Linear tetrahedral finite elements for thermal shock problems

The paper seeks to present an original method for the numerical treatment of thermal shocks in non‐linear heat transfer finite element analysis.

The 3D finite element thermal analysis using linear standard tetrahedral elements may be affected by spurious local extrema in the regions affected by thermal shocks, in such a severe ways to directly discourage the use of these elements. This is especially true in the case of solidification problems, in which melted alloys at very high temperature contact low diffusive mould materials. The present work proposes a slight modification to the discrete heat equation in order to obtain a system matrix in M‐matrix form, which ensures an oscillation‐free solution.

The proposed “diffusion‐split” method consists basically of using a modified conductivity matrix. It allows for solutions based on linear tetrahedral elements. The performance of the method is evaluated by means of a test case with analytical solution, as well as an industrial application, for which a well‐behaved numerical solution is available.

The proposed method should be helpful for computational engineers and software developers in the field of heat transfer analysis. It can be implemented in most existing finite element codes with minimal effort.