Multigrid Heat Transfer Calculations Using Different Iterative Schemes

The full-approximation-storage multigrid strategy has been applied to the heat conduction equation by using several iterative schemes to drive the multilevel process. While aimed at discussing the effectiveness of the most-used solvers when coupled with the multigrid method, this paper includes comparisons between single and multiple grid calculations for both explicit and implicit time-dependent schemes, inaddition to stationary ones. An innovative implementation of the alternating direction implicit (ADI) methods is presented, where a noticeable efficiency improvement is obtained through the introduction of an additional smoothing step. The analysis is carried out on a model problem with mixed Neumann and Dirichlet boundary conditions; then an ADI scheme in conjuction with the multilevel technique is used to compute the temperature distribution in a section of a turbine rotor shaft.