Adaptive explicit and implicit finite element methods for transient thermal analysis
Abstract
The application of adaptive finite element methods to the solution of transient heat conduction problems in two dimensions is investigated. The computational domain is represented by an unstructured assembly of linear triangular elements and the mesh adaptation is achieved by local regeneration of the grid, using an error estimation procedure coupled to an automatic triangular mesh generator. Two alternative solution procedures are considered. In the first procedure, the solution is advanced by explicit timestepping, with domain decomposition being used to improve the computational efficiency of the method. In the second procedure, an algorithm for constructing continuous lines which pass only once through each node of the mesh is employed. The lines are used as the basis of a fully implicit method, in which the equation system is solved by line relaxation using a block tridiagonal equation solver. The numerical performance of the two procedures is compared for the analysis of a problem involving a moving heat source applied to a convectively cooled cylindrical leading edge.
 Publication:

International Journal for Numerical Methods in Engineering
 Pub Date:
 September 1992
 DOI:
 10.1002/nme.1620350404
 Bibcode:
 1992IJNME..35..655P
 Keywords:

 Conductive Heat Transfer;
 Finite Element Method;
 Thermal Analysis;
 Transient Heating;
 Boundary Conditions;
 Computational Grids;
 Error Analysis;
 Grid Generation (Mathematics);
 Temperature Distribution;
 Fluid Mechanics and Heat Transfer