| 摘要: |
| 由Fan等人设计的新局部光滑因子和8阶的全局光滑因子给极值点掉阶问题带来重大突破.但在针对复杂流域进行数值模拟时,采用8阶全局光滑因子所对应的5点WENO-Zη格式会出现数值振荡和分辨率不足的问题.为了充分展现8阶全局光滑因子的优势,本文将格式权函数中的常数1替换为一个关于ξk的函数.该函数在光滑区域为一个大的常值,使得格式更快地趋近于5阶迎风格式；在间断区域, 函数值切换为一个小值,从而强化了局部光滑因子对于权重的影响,缓减了格式在间断附近的数值振荡. 数值实验表明,改进的5点WENO-Zη格式能够在不含极值点的光滑区域以及一阶极值点处达到5阶数值精度,在二阶极值点处达到4阶数值精度. 在非光滑区域,新格式能够更加敏锐地捕捉间断, 同时保持基本无振荡的特性.此外, 新格式可以轻松地推广至更高阶的情形. |
| 关键词: 改进的WENO-Zη格式 8阶全局光滑因子 新权函数 WENO-ZF格式 |
| DOI： |
| 分类号:O241.82 |
| 基金项目: |
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| AN ENHANCED WENO-Zη SCHEME WITH HIGH RESOLUTION AND ENO BEHAVIOR |
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CUI Nuo-ya, ZHANG Xue-ying
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School of Mathematics, Hohai University, Nanjing 211100, China
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| Abstract: |
| The new local smoothness indicators and 8th-order global smoothness indicators designed by Fan et al result in a significant breakthrough in the accuracy at critical points. However, in numerical simulation involving complex flows, the five-point WENO-Zη scheme utilizing eighth-order of global smoothness indicators may exhibit numerical oscillation or suffer from low resolution. To better harness the advantages of the 8th-order global smoothness factor, the numerical value 1 in the original weight relation is substituted with a function about ξk. The function takes on a larger constant in smooth regions, causing the new scheme to swiftly converge towards 5th-order upwind scheme. If the whole stencil is crossed by discontinuities, the function will jump to a small value with the objective of highlighting the influence of the smoothness factor on the weights and thereby mitigating numerical oscillations near discontinuities. As shown in numerical experiments, the modified five-point WENO-Zη scheme will achieve the fifth order of convergence at smooth regions even at the first-order critical points. At the second-order critical points, it will attain the fourth order of convergence. In non-smooth regions, the new scheme will capture discontinuities sharply while preserving ENO behavior. Furthermore, the new scheme can be readily extended to higher-order cases. |
| Key words: an enhanced WENO-Zη scheme the eighth-order global smoothness indicators a new weighting function the WENO-ZF scheme |
