The application of Method of Manufactured Solutions to method of characteristics in planar geometry

The Method of Manufactured Solutions (MMS) is an effective code verification method for assessing the correctness of numerical algorithms and software implementation. It has great flexibility in verifying computational functionalities of a computer code and has seen wide applications in many engineering fields. It has been used for the radiation transport equation but has had limited success in determining whether the observed rate of convergence is consistent with the expected value due to the coupled errors in space and angle. There have also been only limited applications of MMS to eigenvalue problems and very little published research has been performed on applying MMS to multiphysics problems. In this work, MMS is applied to both flat-source and linear-source method of characteristics (MoC) in planar geometry for source problems and eigenvalue problems. A method is developed which allows the angular error to be decoupled from the spatial error, enabling the assessment of the convergence rate with spatial resolution. The angular error removal technique is also applicable to eigenvalue problems. Additionally, two independent approaches to applying MMS to eigenvalue problems are developed, one using an inhomogeneous manufactured source and the other using manufactured cross sections. When the neutronics solver is coupled to a thermal conduction code, MMS is used to investigate the overall order of accuracy of the coupled multiphysics system. Comprehensive tests are devised with a variety of solution structures to verify the theoretical convergence rates. Numerical results show that both the eigenvalue k and the cell-averaged scalar fluxes exhibit orders of accuracy consistent with theoretical predictions, namely, second order for flat-source MoC and fourth order for linear-source MoC. However, for a multiphysics problem coupling neutronics with thermal hydraulics, the overall order of accuracy is limited by the solution field with the slowest rate of convergence.