A High-Accuracy Finite Difference Scheme for Solving Reaction-Convection-Diffusion Problems with a Small Diffusivity  

作　　者：Po-Wen Hsieh Suh-Yuh Yang Cheng-Shu You 

机构地区：[1]Department of Applied Mathematics,Chung Yuan Christian University,Jhongli City,Taoyuan County 32023,Taiwan [2]Department of Mathematics,National Central University,Jhongli City,Taoyuan County 32001,Taiwan

出　　处：《Advances in Applied Mathematics and Mechanics》2014年第5期637-662,共26页应用数学与力学进展（英文）

基　　金：the National Science Council of Taiwan under the grants NSC 101-2811-M-008-032 and NSC 102-2115-M-033-007-MY2;the National Science Council of Taiwan under the grants NSC 99-2115-M-008-012-MY2 and NSC 101-2115-M-008-008-MY2.

摘　　要：This paper is devoted to a new high-accuracy finite difference scheme for solving reaction-convection-diffusion problems with a small diffusivityε.With a novel treatment for the reaction term,we first derive a difference scheme of accuracy O(ε^(2)h+εh^(2)+h^(3))for the 1-D case.Using the alternating direction technique,we then extend the scheme to the 2-D case on a nine-point stencil.We apply the high-accuracy finite difference scheme to solve the 2-D steady incompressible Navier-Stokes equations in the stream function-vorticity formulation.Numerical examples are given to illustrate the effectiveness of the proposed difference scheme.Comparisons made with some high-order compact difference schemes show that the newly proposed scheme can achieve good accuracy with a better stability。

关 键 词：Reaction-convection-diffusion equation incompressible Navier-Stokes equations boundary layer interior layer finite difference scheme 

分 类 号：O17[理学—数学]