy, Y.}, year={2015}, pages={1–29} }
 @article{schunert_azmy_2013, title={Using the Cartesian Discrete Ordinates Code DORT for Assembly-Level Calculations}, volume={173}, ISSN={["1943-748X"]}, DOI={10.13182/nse11-17}, abstractNote={Abstract For the sake of a high-fidelity representation of the curved surfaces characteristic of fuel pins, the standard reactor design process employs the method of collision probabilities (CP), the method of characteristics (MOC), or unstructured-grid discrete ordinates (SN) transport solvers for assembly-level calculations. In this work we provide a proof of principle using highly simplified assembly configurations that an approximate staircased representation of the fuel pin’s circumference via an orthogonal mesh is accurate enough for reactor physics computations. For the purpose of comparing the performance of these approaches, we employ the orthogonal-grid SN code DORT and the lattice code DRAGON (CP and MOC) to perform k-eigenvalue-type computations for both a boiling water reactor (BWR) and pressurized water reactor (PWR) test assembly. In the framework of a computational model refinement study, the multiplication factor and the fission source distribution are computed and compared to a high-fidelity multigroup MCNP reference solution. The accuracy of the considered methods at each considered model refinement level (fidelity of curved surface representation in DORT, number of tracks in MOC, etc.) is quantified via the difference of the multiplication factor from its reference value and via the root-mean-square and maximum norm of the error in the fission source distribution. We find that for the BWR assembly DORT outperforms MOC and CP in both accuracy and computational efficiency, while for the PWR test case, MOC computes the most accurate fission source distribution but fails to compute the multiplication factor accurately.}, number={3}, journal={NUCLEAR SCIENCE AND ENGINEERING}, author={Schunert, Sebastian and Azmy, Yousry}, year={2013}, month={Mar}, pages={233–258} }