摘要
当△τ=(λ△t)/(C_ρ△l^2)<5时,瞬态传热的有限元解会出现不应有的振荡现象。此处,C_ρ,λ,△t及△l分别为比热、密度、导热系数、计算时间步长及有限元网格尺寸。文中给出产生振荡的原因和采用集中热容矩阵可以消除振荡现象的理由。算例表明,当△t小时,在有限元计算中采用集中热容矩阵可以允许较大的网格尺寸,因而可以节省机时,提高计算效率,其优点是明显的。
Spurious wiggles displayed in FEM solutions of transient heat transfer problems when △τ=λ△t/Cp△l^5<0.5 can be eliminated by using lumped capacitance matrix instead of consistent one in FEM formulation. Here, C, p, λ, △t and △l are the specific heat, density, thermal conductivity, time step and mesh size respectively. The cause of the wiggles and the reason for the elimination of the wiggles by adopting the lumped capacitance approach are given. Test runs show clear advantage of computational efficiency of the approach when small △t is used. It allows larger mesh size and needs less CPU time.
基金
国家自然科学基金
关键词
传热
有限元法
热容矩阵
集中矩阵
FEM(finite element methods), heat transfer, numerical analysis
lumped capacitance matrix.
