## 4 Verification and Validation  
The verification and validation (V&V) of the BeSYC software followed a pragmatic approach to ensure the proper execution of all the scripts in each scenario. The V&V is eased by the independent nature of the BeSYC software. Indeed, given the fact that the software runs independently from the system codes, the original validation done by the RELAP5-3D and MELCOR 1.8.6 developer holds also in conjunction with the BeSYC software. The V&V activity was divided into two parts: the V&V of the ancillary scripts, i.e., those not involved in the application of the numerical framework, and the V&V of the script applying the numerical framework. For the scripts in charge of writing textual file, the sole verification was sufficient to assess their correctness (scripts to write input decks, bash/bat files, and output reports). In this frame, it was noticed how the parameters having a default value of 0 cannot be used in the best-estimate methodology because the variation in terms of percentage would results in two sensitivity input decks identical to the default one. This limitation is not really correlated with BeSYC, but it derives from the brute force method adopted to calculate the sensitivities [10]. Instead, more demanding efforts were required to verify and validate the scripts to run the calculations and apply the mathematical framework. The script to run the calculations must ensure a good compromise between dead times (time between the end of a calculation and the start of a new one) and the correct handling of the code runs. The testing of this  
Figure 2: Flowchart of the BeSYC software: (a) main panel; (b) responses panel; (c) parameters panel. script was mostly done while testing the script to apply the mathematical framework. Three different checks were performed on this last script:  
* A V&V against the examples provided in [18] to demonstrate the correctness in the implementation of the mathematical framework;
* A check for the Pearson, Spearman's, and [PERSON]'s tau correlation coefficients against the results of the MATLAB built-in _corr_ function [19]. This function is available in the Statistics Toolbox, but it is not used in BeSYC to avoid any dependency with optional MATLAB toolboxes. * A V&V against hand-made test cases to test the correct handling of the different input data that can be used as input for BeSYC (non-null C\({}_{\alpha\alpha}\) matrix, a C\({}_{\alpha\alpha}\) matrix instead of the parameter's standard deviation, and a _sensitivity matrix_ instead of the use of the brute-force method). The results of these _test cases_ have been cross-checked through hand calculations. The geometry of the test cases (Figure 3) consists in three pipes (P1, P2, and P3) connected through a branch (B). Two pipes (P1 and P3) are equipped with a heat structure characterized by a heat flux boundary condition on the external side. The mass flow rate through the system is established imposing different pressures in the _In_ (8.01 MPa) and the _Out_ (7.95 MPa) volumes. The three pipes have a length of 0.1 m, while the branch is 1-m long. The flow area of both the pipes and the branch is 1 m\({}^{2}\). The test matrix consisted of 11 tests: (Table 1): five tests to investigate the behavior with different types of parameters and responses and six to investigate the _non-default_ BeSYC options. The typical responses adopted in these tests are the mass flow rates through the junctions that connect P2 and P3 pipes with the _Out_ volume (J2 and J3, respectively). Instead, the parameters of the system are:  
* The concentrated pressure drop coefficients (K2 and K3) between the branch and the two P2 and P3 pipes (parameters requiring the variation of a single input datum in the input deck);
* The surface roughness (\(\varepsilon\)) of the three pipes and the branch (parameter requiring the variation of more than one input datum in the input decks);
* The heat flow (\(\dot{Q}_{3}\)) from the heat structure connected to P3 (parameter changing in time). Figure 3: Geometry of the test cases.