热冲击作用下层合皮肤组织热传导过程数值模拟

摘要

在急剧温度变化等强间断温度冲击作用下的生物层合组织非傅里叶热传导分析中,经典时域连续有限元方法(如Newmark等方法)会在波阵面以后的和层合组织界面附近的区域表现出强烈的数值振荡.这类数值振荡会影响问题求解精度,并带来较大不确定性.针对这类现象,本文发展了改进时域间断Galerkin有限元方法,进一步开展了相关问题的数值模拟.其控制方程的基本未知数(温度)及其时间导数在指定时间间隔内假设存在间断且独立插值.在有限元离散列式中引入比例刚度阵人工阻尼,以成功消除波前位置的虚假数值振荡行为.通过算例对比分析,相比Newmark方法和传统间断Galerkin方法,所提出的改进时域间断Galerkin有限元方法较好消除了波前、波后以及组织界面处的数值振荡,有效捕捉了波阵面的间断行为,提高了计算的精度.%At present,the traditional time-stepping numerical method,such as Newmark method,produces numerical oscillations at the wave-after,wave-front stage in solving the non-Fourier bio-heat problems of multilayer tissue under high frequency heat load.The spurious non-physical oscillations obviously decrease the accuracy and stability of the simulated reaults.This paper presents a modified time discontinuous Galerkin finite element method (MDGFEM).The basic unknown variable (temperature)and its time derivative are assumed to be discontinuous and interpolated individually at each time level in time domain respectively,The artificial damping term is induced to eliminate spurious numerical oscillations the wave-front stage,Numerical simulations show the advantages of the present MDGFEM in eliminating the spurious numerical oscillations at the wave-after,wave-front stage and the interface between layers and in catching the discontinuous behavior in wave front surface than that of Newmark and former DGFEM.