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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.

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This thesis can be divided into five main parts. The first part deals with theoretical analysis of power flow calculation in power network during steady state condition. Load flow calculation is presented here as a linear and nonlinear problem. Newton iteration method is proposed for solving power flow as nonlinear problem. The second part of this thesis deals with the analysis of short-circuit calculation in accordance with valid International Standard IEC 60909. The equivalent voltage source method is adopted in case of the short-circuit calculation. For the calculation of unbalanced short-circuit currents, the symmetrical components method is also presented. The last three parts of this paper are focused on calculations of power flow and short-circuit conditions in power grid Sokolnice. So in the third part is the description of nodal area Sokolnice with its substations and the calculation of load flow and short-circuit conditions for two different power supply options. For each supply option is also considered an abnormal (fault) grid condition. (overall there are solved four different options) The fourth part of this thesis deals with the result analysis and also the results of different power supply options are compared. In the last part there are presented necessary technical improvements for fault-free operation of power grid Sokolnice based on the result of power flow and short-circuit conditions in that grid.