Solution of hyperbolic bioheat transfer problems by numerical green's functions: the ExGA-linear θ method

Abstract

This paper presents a time-domain formulation called Explicit Green's approach (ExGA) linear θ method for the solution of the bioheat equation. Starting from the hyperbolic bioheat equation, which includes the parabolic one as a special case, the linear method is incorporated into the standard ExGA time marching scheme. The numerical Green's function is firstly computed in the Laplace transform domain and then back-transformed to the time domain through the Stehfest inversion algorithm. The proposed formulation has the properties of stabilizing the results and suppressing numerical oscillations that appear in the presence of discontinuous solutions as assessed through the analysis of some bioheat transfer problems.