基于时域间断有限元方法的生物组织非傅立叶热行为数值分析

Numerical analysis for non-Fourier thermal behavior of biological tissue by time discontinuous Galerkin finite element method

在热传导分析中,当热流与温度梯度存在时间延迟时,需采用非傅立叶热传导模型进行分析。生物组织具有较强的热松弛时间系数,承受激光、微波及烧烫等作用时,其呈现出较强的非傅立叶行为。本文对脉冲热源作用下生物组织的非傅立叶热传导进行研究,针对强脉冲引起的温度场在空间域的高梯度变化、波阵面的间断行为以及通用传统时域数值方法会带来虚假数值振荡的特点,提出采用所发展的时域间断Galerkin有限元法(DGFEM)进行求解计算。对多种脉冲热源作用下的非傅立叶热传导过程进行数值模拟,通过考量强脉冲作用下温度场分布和热致生物组织损伤行为的影响,表明了本文所发展的DGFEM能够有效、准确地描述温度场空间分布和热传导过程以及非傅立叶行为下的生物热损伤更为明显,在生物组织热行为分析中应该受到重视。

Non-Fourier theory needs to be taken into account for the reason of time delay behavior existing between heat flux vector and temperature gradient. Biological tissue behaves the strong non-Fourier af- fection and possess the large time relax parameter when bearing the laser,microwave,burn,injury etc. The present paper performs the research work, focused on the the high gradient in spatial domain , seiz- ing the discontinuous of wave front and the spurious numerical oscillations of the general traditional method, for non-Fourier thermal behavior of biological tissue by using time discontinuous Galerkin finite element method （DGFEM）. Simulation of non-Fourier heat conduction under different impulse thermal sources is carried out. Observing the simulated results,it is indicated that the DGFEM is effective and ac- curate for the simulation of temperature field and heat conduction, non-Fourier effect is necessary when considering the tissue heat conduction and heat damage problems with impulse thermal sources. Special attention should be paid for thermal behavior of biological tissue.