Efficient variable stiffness methods for cooling of hot-rolled steel sections

An industrial finite element package for the simulation of alternative cool ing strategies for hot-rolled steel sections has been enhanced by the incor poration of a variable stiffness second-order time-integration scheme, base d on a specially-developed family of extended-stability explicit Runge-Kutt a methods, and an L-stable semi-implicit formula. The integration scheme us es local error estimation to vary step-size, and Runge-Kutta method selecti on is achieved by monitoring the numerical stiffness through the solution p eriod, using a computationally inexpensive estimate for the spectral radius of the system Jacobian. Numerical tests on a range of section-cooling prob lems indicate that the variable stiffness RK code developed is considerably more efficient than standard first-order integration methods. For the leve ls of accuracy required for industrial simulations, the efficiency compares favorably with other high efficiency codes, such as the variable order bac kward differentiation formulae (VODE) and the 'nearly stiff' (RKC) explicit solver. (C) 2000 Elsevier Science Ltd. All rights reserved.