Third-Order Modified Coefficient Scheme Based on the Essentially Non-Oscillatory Scheme
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摘要: 不增加基点，仅摄动二阶ENO格式的系数(简记为MCENO)，得到一类求解双曲型守恒律方程的三阶MCENO格式．由MCENO格式的构造过程可以看出，MCENO格式保留了ENO格式的许多性质,例如本质无振荡性、TVB性质等,且能提高一阶精度．进一步,利用MCENO格式模拟二维Rayleigh-Taylor(RT)不稳定性和Lax激波管的数值求解问题．数值结果表明，t=2.0时，MCENO格式的密度曲线处于三阶WENO格式和五阶WENO格式之间，是一个高效高精度格式．值得注意的是，三阶MCENO格式，三阶WENO格式和五阶WENO格式的CPU时间之比为0.62:1:2.19．表明相对于原始ENO格式，MCENO格式在光滑区域有较高精度，能提高格式精度．
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关键词:
- ENO格式 /
- 修正系数格式 /
- Lax激波管 /
- Rayleigh-Taylor(RT)不稳定性
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. -
[1] Harten A,Engquist B,Osher S,et al.Uniformly high order accurate essentially non-oscillatory schemes Ⅲ[J].J Comput Phys,1987,71:231-303;ICASE Report No 86-22, April 1986. doi: 10.1016/0021-9991(87)90031-3 [2] Liu X-D,Osher S. Convex ENO high order multi-dimensional schemes without field by field decomposition or staggered grids[J].J Comput Phys,1998,142(2):304-330. doi: 10.1006/jcph.1998.5937 [3] Liu X-D,Osher S,Chan T. Weighted essentially non-oscillatory schemes[J].J Comput Phys,1994,115(1):200-212. doi: 10.1006/jcph.1994.1187 [4] Shu C-W,Osher S. Efficient implementation of essentially non-oscillatory shock-capturing schemes[J].J Comput Phys,1988,77(2):439-471. doi: 10.1016/0021-9991(88)90177-5 [5] Shu C-W,Osher S.Efficient implementation of essentially non-oscillatory shock-capturing schemes Ⅱ[J].J Comput Phys,1989,83(1):32-78. doi: 10.1016/0021-9991(89)90222-2 [6] Jiang G-S,Shu C-W. Efficient implementation of weighted ENO schemes[J].J Comput Phys,1996,126:202-228. doi: 10.1006/jcph.1996.0130 [7] 高智.摄动有限研究进展[J].力学进展,2000，30(2)：200-215. [8] Gao Z,YANG G W. Perturbation finite volume method for convective-diffusion integral equation[J].Acta Mechanica Sinica,2004,20(6):580-590. doi: 10.1007/BF02485861 [9] 高智，柏威. 对流扩散方程的摄动有限体积（PFV）方法及讨论[J].力学学报,2004,36(1):88-93. [10] Glimm J,Grove J,LI X,et al.The dynamics of bubble growth for Rayleigh-Taylor unstable interface[J].Physics of Fluids,1988,31:447-465. doi: 10.1063/1.866826 [11] Xu Z F,Shu C W.Anti-diffusive flux corrections for high order finite difference WENO schemes[J].J Comput Phys,2005,205(2):458-485. doi: 10.1016/j.jcp.2004.11.014 -
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