A diffusion-split method to deal with thermal shocks using standard linear tetrahedral finite elements

Abstract : The thermal analysis using linear standard tetrahedral finite elements may be affected by spurious local extrema in the regions affected by thermal shocks, in such a severe way to directly discourage the use of these elements. The present work proposes a slight modification to the discrete heat equation in order to obtain a system matrix in M-matrix form, which assures an oscillation-free solution. The performance of this method is evaluated by means of test case with analytical solution, as well as an industrial application, for which a well-behaved numerical solution is available.