High‐order k‐exact WENO finite volume schemes for solving gas dynamic Euler equations on unstructured grids
High‐order k‐exact WENO finite volume schemes for solving gas dynamic Euler equations on unstructured grids
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DOI：
10.1002/fld.2710
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发表时间：
2012-10
影响因子：
1.8
通讯作者：
Wanai Li;Yu-xin Ren
中科院分区：
文献类型：
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作者：
Wanai Li;Yu-xin Ren
本文提出了一系列适用于非结构化网格的高阶有限体积方案。在每个控制体积上执行 k 精确重建作为初级重建。在感兴趣的细胞上，除了初级重建之外，还通过非常简单且有效的“次级”重建提供额外的候选重建多项式。然后将WENO方案的加权平均过程应用于初级和次级重建，以确保该方案的冲击捕获能力。该过程结合了 k 精确重建的简单性和 WENO 方案的鲁棒性，代表了构建高阶精确冲击捕获方案的系统且统一的方法。为了进一步提高效率，引入了一种高效的与问题无关的冲击检测器。提出了几个测试用例来证明所提出方案的准确性和非振荡特性。结果表明，所提出的方案能够以一致的高阶精度预测平滑解，并能够以高分辨率捕获冲击波和接触不连续性。版权所有 © 2011 约翰·威利父子有限公司
This paper presents a family of High‐order finite volume schemes applicable on unstructured grids. The k‐exact reconstruction is performed on every control volume as the primary reconstruction. On a cell of interest, besides the primary reconstruction, additional candidate reconstruction polynomials are provided by means of very simple and efficient ‘secondary’ reconstructions. The weighted average procedure of the WENO scheme is then applied to the primary and secondary reconstructions to ensure the shock‐capturing capability of the scheme. This procedure combines the simplicity of the k‐exact reconstruction with the robustness of the WENO schemes and represents a systematic and unified way to construct High‐order accurate shock capturing schemes. To further improve the efficiency, an efficient problem‐independent shock detector is introduced. Several test cases are presented to demonstrate the accuracy and non‐oscillation property of the proposed schemes. The results show that the proposed schemes can predict the smooth solutions with uniformly High‐order accuracy and can capture the shock waves and contact discontinuities in high resolution. Copyright © 2011 John Wiley & Sons, Ltd.