对流扩散方程的非振荡守恒特征差分法  

Non Oscillation Conservative Characteristic Difference Method for Solving Convection Diffusion Equations

作　　者：王钱钱 李琳 赵玉庆 周忠国 

机构地区：[1]山东农业大学信息科学与工程学院应用数学系,山东泰安

出　　处：《应用数学进展》2018年第11期1446-1457,共12页Advances in Applied Mathematics

基　　金：国家自然科学基金资助项目(61703250, 61503227);山东自然科学基金资助项目(ZR2017BA029, ZR2017BF002)。

摘　　要：当求解对流占优扩散问题时,采用传统的二次拉格朗日插值的特征差分法,会出现数值振荡,且不满足质量守恒。结合算子分裂,本质非震荡和MMOCAA质量校正,提出了求解对流扩散方程的非震荡的守恒特征差分法。首先采用局部一维(LOD)法把一个二维偏微分方程分裂成x方向和y方向的两个一维的偏微分方程组;其次在每个方向上利用二阶本质非振荡和MMOCAA格式进行数值计算。数值实验验证格式满足非震荡和质量守恒,能够有效地解决大型对流占优扩散问题。The characteristic difference method based on quadratic Lagrange interpolation is used to solve the convection dominated diffusion problem, but there will be a larger numerical oscillation and not conservative. Combining the operator splitting, non-oscillatory and mass correction methods, the non-oscillation conservative characteristic difference methods are proposed to solve the convection diffusion equations. Firstly, the partial differential equations in two dimensions are splitting into two one-dimensional partial differential equations along the x-direction and the y-direction, respectively. Secondly, the second-order essentially non-oscillation and MMOCAA schemes are presented to compute the equations. By the numerical results, it shows that the scheme not only meets non-oscillatory and mass conservation, but also effectively solves the convection-dominant diffusion problems.

关 键 词：对流扩散方程 算子分裂 特征差分法 本质非振荡插值 MMOCAA格式 

分 类 号：O24[理学—计算数学]