Solution of hyperbolic bioheat conduction models based on adaptive time integrators

Abstract

In this work, a new time marching technique is proposed to analyze hyperbolic bioheat transfer problems. In this new approach, time integration parameters adapt themselves along the solution process, in accordance to the properties and results of the model. Thus, the time integrators are locally evaluated, assuming different values along the spatial and temporal discretizations, enabling a more accurate and effective solution algorithm. The proposed technique has guaranteed stability, it is truly self-starting, and it is formulated as a non-iterative single-step/solver procedure, demanding low computational efforts. As illustrated in the manuscript, the methodology is very accurate, robust and simple to implement, providing a suitable numerical approach to analyze hyperbolic bioheat conduction models.