Implementation of Smoothed-Particle Hydrodynamics for non-linear Pennes' bioheat transfer equation

We developed a novel SPH method for the solution of Pennes' bioheat equation.SPH scheme is presented for the combination of Pennes' model with CV and DPL models.Discretization contains a third-order temporal-spatial derivative and source term.Non-linear behavior is captured through the temperature-dependent conductivity.The boundary conditions are precisely applied to the SPH method. Non-linear Pennes' bioheat equation including the thermal wave model of bioheat transfer as well as the dual-phase-lag model has been discretized using a mesh-free Smoothed-Particle Hydrodynamics (SPH) procedure. The time evolution of the temperature distribution within a living tissue and effect of non-linearity in the PDEs on the solution have been investigated. The thermal conductivities for Fourier and non-Fourier based bioheat models are varied. The results obtained using the SPH method were compared with the previously published data for benchmark problems. It is shown that these SPH results show an excellent agreement in comparison with the previous results obtained using other numerical methods which proves suitability of SPH scheme towards simulations for bioheat equation.

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