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| 求解双曲守恒律的修正模板近似的五阶WENO格式 |
| Fifth-order Modified Stencil WENO Schemes for Hyperbolic Conservation Laws |
| 投稿时间：2022-10-05 修订日期：2022-12-24 |
| DOI： |
| 中文关键词: 双曲守恒律 WENO 修正模板 非线性权 |
| 英文关键词:Hyperbolic conservation laws WENO Modified stencil Nonlinear weights |
| 基金项目:国家自然科学基金项目（面上项目，重点项目，重大项目） |
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| 中文摘要: |
| 针对经典的五阶加权本质无振荡(WENO)格式在间断附近耗散过大以及临界点不能保精度的这些问题,这里提出了一种新的修正模板近似方法.改进了经典五阶WENO-JS格式中各候选子模板上数值通量的二阶多项式逼近,通过加入三次修正项使模板逼近达到四阶精度.并且通过引入可调函数使得新的格式具有ENO性质,理论分析新的格式具有保精度特性,通过一系列数值算例证明了新的格式的高效性。 |
| 英文摘要: |
| In order to solve the problems of the classical fifth order weighted essentially non oscillatory (WENO) scheme, such as the excessive dissipation near the discontinuity and the inaccuracy preserving of the critical point, a new modified stencil approximation method is proposed.The second order polynomial approximation of the numerical flux on each candidate sub-stencil in the classical fifth order WENO-JS scheme is improved, and the stencil approximation reaches the fourth order accuracy by adding a cubic correction term.The new scheme has ENO property by introducing adjustable function , and the theoretical analysis shows that the new scheme has accuracy preserving property. A series of numerical examples show the efficiency of the new scheme. |
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