对流扩散方程的特征有限体积两重网格算法与误差估计  

The Two-Grid Method of Characteristic Finite Volume for Nonlinear Convection Diffusion Equations and Error Estimate

作　　者：龚春琼[1] 秦新强[1] 张爱君[1] 

机构地区：[1]西安理工大学理学院,陕西西安710048

出　　处：《西安理工大学学报》2010年第2期228-232,共5页Journal of Xi'an University of Technology

基　　金：西安理工大学校青年科学研究计划基金资助项目(108-210711)

摘　　要：对于非线性对流扩散方程,构造了特征有限体积算法格式,再用两重网格算法计算非线性系统,先通过非线性迭代求出粗网格ΔH上的解uH,再利用粗网格上的解uH将问题线性化并求出细网格Δh上的近似解h(H>h)。理论分析及数值例子的计算结果均表明,在收敛阶保持不变的情况下,此算法既可消除非线性对流占优扩散问题数值震荡现象,又可简化计算,提高计算效率。For solving a nonlinear convection diffusion equation,a two-grid method based on the characteristic finite volume solution is proposed in this study.The nonlinearities are expanded about the coarse grid solution uH,and the resulting approximation solution h linear system is solved on a fine grid,Hh.Theoretical analysis and the numerical example result show that,with the same convergence level,this method can eliminate numerical oscillations in the non-linear convection dominated-diffusion problem,simplify the computation and improve the computation efficiency.

关 键 词：对流占优扩散方程 特征有限体积法 两重网格算法 误差估计 

分 类 号：O241.8[理学—计算数学]