Third-Order Modified Coefficient Scheme Based on the Essentially Non-Oscillatory Scheme

LI Ming-jun; YANG Yu-yue; SHU Shi

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LI Ming-jun, YANG Yu-yue, SHU Shi. Third-Order Modified Coefficient Scheme Based on the Essentially Non-Oscillatory Scheme[J]. Applied Mathematics and Mechanics, 2008, 29(11): 1337-1346.

Citation:

LI Ming-jun, YANG Yu-yue, SHU Shi. Third-Order Modified Coefficient Scheme Based on the Essentially Non-Oscillatory Scheme[J]. Applied Mathematics and Mechanics, 2008, 29(11): 1337-1346.

Citation:

LI Ming-jun, YANG Yu-yue, SHU Shi. Third-Order Modified Coefficient Scheme Based on the Essentially Non-Oscillatory Scheme[J]. Applied Mathematics and Mechanics, 2008, 29(11): 1337-1346.

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Third-Order Modified Coefficient Scheme Based on the Essentially Non-Oscillatory Scheme

School of Mathematics and Computational Science, Xiangtan University, Xiangtan, Hunan 411105, P. R. China

Received Date: 2007-10-30
Rev Recd Date: 2008-08-24
Publish Date: 2008-11-15

Abstract

Abstract

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

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References(11)

References

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