A new paradigm of dissipation-adjustable, multi-scale resolving schemes for compressible flows
A new paradigm of dissipation-adjustable, multi-scale resolving schemes for compressible flows
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DOI：
10.1016/j.jcp.2022.111287
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发表时间：
2022-05
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影响因子：
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通讯作者：
X. Deng;Zhen-hua Jiang;P. Vincent;F. Xiao;Chao Yan
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文献类型：
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作者：
X. Deng;Zhen-hua Jiang;P. Vincent;F. Xiao;Chao Yan
通过直接数值模拟（DNS）或大涡模拟（LES）对高速可压缩流动进行尺度分辨模拟，要求激波捕获格式在分辨宽带湍流时更加精确，在捕获强激波时更加稳健。在这项工作中，我们开发了一种新的耗散可调的冲击捕获方案范式来解决高速可压缩流中的多尺度流动结构。新方案采用了一个多项式的n次和非多项式THINC（双曲线的切线内面捕捉）的m级陡度函数作为重建候选人。这些重构候选被表示为Pn T m。从这些候选者中，通过边界变差递减（BVD）算法选择分段重建函数。与其他激波捕捉技术不同，BVD算法有效地抑制了数值振荡，而不会引入过多的数值耗散。然后，一个可调耗散（AD）算法设计的尺度分辨模拟。这种新的激波捕获方案被命名为Pn T m− BVD− AD。所提出的P n T m− BVD− AD方案具有以下期望的性质。首先，它可以捕捉大规模的不连续结构，如强冲击波没有明显的非物理振荡，同时解决尖锐的接触，材料界面和剪切层。其次，通过一个简单的可调参数λ，可以在n+ 1阶迎风偏置格式和n+ 2阶中心格式之间有效地调节Pn Tm − BVD− AD的数值耗散特性.当λ= 0.5时，该格式可以恢复到n+ 2阶无耗散中心插值，在所有波数上都能获得光滑解，这不仅适用于DNS中的小尺度结构，而且适用于显式LES中的可分解尺度。最后，低分辨率的小尺度可以通过所谓的隐式LES（ILES）方法与耗散可调算法解决。通过对多尺度流场结构的数值模拟以及与其他中心迎风格式的比较，证明了该格式的优越性。以超声速平面喷流为例，数值模拟结果表明，PnTm-BVD-AD格式与采用高次重构多项式的Pn + 2 Tm-BVD格式相比，具有很好的性能。因此，与以前的工作相比，所提出的P n T m− BVD− AD方案具有更紧凑的模板和更低的成本的优点。总之，这项工作提供了一个解决高速可压缩流的多尺度问题的替代方案。
The scale-resolving simulation of high speed compressible flow through direct numerical simulation (DNS) or large eddy simulation (LES) requires shock-capturing schemes to be more accurate for resolving broadband turbulence and robust for capturing strong shock waves. In this work, we develop a new paradigm of dissipation-adjustable, shock capturing scheme to resolve multi-scale flow structures in high speed compressible flow. The new scheme employs a polynomial of n-degree and non-polynomial THINC (Tangent of Hyperbola for INterface Capturing) functions of m-level steepness as reconstruction candidates. These reconstruction candidates are denoted as P n T m. From these candidates, the piecewise reconstruction function is selected through the boundary variation diminishing (BVD) algorithm. Unlike other shock-capturing techniques, the BVD algorithm effectively suppresses numerical oscillations without introducing excess numerical dissipation. Then, an adjustable dissipation (AD) algorithm is designed for scale-resolving simulations. This novel paradigm of shock-capturing scheme is named as P n T m− BVD− AD. The proposed P n T m− BVD− AD scheme has following desirable properties. First, it can capture large-scale discontinuous structures such as strong shock waves without obvious non-physical oscillations while resolving sharp contact, material interface and shear layer. Secondly, the numerical dissipation property of P n T m− BVD− AD can be effectively adjusted between n+ 1 order upwind-biased scheme and non-dissipative n+ 2 order central scheme through a simple tunable parameter λ. Thirdly, with λ= 0.5 the scheme can recover to n+ 2 order non-dissipative central interpolation for smooth solution over all wavenumber, which is preferable for solving small-scale structures in DNS as well as resolvable-scale in explicit LES. Finally, the under-resolved small-scale can be solved with the dissipation adjustable algorithm through the so-called implicit LES (ILES) approach. Through simulating benchmark tests involving multi-scale flow structures and comparing with other central-upwind schemes, the superiority of the proposed scheme is evident. For instance, the simulation results of the supersonic planar jet show that P n T m− BVD− AD schemes can achieve competitive results as P n+ 2 T m− BVD schemes which utilize a higher degree of reconstruction polynomial. Thus, in comparison with the previous work, the proposed P n T m− BVD− AD schemes have the benefit of a more compact stencil and lower cost. In summary, this work provides an alternative scheme for solving multi-scale problems in high speed compressible flows.