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| 摘要: |
| 本文在WENO-MZQ3格式的基础上, 将其模板推广到五阶WENO,即在经典五阶WENO格式的三个三点模板的基础上引入五点模板,并引入新的改进的全局光滑因子,对其进行加权处理得到新的五阶WENO格式.理论分析表明新的五阶WENO格式在光滑区域比五阶WENO-JS格式具有更高阶的计算精度,通过一系列一维和二维数值算例也验证了新的五阶WENO格式具有更高的精度和分辨率. |
| 关键词: WENO 格式 五点模板 全局光滑因子 |
| DOI： |
| 分类号:O241.82 |
| 基金项目:河海大学2023年新工科、新农科、新文科研究与改革实践项目资助(B2301914);河海大学2023年研究生“课程思政”示范课程建设项目资助(421203160). |
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| APPLICATION OF THE IMPROVED FIFTH ORDER WENO SCHEMES BASED ON A HYBRID TEMPLATE IN SOLVING HYPERBOLIC CONSERVATION EQUATION |
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GAO Zhi-hui,ZHANG Xue-ying
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| Abstract: |
| In this paper, we extend the template of WENO-MZQ3 scheme to fifth-order WENO schemes. This means that we introduce a five-point template based on the three three-point templates of the conventional fifth-order WENO scheme. We introduce a new improved global smoothness indicator and apply weighted treatment to obtain a new fifth-order WENO scheme. Theoretical analysis demonstrate that the new fifth-order WENO scheme achieves higher computational accuracy in smooth regions compared to the fifth-order WENO-JS scheme. A series of one-dimensional and two-dimensional numerical examples validate the higher accuracy and resolution of the new fifth-order WENO scheme. |
| Key words: WENO scheme five-point template global smoothness indicator |
