A LOW-DIMENSIONAL APPROACH FOR LINEAR AND NONLINEAR HEAT CONDUCTION IN PERIODIC DOMAINS

Abstract

A low-order spectral method is used to solve steady-state linear and nonlinear heat conduction problems with periodic boundary conditions and periodic geometry. The study consists of first mapping the complex geometry into a rectangular domain. The Galerkin projection method is applied to solve the mapped equations. It is found that a low number of modes usually are sufficient to capture an accurate solution. Good agreement is obtained between the low-order description and existing formulations. Both the finite element method (FEM) and boundary element methods (BEM) are used for comparison.