Study On The Multilevel Acceleration Theory For High-fidelity Time-dependent Neutron Transport Calculation

Numerical nuclear reactor study enhances the understanding of the basic physical phenomena and laws in nuclear reactors.As the "heart" of the numerical nuclear reactor,neutronics calculation is the basis of all calculations in nuclear reactors.With the rapid development of high-performance computing clusters and advanced numerical methods,the high-fidelity "one-step" method for directly solving the neutron transport equation has gradually become a research hotspot.However,the high-fidelity time-dependent neutron transport calculation faces the challenges of huge computational volume and especially the runtime burden.and if the actual engineering design requirements are taken into account.If the actual engineering design requirements are considered,it leads to multi-level and repeated iterations,which makes the run time grow geometrically.Therefore,it is urgent to study efficient acceleration methods for high-fidelity time-dependent neutron transport calculations.At present,the acceleration methods for neutron transport calculations mainly focus on iterative acceleration methods,while less research has been done on time-step acceleration methods,and the acceleration schemes are independent of each other,where the integration advantages are not obvious,resulting in limited acceleration effects.Therefore,it is both urgent and challenging to carry out systematic acceleration theory research.Starting from the numerical discretization and solution method of the neutron transport equation,this paper introduces the concepts of time,space,energy,and angular resolution.By establishing a low-resolution system equivalent to high-fidelity time-dependent neutron transport calculations,the resolution equivalent fast solver system accelerates the high-fidelity time-dependent neutron transport calculation step by step.For iterative acceleration,an equivalent low-order fast solver system is built to reduce the iterations of high-order neutron transport calculations,forming a multi-level iterative acceleration.For time-step acceleration,a multi-level predictor-corrector system is built to realize transient calculation acceleration.Based on the above,a multi-level acceleration framework for transient transport calculations is constructed,and the problem of strict equivalence between different resolution systems is studied in depth,and then the multi-level acceleration theory for transient transport calculations is proposed systematically from the mathematical mechanism.In the specific study of multi-level acceleration theory for transient transport calculation,the solution process is studied,and the key problems of iterative process and time discretization process are analyzed.The two-level transient g CMFD iterative acceleration method is proposed for the iterative process,and the multi-level predictor-corrector quasi-static method is proposed for the time-discrete process,and the iterative acceleration method and the time-step acceleration method are innovatively integrated into the unified multi-level acceleration theory.A transient transport calculation acceleration model composed of 4 time grids,3 space grids and 2 energy grids is established as the specific implementation schemes for the application of multi-level acceleration theory.Based on the multi-level acceleration theory,the transient transport calculation module of the high-fidelity neutron transport calculation program HNET was developed independently,and the accuracy and efficiency of the HNET program in pin-resolved transient transport calculations were verified and analyzed using the recognized C5G7-TD transient benchmark problem.The numerical results show that the accuracy of the HNET program reaches the same level as that of the international same-type programs,and the efficiency is significantly better than that of similar programs,the total running time can be reduced by 85% for the best case.The numerical results indicate that the successful application of the multi-level acceleration theory has realized high-precision and high-efficiency transient transport calculations,making the high-fidelity transient transport another important step toward engineering practicality.