对流扩散方程区域分裂特征差分方法

1引言对流扩散方程是许多物理问题的数学模型,研究其稳定的数值解法具有重要的应用价值．而标准的差分法和有限元法通常会失效,出现数值振荡．80年代,Douglas和Russel提出了特征线方法,在一定程度上克服了数值振荡,保证了数值的稳定,尤其对“对流占优”问题,更能突出特征法的优越性,并有了大量的理论成果1,2,3]．区域分裂是一种解决大规模的科学与工程计算问题的有效方法,Dawson,Du和Dupont对热传导方程给出了非重叠区域分裂格式及分析,由于内边界的显格式,需要一定的稳定性条件Δt≤CH2;而Du等在5]给出了抛物方程的几种区域分裂格式,对区域分裂法的

DOMAIN DECOMPOSITION CHARACTERISTICS DIFFERENCE SCHEMES FOR CONVECTION DIFFUSION PARABOLIC PROBLEMS

The presented methods mean that domain decomposition characteristics difference schemes with two different interpolation ways for convection diffusion parabolic problems based on nonoverlapping subdomains. The proposed schemes rely on implicit procedures in subdomains and explicit calculation on the inter-domain boundaries. With certain stability conditions, convergence anlysis is discussed by the maximum principle. Finally, numerical examples illustrating the value, accuracy and parallelism are shown.