Development of a Quantitative Decision Metric for Selecting the Most Suitable Discretization Method for SN Transport Problems

In this work we develop a quantitative decision metric for spatial discretization methods of the SN equations. The quantitative decision metric utilizes performance data from selected test problems for computing a fitness score that is used for the selection of the most suitable discretization method for a particular SN transport application. The fitness score is aggregated as a weighted geometric mean of single performance indicators representing various performance aspects relevant to the user. Thus, the fitness function can be adjusted to the particular needs of the code practitioner by adding/removing single performance indicators or changing their importance via the supplied weights. Within this work a special, broad class of methods is considered, referred to as nodal methods. This class is naturally comprised of the DGFEM methods of all function space families. Within this work it is also shown that the Higher Order Diamond Difference (HODD) method is a nodal method. Building on earlier findings that the Arbitrarily High Order Method of the Nodal type (AHOTN) is also a nodal method, a generalized finite-element framework is created to yield as special cases various methods that were developed independently using profoundly different formalisms. A selection of test problems related to a certain performance aspect are considered: an Method of Manufactured Solutions (MMS) test suite for assessing accuracy and execution time, Lathrop's test problem for assessing resilience against occurrence of negative fluxes, and a simple, homogeneous cube test problem to verify if a method possesses the thick diffusive limit. The contending methods are implemented as efficiently as possible under a common SN transport code framework to level the playing field for a fair comparison of their computational load. Numerical results are presented for all three test problems and a qualitative rating of each method's performance is provided for each aspect: accuracy/efficiency, resilience against negative fluxes, and possession of the thick diffusion limit, separately. The choice of the most efficient method depends on the utilized error norm: in Lp error norms higher order methods such as the AHOTN method of order three perform best, while for computing integral quantities the linear nodal (LN) method is most efficient. The most resilient method against occurrence of negative fluxes is the simple corner balance (SCB) method. A validation of the quantitative decision metric is performed based on the NEA box-inbox suite of test problems. The validation exercise comprises two stages: first prediction of the contending methods' performance via the decision metric and second computing the actual scores based on data obtained from the NEA benchmark problem. The comparison of predicted and actual scores via a penalty function (ratio of predicted best performer's score to actual best score) completes the validation exercise. It is found that the decision metric is capable of very accurate predictions (penalty < 10%) in more than 83% of the considered cases and features penalties up to 20% for the remaining cases. An exception to this rule is the third test case NEA-III intentionally set up to incorporate a poor match of the benchmark with the "data" problems. However, even under these worst case conditions the decision metric's suggestions are never detrimental. Suggestions for improving the decision metric's accuracy are to increase the pool of employed data, to refine the mapping of a given configuration to a case in the database, and to better characterize the desired target quantities.