| 郭城,王亚辉.求解双曲守恒律的修正模板近似的五阶WENO格式[J].计算力学学报,2024,41(3):564~571 |
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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：10.7511/jslx20221005002 |
| 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(12071470);河南省高等学校重点科研项目(22B110020)资助. |
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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问题,本文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φ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说明了新格式的高效性。 |
| 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 inaccurate 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 φ,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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