Solution of non‐linear thermal transient problems by a reduction method

Published in Int. J. Numer. Meth. Engng. Vol. 23 (6), pp. 1023-1042, 1986
doi: 10.1002/nme.1620230604

Abstract

A new algorithm for solving transient thermal problems in a reduced subspace of the original space of discretization is described. The basis of the subspace is formed by using the system response at the first time step (or an approximation to it) and a set of orthogonal vectors obtained by the algorithm of Lanczos. Derivatives of these vectors are included when treating non‐linear cases. The method allows one to handle the sharp gradients that appear in thermally loaded structures, and the response is accurately predicted by using only a small number of degrees of freedom in the reduced system. The algorithm is specially well suited for treating large‐scale problems. Examples dealing with one‐, two‐ and three‐dimensional cases of linear and non‐linear conduction problems are presented.