| 求解双曲守恒律方程的三阶修正模板WENO格式北大核心CSCD |
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| 引用本文： | 王亚辉.求解双曲守恒律方程的三阶修正模板WENO格式北大核心CSCD[J].应用数学和力学,2022,43(2):224-236. |
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| 作者姓名： | 王亚辉 |
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| 作者单位： | 郑州师范学院 数学与统计学院，郑州 450044 |
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| 基金项目： | 国家自然科学基金(12071470);河南省高等学校重点科研项目(22B110020)。 |
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| 摘 要： | 为了降低经典的三阶加权本质无振荡(WENO)格式的数值耗散,提出了一种新的三阶WENO格式的修正模板近似方法.改进了经典WENO-JS格式中各候选模板上数值通量的一阶多项式逼近,通过加入二次项使模板逼近达到三阶精度.计算了相应的候选通量,并且通过引入可调函数φ(x),使得新的格式具有ENO性质.最后给出了一系列数值算例,证明了该方法的有效性.
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| 关 键 词： | 双曲守恒律 WENO 修正模板 非线性权 |
| 收稿时间： | 2021-04-10 |
A 3rd-Order Modified Stencil WENO Scheme for Solution of Hyperbolic Conservation Law Equations |
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| WANG Yahui.A 3rd-Order Modified Stencil WENO Scheme for Solution of Hyperbolic Conservation Law Equations[J].Applied Mathematics and Mechanics,2022,43(2):224-236. |
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| Authors: | WANG Yahui |
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| Affiliation: | School of Mathematics and Statistics, Zhengzhou Normal University, Zhengzhou 450044, P.R.China |
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| Abstract: | In order to reduce the numerical dissipation of the classical 3rd-order weighted essentially non-oscillatory(WENO) scheme, a new modified stencil approximation of the 3rd-order WENO scheme was proposed. The 1st-order polynomial approximation of numerical flux on each candidate stencil in the classical WENO-JS3 scheme was improved,and the quadratic term was added to make the stencil approximation reach the 3rd-order accuracy. The corresponding candidate fluxes were calculated. Moreover, the new scheme has essentially non-oscillatory properties through introduction of tunable function φ(x). A series of numerical examples show the effectiveness of the new method. |
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| Keywords: | hyperbolic conservation law WENO modified stencil nonlinear weight |
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