Third-order modified coeffcient scheme based on essentially non-oscillatory scheme  

作　　者：李明军 杨玉月 舒适 

机构地区：[1]School of Mathematics and Computational Science,Xiangtan University,Xiangtan 411105,Hunan Province,P. R. China

出　　处：《Applied Mathematics and Mechanics(English Edition)》2008年第11期1477-1486,共10页应用数学和力学（英文版）

基　　金：the National Natural Science Foundation of China(Nos.10676031,50675185);the Ph.D. Programs Foundation of Ministry of Education of China(No.20070530003);the Key Project of Chinese Ministry of Education(No.208093);the Scientific Research Fund of Hunan Provincial Education Department(No.07A068)

摘　　要：A third-order numerical scheme is presented to give approximate solutions to multi-dimensional hyperbolic conservation laws only using modified coefficients of an essentially non-oscillatory （MCENO） scheme without increasing the base points during construction of the scheme. The construction process shows that the modified coefficient approach preserves favourable properties inherent in the original essentially nonoscillatory （ENO） scheme for its essential non-oscillation, total variation bounded （TVB）, etc. The new scheme improves accuracy by one order compared to the original one. The proposed MCENO scheme is applied to simulate two-dimensional Rayleigh-Taylor （RT） instability with densities 1：3 and 1：100, and solve the Lax shock-wave tube numerically. The ratio of CPU time used to implement MCENO, the .third-order ENO and fifth-order weighed ENO （WENO） schemes is 0.62：1：2.19. This indicates that MCENO improves accuracy in smooth regions and has higher accuracy and better efficiency compared to the original ENO scheme.A third-order numerical scheme is presented to give approximate solutions to multi-dimensional hyperbolic conservation laws only using modified coefficients of an essentially non-oscillatory （MCENO） scheme without increasing the base points during construction of the scheme. The construction process shows that the modified coefficient approach preserves favourable properties inherent in the original essentially nonoscillatory （ENO） scheme for its essential non-oscillation, total variation bounded （TVB）, etc. The new scheme improves accuracy by one order compared to the original one. The proposed MCENO scheme is applied to simulate two-dimensional Rayleigh-Taylor （RT） instability with densities 1：3 and 1：100, and solve the Lax shock-wave tube numerically. The ratio of CPU time used to implement MCENO, the .third-order ENO and fifth-order weighed ENO （WENO） schemes is 0.62：1：2.19. This indicates that MCENO improves accuracy in smooth regions and has higher accuracy and better efficiency compared to the original ENO scheme.

关 键 词：essentially non-oscillatory scheme modified coefficient scheme the Lax shock-wave tube Rayleigh-Taylor instability 

分 类 号：O351[理学—流体力学] O175[理学—力学]