Improved Alternating-Direction Implicit Method for Solving Transient Three-Dimensional Heat Diffusion Problems

The conventional three-dimensional alternating-direction implicit (ADI) method is modified by introducing an f factor (0 < f < 1). This modification allows the time step limit to be increased by a factor of 1/f with the solutions remaining stable and high accuracy being retained. This new method is tested for two different boundary conditions: a constant heat flux and a sudden heating of the surface to a constant temperature. In addition, it is compared with the popular Brian and Douglas methods, the results showing that the new ADI method has higher accuracy and requires less computer storage than those methods.