Solution strategies for coupled conduction/radiation problems

Abstract

SUMMARYSolution strategies and algorithms for solving coupled systems of equations that arise from the finite element formulation of heat conduction and enclosure radiation problems are presented and evaluated. Solution methods that vary from sequential equation processing to fully coupled procedures are tested for convergence, robustness and computational efficiency, in both transient and time-independent modeling situations.

Reduced order models for thermal analysis : final report : LDRD Project No. 137807.

“…Previous work on fully coupled methods [8] has shown the effectiveness of the approach in terms of computational efficiency and rate of convergence. The previous implementation was limited to small problems as the algorithm was constructed using methods appropriate for single processor applications.…”

“…Following the description in [8], the fully coupled solution method first combines the finite element form of the conduction equation (2.10) with the discrete form of the enclosure radiation equation (2.12) to form the matrix system é ùì ü ì ü ï ï ï ï ï ï ï ï ê ú í ý í ý ê ú ï ï ï ï ê úï ï ï ï ë ûî þ î þ…”

“…Manipulations to transform (uniform) surface temperatures in the enclosure to nodal point temperatures are not detailed here but may be found in [8]. Note that the conduction portions of the problem lead to sparse, symmetric matrices; the matrix associated with enclosure radiation is fully populated and unsymmetric.…”

“…These problems were used in [8] to test various solution strategies and were all run on a single processor with a research version of the finite element thermal analysis software. These tests were rerun with the new version of the parallel code and found to produce the same results.…”

Editorial

“…These papers include research on aposteriori error estimation for boundary fluxes [1], general elements for fluid dynamics [2], mesh propagation patterns in certain local refinement schemes [3], fuzzy controllers in adaptivity [4], meshing deforming domains [5], multiscale algorithms [6], Sobolev gradient concepts for imaging [7], adaptivity for multiphysics problems [8] and coupled conduction-radiation problems [9].…”