Nonlinearly consistent schemes for coupled problems in reactor analysis

Abstract

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.