An enhanced explicit technique for the solution of non-Fourier heat transfer problems. (August 2018) - Soares, Delfim
Highlights: A novel technique is proposed for hyperbolic heat conduction analyzes. The technique stands as a very simple, single-step, self-starting procedure. It is explicit and very efficient, requiring the solution of no system of equations. It exhibits high stability limits, allowing large time-steps to be considered. It provides enhanced accuracy and algorithmic dissipation of spurious modes. Abstract: In this work, an enhanced explicit technique is proposed to analyze hyperbolic heat conduction models. As usual, the explicit approach allows the solution of the problem to be carried out without dealing with any system of equations, featuring a very efficient methodology. In addition, the proposed technique enables algorithmic dissipation, allowing the influence of spurious high modes to be properly eliminated, without introducing significant period elongation and amplitude decay errors into the analysis. As an explicit approach, the technique is conditionally stable; however, it exhibits high stability limits (its critical time-step is around 1.8 times that of the Central Difference Method), emphasizing its effectiveness. The technique is very accurate, truly self-starting and extremely direct to implement. At the end of the manuscript, numerical results are presented, illustrating the good performance of the discussed technique.