重庆理工大学学报：自然科学
重慶理工大學學報：自然科學
중경리공대학학보：자연과학
Journal of Chongqing Institute of Technology
2012年
7期
100-104
,共5页
高精度%对流扩散反应方程%有限差分方法%非定常
高精度%對流擴散反應方程%有限差分方法%非定常
고정도%대류확산반응방정%유한차분방법%비정상
high-accuracy%convection-diffusion-reaction equation%finite difference method%unsteady
通过指数变换将原方程变换为对流扩散方程，对变换后方程中的对流项和扩散项分别采用高阶迎风紧致格式和对称紧致格式进行离散，在时间上采用四阶龙格库塔方法进行推进，从而得到了一种具有O（h^4＋τ^4）阶收敛精度求解非定常对流扩散反应问题的紧致格式。通过数值算例并与已有格式的结果进行对比，验证了格式具有良好性能。
通過指數變換將原方程變換為對流擴散方程，對變換後方程中的對流項和擴散項分彆採用高階迎風緊緻格式和對稱緊緻格式進行離散，在時間上採用四階龍格庫塔方法進行推進，從而得到瞭一種具有O（h^4＋τ^4）階收斂精度求解非定常對流擴散反應問題的緊緻格式。通過數值算例併與已有格式的結果進行對比，驗證瞭格式具有良好性能。
통과지수변환장원방정변환위대류확산방정，대변환후방정중적대류항화확산항분별채용고계영풍긴치격식화대칭긴치격식진행리산，재시간상채용사계룡격고탑방법진행추진，종이득도료일충구유O（h^4＋τ^4）계수렴정도구해비정상대류확산반응문제적긴치격식。통과수치산례병여이유격식적결과진행대비，험증료격식구유량호성능。
A fourth-order compact upwind finite difference scheme was proposed for solving 1 D unsteady convection-diffusion-reaction equation. By using an exponential function, the convection-diffu-sion-reaction equation was rewritten in the form of the convection-diffusion equation. Convection terms and diffusion terms were discretized by fourth-order compact upwind schemes and fourth-order compact symmetric schemes, respectively. Then, the spatial semi-discretized equation was solved by fourth-order Runge-Kutta formula in time. The truncation error of the present scheme is O（h^4＋τ^4）.Its excellent properties are proved by numerical examples in comparison with literature results.
