Anti-diffusive flux corrections for high order finite difference WENO schemes
Anti-diffusive flux corrections for high order finite difference WENO schemes
复制标题
DOI：
10.1016/j.jcp.2004.11.014
复制
发表时间：
2005-05
影响因子：
4.1
通讯作者：
Zhengfu Xu;Chi-Wang Shu
中科院分区：
文献类型：
--
作者：
Zhengfu Xu;Chi-Wang Shu
本文将Després和Lagoutière [Journal of Scientific Computing 16（2001）479-524]最近提出的一阶格式的反扩散通量修正技术推广到高阶有限差分加权基本无振荡（韦诺）格式.其目标是获得接触不连续性的高分辨率，接近离散行波的质量，在较长时间内不会逐渐涂抹，同时保持光滑区域的高阶精度和不连续性的非振荡特性。对一维和二维标量问题和系统的数值算例表明了这种通量校正的良好性能。与原韦诺格式相比，在相同的网格上，该格式保持了高精度，接触不连续性得到明显改善。
In this paper, we generalize a technique of anti-diffusive flux corrections, recently introduced by Després and Lagoutière [Journal of Scientific Computing 16 (2001) 479–524] for first-order schemes, to high order finite difference weighted essentially non-oscillatory (WENO) schemes. The objective is to obtain sharp resolution for contact discontinuities, close to the quality of discrete traveling waves which do not smear progressively for longer time, while maintaining high order accuracy in smooth regions and non-oscillatory property for discontinuities. Numerical examples for one and two space dimensional scalar problems and systems demonstrate the good quality of this flux correction. High order accuracy is maintained and contact discontinuities are sharpened significantly compared with the original WENO schemes on the same meshes.