High-Order Flux Reconstruction Schemes with Minimal Dispersion and Dissipation
High-Order Flux Reconstruction Schemes with Minimal Dispersion and Dissipation
复制标题
具有最小色散和耗散的高阶通量重构方案
DOI：
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发表时间：
2015
影响因子：
2.5
通讯作者：
A. Jameson
中科院分区：
文献类型：
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作者：
K. Asthana;A. Jameson
对通量重构(FR)公式进行了模式分析，得到了半离散和全离散的色散关系，并利用该关系表征了物理模式和杂散模式的波动特性。研究了多项式阶数、修正函数和解点对模色散、耗散和相对能量的影响。利用这一框架，提出了一组新的线性稳定的高阶FR格式，使波传播误差在可分辨的波数范围内达到最小。与不连续Galerkin格式相比，这些格式提供了相当小的平流误差，并受益于显式差分更新。与标准的高阶紧致有限差分格式相比，相应的分辨率更高。通过在均匀网格和非均匀网格上对标量平流的改进和现有FR格式的比较，验证了这些理论期望。
Modal analysis of the flux reconstruction (FR) formulation is performed to obtain the semi-discrete and fully-discrete dispersion relations, using which, the wave properties of physical as well as spurious modes are characterized. The effect of polynomial order, correction function and solution points on the dispersion, dissipation and relative energies of the modes are investigated. Using this framework, a new set of linearly stable high-order FR schemes is proposed that minimizes wave propagation errors for the range of resolvable wavenumbers. These schemes provide considerably reduced error for advection in comparison to the Discontinuous Galerkin scheme and benefit from having an explicit differential update. The corresponding resolving efficiencies compare favorably to those of standard high-order compact finite difference schemes. These theoretical expectations are verified by a comparison of proposed and existing FR schemes in advecting a scalar quantity on uniform as well as non-uniform grids.