A locally stabilized explicit approach for nonlinear heat conduction analysis

Abstract

This work proposes a locally stabilized, forward Euler method for time domain analyses, which performs considering the relation between the adopted temporal and spatial discretizations. Here, the standard expression of the forward Euler method is considered to approximate the time derivative of the unknown variable, and the local (or element) matrices of the spatially discretized model are modified, if the stability criterion of the forward Euler method is not locally fulfilled. Thus, a locally defined, adaptive time marching methodology is provided, which has guaranteed stability, very good accuracy, and is highly versatile and effective. In the new technique, only reduced systems of equations have to be dealt with (in order to ensure stability), and iterative procedures are never required when nonlinear models are considered. Thus, the proposed methodology is very efficient. In addition, the new technique 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 paper, illustrating the performance and effectiveness of the new approach.