高阶通量重建在拉伸和扭曲网格上的应用
High Order Flux Reconstruction on Stretched and Warped Meshes
AI总结：
本文研究了在拉伸和扭曲网格上高阶通量重建方法的分析和数值行为，针对一维线性输运方程和二维欧拉方程，探讨了其稳定性极限和与有限差分和有限体积方案的对比。
摘要：
高阶计算流体力学正在成为未来工业工具的热门研究方向，其中通量重建（FR）是一种方法。然而，由于需要对复杂几何进行网格划分，如果FR要取代当前方法，则必须应用于拉伸和扭曲网格。因此，本文提出研究FR在变形网格上对于一维线性输运方程和二维欧拉方程的分析和数值行为。本文的工作基础是基于修改的von Neumann分析，用于线性变形网格。此外，还分析了此类网格上线性输运的时间稳定性极限，确定了几种Runge-Kutta方案的CFL限制，主要趋势是收缩网格区域导致更高的CFL限制，而扩展网格则导致更低的CFL限制。最后，FR方法与有限差分和有限体积方案的基准测试进行了比较，结果显示在扭曲和拉伸网格上，FR具有更强的波传播能力，因此对网格变形更具鲁棒性。
英文摘要：
High-order CFD is gathering a broadening interest as a future industrial tool, with one such approach being Flux Reconstruction (FR). However, due to the need to mesh complex geometries if FR is to displace current, lower order methods, FR will likely have to be applied to stretched and warped meshes. Therefore, it is proposed that the analytical and numerical behaviour of FR on deformed meshes for both the 1D linear advection and the 2D Euler equations is investigated. The analytical foundation of this work is based on a modified von Neumann analysis for linearly deformed grids that is presented. The temporal stability limits for linear advection on such grids are also explored analytically and numerically, with CFL limits set out for several Runge-Kutta schemes, with the primary trend being that contracting mesh regions give rise to higher CFL limits whereas expansion leads to lower CFL limits. Lastly, the benchmarks of FR are compared to finite difference and finite volumes schemes, as are common in industry, with the comparison showing the increased wave propagating ability on warped and stretched meshes, and hence, FR;s increased resilience to mesh deformation.
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