Nonlinear analysis of non-Fourier heat conduction problems by a locally stabilized explicit approach

In this paper, a stabilized, locally defined, explicit approach is considered to analyse nonlinear, non-Fourier heat conduction problems. In this sense, a modified central difference method is applied, which performs adapting itself along the solution process, considering the properties and results of the model, as well as the relations between the adopted temporal and spatial discretizations. The proposed technique is highly accurate, versatile and efficient. In fact, the new approach stands as a non-iterative, single-solve framework based on reduced systems of equations; thus, it demands very low computational efforts. In addition, the procedure is very simple to implement and entirely automatized, requiring no decision or expertise from the user. Numerical results are presented at the end of the manuscript, illustrating the performance and effectiveness of the novel methodology.