Bifurcating Solutions and Stabilities for Multigroup Neutron Fission Systems with Temperature Feedback

Robust Control of Bifurcating Power Systems by Feedback Linearization

{In many power systems, the operating margin may be investigated and improved by considering the bifurcations in their models. Control of (unstable) bifur-cations, i.e. delay or elimination of them, may be possible through feedback linearizing control. Two major issues in implementing this approach are the relative degree of the system and the eeects of model uncertainties. In this work, contro...

Three-dimensional h-adaptivity for the multigroup neutron diffusion equations

Adaptive mesh refinement (AMR) has been shown to allow solving partial differential equations to significantly higher accuracy at reduced numerical cost. This paper presents a state-of-the-art AMR algorithm applied to the multigroup neutron diffusion equation for reactor applications. In order to follow the physics closely, energy group-dependent meshes are employed. We present a novel algorith...

Parallel Solvers for the Transient Multigroup Neutron Diffusion Equations

Multilevel NDA Methods for Solving Multigroup Eigenvalue Neutron Transport Problems

The nonlinear diffusion acceleration (NDA) method is an efficient and flexible transport iterative scheme for solving reactor-physics problems. This paper presents a fast iterative algorithm for solving multigroup neutron transport eigenvalue problems in one-dimensional slab geometry. The proposed method is defined by a multilevel system of equations that includes multigroup and effective onegr...

Direction and stability of bifurcating solutions for a Signorini problem

The equation ∆u + λu + g(λ, u)u = 0 is considered in a bounded domain in R2 with a Signorini condition on a straight part of the boundary and with mixed boundary conditions on the rest of the boundary. It is assumed that g(λ, 0) = 0 for λ ∈ R, λ is a bifurcation parameter. A given eigenvalue of the linearized equation with the same boundary conditions is considered. A smooth local bifurcation b...