Verification and validation of the modular ray tracing MOC using the coupled forward-adjoint approach and application to C5G7 benchmark

Highlights: • Synchronized implementation of the method of characteristic (MOC) for neutron transport in forward and adjoint. • Verification and the validation of the numerical scheme without necessity for experimental benchmarks. • Fast and accurate numerical computation which could be extended to full core calculations. - Abstract: Neutron transport adjoint calculations are useful in many reactor physics applications. Among various applications, the adjoint flux can be used in perturbation theory to prevent large calculations and computational costs when estimating a small reactivity insertion into the system. Furthermore, they can serve as validation tests for numerical schemes, since both direct and adjoint calculations for a given system should lead to the same eigenvalue, although using two different physicomathematical formulations of the transport model. The synchronized implementation of the method of characteristic (MOC) for neutron transport in forward and adjoint approaches is accomplished in this work. The result is validated using the C5G7 benchmark with comparisons of the multiplication factor and pin power values. Differences between forward and adjoint multiplication factors in the results are achieved in the order of 1.0E-6. Meanwhile, the difference between the multiplication factor and the C5G7 benchmark is in order of 1.0E-5, using an S₁₆ level symmetric angular discretization and a track spacing of 0.01 cm.