Application of high-order implicit schemes for nonlinear multi-physics simulations

Implicit Runge Kutta (IRK) methods were applied to solve the nonlinear point reactor kinetic equations with feedback. These methods preserve their high accuracy order, even for stiff nonlinear problems and are viable candidates for implementation into multi-physics simulation software. Adaptive time stepping strategies associated with these methods can significantly reduce the computational time and do offset the drawback of having to carry out a nonlinear solve per time step to regain lost accuracy in conventional Operator Split (OS) methods. Results for the lumped point kinetics with feedback model clearly show the gain in performance and accuracy using adaptive IRK methods over OS methods. (authors)