The modeling of nuclear reactors involves the solution of a multi-physics problem with widely varying time and length scales. This translates mathematically to solving a system of coupled, non-linear, and stiff partial differential equations (PDEs). Multi-physics applications possess the added complexity that most of the solution fields participate in various physics components, potentially yielding spatial and/or temporal coupling errors. This dissertation deals with the verification aspects associated with such a multi-physics code, i.e., the substantiation that the mathematical description of the multi-physics equations are solved correctly (both in time and space). Conventional paradigms used in reactor analysis problems employed to couple various physics components are often non-iterative and can be inconsistent in their treatment of the non-linear terms. This leads to the usage of smaller time steps to maintain stability and accuracy requirements, thereby increasing the overall computational time for simulation. The inconsistencies of these weakly coupled solution methods can be overcome using tighter coupling strategies and yield a better approximation to the coupled non-linear operator, by resolving the dominant spatial and temporal scales involved in the multi-physics simulation. A multi-physics framework, KARMA (K(c)ode for Analysis of Reactor and other Multi-physics Applications), is presented. KARMA uses tight coupling strategies for various physical models based on a Matrix-free Nonlinear-Krylov (MFNK) framework in order to attain high-order spatio-temporal accuracy for all solution fields in amenable wall clock times, for various test problems. The framework also utilizes traditional loosely coupled methods as lower-order solvers, which serve as efficient preconditioners for the tightly coupled solution. Since the software platform employs both lower and higher-order coupling strategies, it can easily be used to test and evaluate different coupling strategies and numerical methods and to compare their efficiency for problems of interest. Multi-physics code verification efforts pertaining to reactor applications are described and associated numerical results obtained using the developed multi-physics framework are provided. The versatility of numerical methods used here for coupled problems and feasibility of general non-linear solvers with appropriate physics-based preconditioners in the KARMA framework offer significantly efficient techniques to solve multi-physics problems in reactor analysis.

Conventional coupling paradigms used nowadays to couple various physics components in reactor analysis problems can be inconsistent in their treatment of the nonlinear terms. This leads to usage of smaller time steps to maintain stability and accuracy requirements thereby increasing the computational time. These inconsistencies can be overcome using better approximations to the nonlinear operator in a time stepping strategy to regain the lost accuracy. This research aims at finding remedies that provide consistent coupling and time stepping strategies with good stability properties and higher orders of accuracy. Consistent coupling strategies, namely predictive and accelerated methods, were introduced for several reactor transient accident problems and the performance was analyzed for a 0-D and 1-D model. The results indicate that consistent approximations can be made to enhance the overall accuracy in conventional codes with such simple nonintrusive techniques. A detailed analysis of a monoblock coupling strategy using time adaptation was also implemented for several higher order Implicit Runge-Kutta (IRK) schemes. The conclusion from the results indicate that adaptive time stepping provided better accuracy and reliability in the solution fields than constant stepping methods even during discontinuities in the transients. Also, the computational and the total memory requirements for such schemes make them attractive alternatives to be used for conventional coupling codes.

Kyoto University (京都大学) / 0048 / 新制・課程博士 / 博士(工学) / 甲第17234号 / 工博第3661号 / 新制||工||1556(附属図書館) / 29980 / 京都大学大学院工学研究科原子核工学専攻 / (主査)教授 中島 健, 教授 福山 淳, 准教授 山本 俊弘 / 学位規則第4条第1項該当