The Solution of the Heat Conduction Equation in 3D Anisotropic Environment and Possibilities of its Improvement

Abstract

Nowadays there are high speed improvements in processors frequencies and processors amount on a single map. So these opportunities have to be used in such fields as modeling and simulation, prediction models and simulations. One of these fields is strictly connected with the article's subject (heat conduction). Heat conduction calculation in 3D space is quite a problem for 3D space calculations because the time spent on calculation for usual approaches is quite long. It is possible to separate full iteration of heat conduction calculation into several portions. These portions of calculation could contain separate calculation blocks. It is possible to implement using ADI (Alternating Direction Implicit) principles in dividing full iteration of heat conduction calculation into 3 parts. Each of these parts ignores one of the directions of coordinate axes, but allows to calculate only three diagonal matrix using Thomas algorithm. It means that additional effort on difference scheme construction has the payback of calculation time reducing because of separated calculable blocks. Another boost of calculation speed is dynamic time step implementation by taking into account the prediction matrix of next iteration heat transfer calculations. This approach has no strict impact on time step calculations for each next iteration, but it can be bordered between the possible minimal and maximal time step defined values. Provided solutions allow to manage algorithm calculation time by applying as many computers as many times as needed to reduce the calculation time.