固体介质瞬态传热问题的等几何分析

Isogeometric analysis for transient heat conduction of solid medium

为拓展等几何分析法在瞬态或者动力学问题领域的应用,以固体介质的瞬态热传导为例,将等几何分析方法扩展到瞬态问题,并提出了先对问题的空间域进行等几何方式离散,再对时间域进行有限差分离散的"半离散化"方法,得到了问题的后向差分格式。给出了一种鲁棒的边界约束处理方法,解决了非均匀有理B样条基函数缺乏插值性所造成的Dirichlet边界处理误差。实验结果表明,等几何分析的收敛速度优于传统有限元方法。

To expand application of isogeometric analysis method in transient or dynamics domain,by taking transient heat conduction of solid medium as example,isogeometric analysis method was extended to transient problems.The propoesd problem＇s space domain was discretized by isogeometric way firstly,and then time domain was discretized with finite difference by semi-discretization method,thus,the backward difference schema of the iteration linear system was obtained.To solve the Dirichlet boundary processing error caused by lack interpolation of Non-Uniform Rational B-Splines（NURBS） basis function,a robust boundary constraint method was proposed by selecting a set of interpolated boundary points.The experiment results demonstrated that isogeometric analysis could achieve better convergence speed than traditional finite element method.