Métodos de redução de base para problemas térmicos em regime transiente com condições de contorno de radiação e convecção

Abstract

ln the past few years there have been a renewed interest in reduction methods for transient heat transfer analysis. Particularly, for transient heat conduction, it has been shown that reduction methods based on Lanczos-type algorithms or Ritz methods are most effective than the usual direct approach (α-methods) or classical modal methods. For transient heat transfer including nonlinear material laws, it can be shown that reduction methods, embedded within a trapezoidal rule algorithm for time marching with a Newton-Raphson scheme, provide an accurate, reliable and fast solution strategy. However, when the nonlinearities are restricted to the boundaries, as in the case of radiation boundaries, another strategy can be proposed which is the subject of the present dissertation. It is based on the utilization of the pseudo-force algorithm, which is widely used in structural dynamics problems with localized nonlinearities. Its key aspect is that no costly matrix updates are needed, since all the nonlinear terms are grouped in the right hand side of the heat transfer equations. The computer effectivness of this solution strategy is demonstrated by numerical experiments performed in standard tests and through comparisons against the usual numerical solution strategies.